Letteratura scientifica selezionata sul tema "Low Mach regime"

In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.

An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) Me is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with Me = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As Me is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1–6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of Me the type of regime may be the dominant factor governing the energetics.

A lower combustor inlet Mach number is desirable in order to design a compact, lightweight combustor and boost the overall performance of the scramjet engine. In this study, a thrust control strategy is proposed for a hydrogen-fueled scramjet taking into account the operating limitations, which is called the minimum combustor inlet Mach number rule since the combustor inlet Mach number is used as the control variable. By scheduling the fuel supply and modifying the intake geometry, the combustor inlet Mach number can be minimized while ensuring a certain thrust output within the operation constraints. In this manner, the scramjet engine can be operated with high specific thrust and low fuel consumption throughout the flight envelope. The thrust control strategy is further applied to a hydrogen-fueled scramjet in the hypersonic flight regime. Because the combustor inlet Mach number varies with flight conditions, the thrust strategy can be applied in practice by monitoring the following aerothermodynamic parameters in different flight regimes instead: (1) combustor outlet Mach number, (2) combustor inlet static temperature, and (3) combustor outlet static temperature. Furthermore, the effects of the thrust output on the division of flight regime are investigated, and the overall performance of the hydrogen-fueled scramjet engine obtained from applying the thrust control strategy is discussed in detail.

This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e., low-Mach-number–slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a Gauss–Legendre collocation in space and an α-method in time.

The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large channel aspect ratio L/d ∼ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytical results are presented which show, somewhat unexpectedly, that for forced channel flow, steady-state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady-state friction factor and heat transfer coefficient have no validity.

This paper presents an experimental investigation of laminar gas flow through microchannels. The independent variables: relative surface roughness, Knudsen number and Mach number were systematically varied to determine their influence on the friction factor. The microchannels were etched into silicon wafers, capped with glass, and have hydraulic diameters between 5 and 96 μm. The pressure was measured at seven locations along the channel length to determine local values of Knudsen number, Mach number and friction factor. All measurements were made in the laminar flow regime with Reynolds numbers ranging from 0.1 to 1000. The results show close agreement for the friction factor in the limiting case of low Ma and low Kn with the incompressible continuum flow theory. The effect of compressibility is observed to have a mild (8 percent) increase in the friction factor as the Mach number approaches 0.35. A 50 percent decrease in the friction factor was seen as the Knudsen number was increased to 0.15. Finally, the influence of surface roughness on the friction factor was shown to be insignificant for both continuum and slip flow regimes.

We have studied numerically the stability of a two-dimensional Couette flow in a polytropic fluid subjected to a localized shear, using a pseudo-spectral method (Fourier-Chebyshev). The polytropic index has been chosen equal to 2 and a radial force (pseudo-gravity) is introduced in order to perform comparisons with the shallow water experimental results. When the Reynolds number is not too low, the initial flow which is purely azimuthal becomes unstable and a stable rotating pattern is formed, with a number of azimuthal modes which decreases when the Mach number increases. A qualitative agreement is found with the experimental results, although the spatial resolution constraint strongly limits the numerical Reynolds and Mach numbers. From the variation of the linear growth rate of the unstable modes with the Mach number, we are able to show the transition between a flow subjected to Kelvin-Helmholtz instability towards one essentially driven by a centrifugal instability, which is efficient for rotating supersonic flows if the angular momentum decreases outwards. The latter situation may occur for some flows in astrophysical disks.

Airfoil tonal noise emission at low-to-moderate Reynolds number and flow conditions featuring a laminar separation bubble close to the trailing edge is often related to an aeroacoustic feedback mechanism and, therefore, the Mach number is a primary parameter for the flow field and noise generation. This study experimentally explores the effect of the Mach number on airfoil tonal noise generation in the nominally incompressible flow regime. Using airfoil profiles of different chord lengths, the Mach number is varied for a constant Reynolds number. Acoustic and flow field measurements for a range of combinations of Reynolds and Mach numbers were conducted. At zero incidence, the tonal noise regime in the Reynolds number domain is found to be sensitive to the Mach number. At non-zero angle of attack (2°), the noise generation is found to be dominated by vortex shedding over a separation bubble on the pressure side. The details of the separation bubble and shedding process depend on the Mach number. The frequencies of the dominant tones and the frequency intervals between tones increase with the Mach number. Moreover, the measured frequency interval can be collapsed using a relation based on the aeroacoustic feedback loop model. The relation is rewritten to separate the effects of the Reynolds and Mach numbers. As a result, the dependence on the Mach number is identified and tested. In contrast, the tonal noise level shows a more complex dependence on details of the laminar separation bubble and the vortex shedding process.

AbstractAn all speed scheme for the Isentropic Euler equations is presented in this paper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficulty in the low Mach regime. The key idea of our all speed scheme is the special semi-implicit time discretization, in which the low Mach number stiff term is divided into two parts, one being treated explicitly and the other one implicitly. Moreover, the flux of the density equation is also treated implicitly and an elliptic type equation is derived to obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared with previous semi-implicit methods, firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs to be solved implicitly which reduces much computational cost. We develop this semi-implicit time discretization in the framework of a first order Local Lax-Friedrichs (or Rusanov) scheme and numerical tests are displayed to demonstrate its performances.

Une approche d'interface raide est présentée pour le calcul des écoulements diphasiques avec tension superficielle et changement de phase en régime à faible nombre de Mach. Pour développer un tel modèle, où de légers effets compressibles sont pris en compte ainsi que des fermetures thermodynamiques correctes, le liquide et le gaz sont considérés comme compressibles et décrits par un solveur compressible précis. Ce solveur compressible adopte une technique de décomposition appelée "décomposition du transport acoustique" qui décompose le système Euler en deux parties: acoustique et transport. Sur la base du sous-système acoustique, un solveur de Riemann approximatif qui tient compte des effets de tension superficielle et de changement de phase est développé. L'interface de l'écoulement diphasique est capturée par la méthode de Level Set et considérée comme raide. La problème de la capture d'interface de la méthode Level Set dans le cadre Eulérien est le point clé des simulations d'écoulement diphasique, et dans ce travail, nous proposons et adoptons des approches d'ordre élevé pour l'advection de l'interface, la redistanciation et l'estimation de la courbure. En régime à faible nombre de Mach, les solveurs compressibles conventionnels perdent en précision et une correction à faible Mach est alors nécessaire pour réduire la dissipation numérique. Pour une méthode d'interface raide, l'interface est traitée comme la discontinuité de contact via la méthode Ghost Fluid. Sans une région lisse à l'interface, une telle discontinuité existant à l'interface présente un énorme défi pour la conception d'un schéma numérique. La correction à faible Mach bien connue dans la littérature pourrait conduire à une erreur de troncature significative, en particulier pour les écoulements diphasiques avec de grands rapports de densité et de vitesse du son. Pour retrouver une bonne propriété de préservation asymptotique, nous proposons une nouvelle correction à faible Mach avec une analyse asymptotique rigoureuse. Plusieurs cas de test numériques ont été utilisés pour valider la présente approche numérique et montrer ses bonnes performances
A sharp interface approach is presented for computing two-phase flows with surface tension and phase change in low Mach regime. To develop such a model, where slight compressible effects are taken into account as well as correct thermodynamical closures, both the liquid and the gas are considered compressible and described by a precise compressible solver. This compressible solver adopt a splitting technique called "acoustic-transport splitting" which splits the Euler system into two parts: acoustic and transport. Based on the acoustic subsystem, an approximate Riemann solver that accounts for surface tension and phase change effects is developed. The interface between two-phase flows is captured by the Level Set method that is considered to be sharp. The interface capturing issue of the Level Set method within the Eulerian framework is the key point of the two-phase flow simulations, and in this work we propose and adopt high-order approaches for interface advection, redistancing and curvature estimation. In low Mach regime, conventional compressible solvers lose accuracy and a low Mach correction is then necessary to reduce the numerical dissipation. For a sharp interface method, the interface is treated as the shock-wave contact discontinuity via the Ghost Fluid method. Without a smooth region at the interface, such discontinuity existing at the interface presents a huge challenge to the design of a numerical scheme. The well-known low Mach fix in literature could lead to significant truncation error, especially for two-phase flows with large density and sound speed ratios. To recover a good asymptotic-preserving property, we propose a new low Mach correction with rigorous asymptotic analysis. Several numerical test cases have been employed to validate the present numerical approach and enlighten its good performance

La convection est un phénomène omniprésent dans l'univers, jouant un rôle clé dans la structure des océans, des atmosphères planétaires et stellaires. Ce travail se concentre sur les aspects théoriques et numériques de l'étude de la convection. D'abord, les méthodes "tout-régime" et "équilibre" colocalisées, basées sur un splitting d'opérateur et particulièrement adaptées aux phénomènes convectifs, sont reformulées en splitting de flux, améliorant leur flexibilité. Ensuite, une extension de cette méthode à la magnétohydrodynamique est proposée.Sa stabilité est prouvée sans recours au contrôle de la valeur de ∇·B, grâce au splitting et à l'emploi de termes de Powell. Par ailleurs, l'analyse de l'instabilité pour la convection diabatique est étendue à la magnétohydrodynamique et aux écoulements cisaillés.Une nouvelle instabilité "triple diffusive" et des estimations d'intensité de dynamo convective sont dérivées et validées par des simulations utilisant lesméthodes développées. Enfin, une simulation à très grande échelle de dynamo convective sur le super- calculateur Adastra est présentée. L'intégration de PDI et Deisa, outils d'I/O modernes développés à la Maison de la Simulation, dans le code HPC "ARK" basé sur Kokkos+MPI est exposée. En complément, des travaux préliminaires sur l'utilisation de petits réseaux de neurones pour accélérer la méthode GP-MOOD sont présentés
Convection is a ubiquitous phenomenon in the universe, playing a key role in the structure of oceans and planetary and stellar atmospheres. This work focuses on the theoretical and numerical aspects of studying convection. First, the "all-regime" and "equilibrium" collocated methods, based on operator splitting and particularly suited for convective phenomena, are reformulated in terms of flux splitting, enhancing their flexibility. Subsequently, an extension of this method to magnetohydrodynamics is proposed. Its stability is demonstrated without relying on controlling the value of ∇ · B, thanks to the splitting and the use of Powell terms. The analysis for diabatic convection is extended to magnetohydrodynamics and sheared flows. A new "triple diffusive" instability and estimates of convective dynamo intensity are derived and validated through simulations using the developed methods. Finally, a large-scale simulation of convective dynamo on the supercomputer Adastra is presented. The integration of PDI and Deisa,modern I/O tools developed at the Maison de la Simulation, into the HPC code "ARK" based on Kokkos+MPI is discussed. Additionally, prelimi-nary work on the use of small neural networks to accelerate the GP-MOOD method is presented

Analiza los modelos de transmisión del conocimiento de la “maca” Lepidium meyenii Walp en tres distritos de la provincia de Junín, como también estudiar su aspecto biológico y áreas potenciales para su cultivo. La metodología se basa en la observación participante y búsqueda de otras especies del Lepidium a través de las caminatas etnobotánicas y entrevistas a los pobladores. Siendo los datos analizados mediante los índices de importancia cultural (IC), Valor de Uso (VU), análisis estadístico y aplicación de software de predicción. Se registra tres especies de Lepidium incluido un Lepidium meyenii silvestre, entre los cultivares de maca se encuentran diferencias significativas a nivel del filamento, estilo y sépalo como también en su fenología, siendo el cultivar negro y plomo los más precoces. El modelo de predicción muestra áreas óptimas para el cultivo de maca en los departamentos de Junín, Pasco, Huancavelica y el sur del Perú. Los usos son clasificados en 7 categorías de las cuales 6 corresponden a la “maca”, la categoría medicinal presenta el mayor reporte de uso. Las subcategorías medicina general y trastorno del sistema sanguíneo las más mencionadas. Se determina que los conocimientos son transmitidos principalmente bajo el modelo de transmisión vertical, sin embargo el modelo de transmisión transversal es significativamente influyente en los pobladores más jóvenes especialmente en las poblaciones urbanas que están más ligadas al acceso a nuevas tecnologías. El Índice de Valor de Uso (VU) es el más adecuado para analizar y comparar el conocimiento entre y dentro de las poblaciones. Determinándose que el distrito de Ondores presenta un mayor nivel de conocimiento y por ende una mejor eficacia en la transmisión.
Tesis

Dans cette thèse on s’intéresse à la simulation numérique d’écoulements des matériaux compressibles, voir fluides et solides élastiques. Les matériaux considérés sont décrits avec un modèle monolithique eulérian, fermé avec une loi d’état hyperélastique qui considère les différents comportements des matériaux. On propose un nouveau schéma de relaxation qui résout les écoulements compressibles dans des différents régimes, avec des nombres de Mach très petits jusqu’à l’ordre 1. Le schéma a une formulation générale qui est la même pour tous le matériaux considérés, parce que il ne dépend pas directement de la loi d’état. Il se base sur une discrétisation complétement implicite, facile à implémenter grâce à la linéarité de l’opérateur de transport du système de relaxation. La discrétisation en espace est donnée par la combinaison de flux upwind et centrés, pour retrouver la correcte viscosité numérique dans les différents régimes. L’utilisation de mailles cartésiennes pour les cas 2D s’adapte bien à une parallélisation massive, qui permet de réduire drastiquement le temps de calcul. De plus, le schéma a été adapté pour la résolution sur des mailles quadtree, pour implémenter l’adaptativité de la maille avec des critères entropiques. La dernière partie de la thèse concerne la simulation numérique d’écoulements multi-matériaux. On a proposé une nouvelle méthode d’interface “sharp”, en dérivant les conditions d’équilibre en implicite. L’objectif est la résolution d’interfaces physiques dans des régimes faiblement compressibles et avec un nombre de Mach faible, donc les conditions multi-matériaux sont couplées au schéma implicite de relaxation
In this thesis we are concerned with the numerical simulation of compressible materials flows, including gases, liquids and elastic solids. These materials are described by a monolithic Eulerian model of conservation laws, closed by an hyperelastic state law that includes the different behaviours of the considered materials. A novel implicit relaxation scheme to solve compressible flows at all speeds is proposed, with Mach numbers ranging from very small to the order of unity. The scheme is general and has the same formulation for all the considered materials, since a direct dependence on the state law is avoided via the relaxation. It is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in different Mach regimes. The scheme is validated with one and two dimensional simulations of fluid flows and of deformations of compressible solids. We exploit the domain discretization through Cartesian grids, allowing for massively parallel computations (HPC) that drastically reduce the computational times on 2D test cases. Moreover, the scheme is adapted to the resolution on adaptive grids based on quadtrees, implementing adaptive mesh refinement techinques. The last part of the thesis is devoted to the numerical simulation of heterogeneous multi-material flows. A novel sharp interface method is proposed, with the derivation of implicit equilibrium conditions. The aim of the implicit framework is the solution of weakly compressible and low Mach flows, thus the proposed multi-material conditions are coupled with the implicit relaxation scheme that is solved in the bulk of the flow

Ce travail de thèse a pour objectif l'étude des propriétés acoustiques de systèmes incorporant des plaques micro-perforées (MPP) et des matériaux absorbants sous forts niveaux d'excitation.Le premier chapitre traite des systèmes composés d'une MPP couplée à une cavité d'air et une paroi rigide. Un modèle analytique intégrant deux paramètres adimensionnels et un nombre de Mach optimal est présenté. La particularité de ce modèle est de décrire la variation du maximum du coefficient d'absorption (coefficient d'absorption à la résonance) avec l'augmentation du niveau d'excitation. Une formule proposée permet de prédire les variations du pic d'absorption avec le nombre de Mach acoustique.Les effets d'interaction entre les perforations sont étudiés sous forts niveaux d'excitation dans le deuxième chapitre. Un modèle basé sur l'approche fluide équivalent est proposé. Dans ce modèle, la tortuosité est corrigée pour prendre en compte les distorsions d'écoulement dues aux effets d'interaction entre perforations et aux effets de turbulence. Cette correction de tortuosité qui n'intègre permet de prédire le comportement de la réactance du système.Les multi-couches composés de MPP et de matériaux poreux sont l'objet d'étude du troisième chapitre. Chaque couche du système est modélisée à forts niveaux d'excitation suivant une loi de Forchheimer. Les différents matériaux sont décrits par la méthode de la matrice de transfert. Le cas où le multi-couche est directement collé à une paroi rigide et le cas où il y a une cavité d'air avant la paroi rigide sont examinés.Dans le dernier chapitre, l'étude sur la transparence acoustique à forts niveaux est initiée. Les perspectives de ce travail sont nombreuses et prometteuses pour l'acoustique des transports
This work deals with the acoustical properties of systems incorporating Micro-Perforated Panels (MPP) and absorbing materials under high level of excitation.In the first chapter, absorbent systems composed of an air-cavity backed MPP are studied at high level of excitations. An analytical model involving two dimensionless parameters and an optimum Mach number is proposed. This model describes the behavior of the maximum of absorption coefficient (absorption coefficient at the resonance) with respect to the Mach number inside the perforations. A formula is proposed that predicts the variations of the absorption peak with the acoustical Mach number.In the second chapter, the holes interaction effects are studied theoretically and experimentally under high levels of excitations. Following an equivalent fluid approach, a model for which the tortuosity is corrected to account for the holes interaction effects coupled to the jet-like effects is developed. Multi-layered absorbents composed of MPP and porous materials are then studied under high level of excitations. The case where the multi-layers are directly attached to a rigid wall and the case where there is an air cavity before the rigid wall are examined. Forchheimer's law is used to model each medium of the multi-layer and the use of the transfer matrix method is made to account for these media.Sound transmission study under high level of excitation is introduced. The perspectives of this work are numerous and promising in the acoustics of transportation systems applications

The UK competition law regime comprises primarily the Competition Act 1998 and the Enterprise Act 2002, supplemented by provisions introduced by the Enterprise and Regulatory Reform Act 2013 and the Consumer Rights Act 2015. The foundation of the modern framework of UK competition law, the Competition Act 1998, has entered its twentieth year of operation, having come into force on 1 March 2000. Since that particular date, UK competition law has developed significantly through both decisional practice and jurisprudence. It has also undergone a process of modernisation, including both institutional and substantive reform. After the passage of an eventful twenty years of enforcement and reform, it is now an appropriate time to engage in a serious process of critical reflection on the current shape of the UK’s competition regime and whether it is performing well its role of ‘making markets work well for consumers’. With this context in mind, the book examines in a robust and critical manner the first twenty years of the operation of the UK’s competition regime. It focuses on the main substantive and procedural issues and provides a comprehensive analysis of how the UK’s contemporary competition regime has dealt with the challenges posed by these issues. By doing so, the book not only articulates those areas of competition law that are working well in the UK, but also those areas where further reflection, refinement and possible reform are required.

This chapter discusses the different theories employed in the field of international criminal law, which is now increasingly supported by theory. Case theories were developed after events had taken place; operational theories were produced to match complex facts; foundational theories were created to justify existing practices; external theories tried to make sense of the phenomenon of international criminal law as it had been observed; and so did the popular theories based on everyday encounters. Ago, rather than cogito, ergo sum was the field’s implicit maxim. Against this background one still finds that factual, operational, foundational, external theories prove to be less coherent when they are considered in light of each other. Rich theories could thus emerge from more joint theorizing among those working on variably factual, operational, foundational, and external theories, between scholars and practitioners, and between scholar-theorists and quotidian theorists.

This chapter examines the utopias called forth by the marriage of human rights accountability mechanisms on the one hand, and, on the other, arguments about the practical significance of these initiatives as preconditions for development, democracy, and political society. Transitional justice is seen to marry the ethical charge of the human rights field’s march against impunity, with an instrumental potential facilitating transition from the rule of violence into the rule of law. If the normative theories and agendas implicated by this marriage are advanced as being in the interests of justice, the accompanying instrumental theories and agendas are advanced in the interests of transition. Justice and transition operate here as allied and mutually reinforcing aspirations of and rationales for transitional justice institutions. Thus, this chapter identifies and analyses the stakes that attend this marriage of ‘ethics’ and ‘expertise’ in constituting the utopian political imagination of transitional justice.

This chapter is concerned with EU’s climate change law and its impact on climate change action at a global level. It investigates whether the international climate change regime ‘tightens’ its own standards so as to match EU climate change law. The corpus of EU climate change law is codified in the Climate and Energy Package, which aims to provide a comprehensive and integrated climate change framework. It includes measures promoting the use of renewable energy, specifying and thus helping to monitor and reduce greenhouse gases from fuel, setting standards for new passenger cars, establishing a framework for the geological storage of carbon dioxide, outlining the effort of Member States to reduce greenhouse gases to meet the 2020 commitments, as well as revising the EU emissions trading regime (ETS).

The Basel pillar 3 regime constitutes a disclosure regime for regulated banks. The aim is to provide sufficient transparency for investors to ensure that the price which banks pay to raise capital in the market reflects the level of risk undertaken by the bank. The pillar 3 regime was restructured in 2015, and is in the process of being further restructured. This chapter discusses the March 2017 standards which were broadly brought into force as from 2017. The most important change introduced by the 2017 standards is the formalisation of the disclosure templates. Regulators have struggled with banks over pillar 3 disclosures for many years — in effect, each bank sought to present information in a way which is most relevant to oits particular business and structure, whereas regulators seek to achieve comparability across banks with different businesses and structures. This process has resulted in a tightening of disclosure standards applicable to pillar three disclosures, to the extent that the regulators now provide detailed disclosure templates for each subdivision of required disclosure.

This chapter discusses the law on creditor claims in Mexico. Insolvency proceedings in Mexico aim for an orderly liquidation procedure of all of the bankrupt’s assets to allow an equally orderly distribution of proceeds among creditors under the principle of par conditio creditorum (equal treatment for all creditors). Ideally, the body of law regulating this procedure should match the insolvency law of each country, so that the process can be effected congruently and logically. However, social policies and other commercial considerations have created systems of priorities in asset distribution that vary from country to country as a function of the policies of each. In many cases, the only commonality in all systems is that ordinary unsecured creditors collect last, if at all. Mexico is no exception, specifically in the treatment of claims arising out of a labour relationship, which in turn is derived from the overly protective and outdated regime established by the federal constitution for workers. The remainder of the chapter deals with insolvency claims, administration claims, and non-enforceable claims in turn. Each section examines: the definition and scope of the claim; rules for submission, verification, and satisfaction or admission of claims; ranking of claims; and voting and other participation rights in insolvency proceedings.

Had Massachusetts legislators been aware of how many mixed marriages existed in their state (and in their region, for that matter), they may not have repealed the law. In their own lives they may have encountered or heard of a couple with mixed ancestry, but that would have been rare. Their experience reinforced the idea that people of African descent and people of European descent preferred to live among their "kind." Even if they didn't find each other physically repugnant, they still had no desire to intermarry. But observations and hearsay did not match reality. During the antebellum period there were at least 410 mixed marriages in New England, scattered through no fewer than 209 cities, towns, and villages. They occurred in all parts of the region and had distinctive characteristics. Their existence substantiated the fluidity of the construction of race (as evidenced in public records) and showed the complexity of New England types of racism and even its absence.

Israel’s rule over the Palestinian people may be characterized as a regime of apartheid, with its individual actions constituting crimes of apartheid. I was one of the legal advisers to the Russell Tribunal On Palestine (RTOP or ‘Russell Tribunal’) which convened on six occasions, not all of which I was able to assist with (from March 2010 to September 2014) (http://www.russelltribunalonpalestine.com/en/index.html). The third session was held in Cape Town in November 2011 and what I will set out in this chapter is an updated summary of the RTOP’s findings – available in full but not updated via this link http://www.russelltribunalonpalestine.com/en/sessions/south-africa/south-africa-session-%E2%80%94-full-findings The Tribunal made findings with regard to Israel’s policies and practices vis-à-vis the Palestinian people with reference to the international legal prohibition of apartheid under the following headings: The definition and status of apartheid under international law; Application of the definition of apartheid to Israeli policies; and practices vis-à-vis the Palestinian people.

Abstract The SMCR regime was first introduced in the UK for banks in March 2016 and is being rolled out to all other financial services firms with effect from 9 December 2019. This chapter focuses primarily on financial services firms that are banks covering the different layers of complexity that a no-deal Brexit will bring to the SMCR requirements. In particular, the chapter covers the difficult position firms may find themselves in when opting into the TPR where the PRA and FCA have adopted different approaches. When entering the TPR, these firms will need to implement a hybrid SMCR regime and implement the regime for third country bank branches on leaving the TPR. In addition, the chapter covers the key issues of responsibility for cross-border business into the UK, dual-hatting, outsourcing and enforcement issues against non-UK senior managers.

Realistic modeling of the vegetation fires based on reliable data from laboratory experiments is a key factor in the prediction of the fire dynamics ‎behavior and its spread rate in wildlands. A robust understating of the fire behavior in different species can provide a pragmatic insight to take precautionary steps to mitigate the fire risks in Wildland-urban interfaces. Computational Fluid Dynamics (CFD) modeling of ‎wildland fires ‎offers a considerably high load of information needed for engineers and policymakers. This paper addresses the numerical modeling of common Ivy (Hedera helix) and grapevine ‎(Vitis)‎ plants using the fire dynamics ‎simulation for the fire behavior analysis. Other species which authors have conducted experiments are Acacia, Apple tree, Arizona cypress, Bay laurel (Laurus nobilis), Blueberry tree (Prunus Spinosa), Cherry Tree, Fig tree, Gum rockrose (Cistus ladanifer), Hydrangea, Kiwi tree, Leyland cypress, Lindens (Tilia), Loquat (Eriobotrya japonica), Nerium oleander, Olive tree, Pacific madrone (Arbutus menziesii), Rhus typhina (Anacardiaceae), The Holly (Ilex Aquifolium), Thuja occidentalis (white cedar), and Wild Blackberry (Rubus Ulmifolius) shrub, in alphabetical order. The corresponding mathematical modelings of these experiments are being carried out by the authors. The current numerical study was performed using the NIST open-source FDS 6.7.7 code, developed by ‎‎the National Institute of Standards and Technology (NIST) with specific emphasis on the heat release rate from fires in different types of indigenous plants common in the Mediterranean climate, especially in Portugal. The validations of the numerical results are realized based on the observations from the ‎experiments conducted at the Laboratório de Estudos Sobre Incêndios Florestais (LEIF) by the authors. The large-eddy ‎simulation (LES) is used in these sets of simulations to close the turbulence equations in the low-Mach regime. The 2nd order accurate finite difference approximation scheme is used to discretize the governing equations on uniformly spaced three-dimensional staggered grids. The flow obstructions are ‎treated using the simple immersed boundary method. Comparing the results of the FDS with those from the practical experiments, it is concluded that mathematical modeling of the vegetation fires can provide reasonably accurate results based on the fuel’s physical and chemical characteristics along with operating boundary conditions.

This chapter discusses the functions and duties of directors in insolvency proceedings. It cites the provisions of the Insolvency Act as amended and associated case law, which particularly affects the functions and duties of directors. The inception of insolvency proceedings and its effects on directors’ powers and directors’ duties provide information about the company’s affairs and assist in investigation procedures under the Insolvency Act. In March 2020, a standalone moratorium became a permanent feature of the insolvency regime in response to the economic and financial impact of COVID-19. The chapter also looks into the liabilities of directors arising from insolvency proceedings.

Chapter 2 considers the application of the Competition Act 1998 to ‘Horizontal Agreements’, and in particular to cartel behaviour, since that piece of legislation entered into force on 1 March 2000. It is a tour de force of the enforcement practice. The chapter notes that early years of the legislation were somewhat disappointing, with a fairly low level of enforcement, although the OFT did score success with pioneering investigations of so-called ‘hub and spoke’ cartels in the Football Shirts and Toys and Games cases. From about 2006 onwards there were more decisions from the OFT, and some of the cases, such as Construction bid-rigging and Fuel surcharges, were high profile ones. Despite this, criticism of under-performance was voiced, not least by the National Audit Office. It is noted that in due course the OFT was replaced by the CMA, and there has been a noticeable increase in enforcement in recent years. Whish suggests that in a post-Brexit world it can be anticipated that there will be yet more enforcement, including of larger cartels which historically would have been investigated by the European Commission in Brussels.

Chapter 8 provides an overview of the resolution regimes under US law applicable to (i) banks; (ii) Fannie Mae, Freddie Mac, and the Federal Home Loan Banks (government-sponsored enterprises or GSEs); and (iii) systemically important financial institutions. This chapter includes a detailed summary of the applicable resolution regimes, as well as a summary of the development of US resolution authority over time, from the establishment of the Federal Deposit Insurance Corporation (FDIC) in the early twentieth century to the creation in the early twenty-first century of a resolution statute for GSEs, to the post-financial crisis establishment of the orderly liquidation authority and resolution planning requirements in the Dodd-Frank Act. The chapter also provides overviews of the supervisory tools that banking regulators use to prevent the failure of banks, the single-point-of-entry recapitalization in resolution strategy that has been adopted by all the US global systemically important banking groups (G-SIBs), and international efforts to coordinate on cross-border resolutions.

Abstract Historically, a uniform age was used to proxy work capacity loss and trigger the payment of pensions. Recently, many have argued that we need several retirement ages to better match the distribution of work (in)capacity across socio-demographic groups. At first sight, the proposal makes perfect sense. Work capacity declines faster among low-income or low-educated individuals. But there is also a lot of unaccounted heterogeneity, even inside narrowly defined socio-economic groups. And this compromises the feasibility and desirability of retirement age differentiation. Under a regime of systematic retirement age differentiation, there would be many situations with no retirement for people with serious work restrictions and, simultaneously, numerous cases where entirely healthy people enjoy retirement. An alternative approach would be to stick to uniform retirement age, backed up by a reinforced disability scheme.

On 7 December 2020, the Council of the European Union adopted two legal instruments, the Council Decision (CFSP) 2020/1999 concerning restrictive measures against serious human rights violations and abuses and the Council Regulation (EU) 2020/1998 concerning restrictive measures against serious human rights violations and abuses, which together make up the European Union Global Human Rights Sanctions Regime as a relatively new tool in its “human rights and foreign policy toolbox’’ that focusses on serious human rights violations. This article focuses on the Action Plan on Human Rights and Democracy 2020 – 2024 as part of the Joint Communication adopted in March 2020 by the High Representative of the Union for Foreign Affairs and Security Policy and the Commission since the European Union Global Human Rights Sanctions Regime is a key deliverable proposed in the Action Plan. More specifically, the article examines whether the European Union Global Human Rights Sanctions Regime has provided greater flexibility to target those responsible for serious human rights violations and abuses worldwide, as well as whether the said regime could be seen as an European Union response to a transnational security threat.

This chapter looks at the spate of protests against the CAA/NRC from December 2019 to March 2020 when the pandemic put in place a different order of public life. The title ‘recalling citizenship’ refers to what was being recalled in these movements, that is, the constitutional ethics of citizenship that informed the constituent moment, and the invocation of constitutional morality which B. R. Ambedkar considered indispensable for the durability of constitutional democracy. Describing this period as one of enhanced consciousness about citizenship, the chapter focuses on specific sites of protests that became iconic elaborations of dissident citizenship. The chapter raises the question why the Constitution of India became emblematic of an idiom of politics which was insurgent and democratic at the same time. In contexts of politics of domination, in which citizenship is itself under siege—dissident citizenship demands, in particular, the restoration of equality as the non-negotiable foundational premise of democracy. Yet, this process of restoration is a fraught one, and has to contend with competing ideas and claims to what it means to be a citizen.

Reducing the rotor tip speed by slowing down the rotor in forward flight is a viable means of extending the cruise speed of a compound helicopter. However, in a high advance ratio flight regime, many aerodynamic phenomena remain unclear, including the thrust reversal and the dynamic stall that occurs in the reverse flow region of the retreating blade. In order to investigate the performance and vibratory loads characteristics of a high advance ratio rotor, wind tunnel tests were conducted with a Mach-scale 4-blade articulated rotor at 900 RPM, up to advance ratio 1.15. Hub loads, control angles, flap angles, blade structural loads and blade surface pressure data were measured from the test. The wind tunnel test data was compared with the predictions from an in-house comprehensive analysis code, UMARC. The performance data correlation was satisfactory for most cases, however it degrades with increasing advance ratio. The hub load and blade structure load showed similar trends; they were insensitive to collective for low advance ratio and increased with collective for high advance ratio. The trend was captured by the analysis, but the analysis tends to under-predict the magnitudes. The pitch cyclic predictions were accurate and could be used as trimming target for future tests. Finally, the pressure data was studied to characterize and understand the dynamic stall in the reverse flow region.

Current work investigates the sensitivity of DES type hybrid methods toward turbulence length scales and anisotropy of grid. Different length scales available from literature are implemented into a compressible, finite volume GPU accelerated Navier-Stokes solver. A novel length scale is proposed based on the properties of available length scales and the grid requirements in mildly separated flows. Predictive capabilities of RANS and DDES method with the conventional and proposed length scales is assessed by conducting static and dynamic stall simulations on SC1095 and modified VR12 airfoils. Two different grids are used to examine the boundary layer resolving capabilities of the turbulence length scales. RANS based Spalart-Allmaras model and DDES method with conventional length scale predicted excessive eddy viscosity in the boundary layer of flows operating in near-stall regime. Proposed length scale demonstrated good predictive capabilities in mildly separated flows by reducing eddy viscosity levels at the outer region boundary layer. Three dimensional dynamic stall simulations are also conducted on flows over modified VR12 airfoil at moderate reduced frequency. When using proposed length scale, DDES method captured multiple lift peaks before stall and enabled flow to enter deep stall. The predictions agreed well with experimental data and captured cycle-to-cycle variation of integrated aerodynamic quantities. This work further employs specialized treatment to model laminar-turbulent transition and very low Mach number flows.

Reverse flow is the source of several unsteady effects that complicate load predictions for high advance ratio rotorcraft. As a way of improving load predictions, an ongoing series of experiments has been aimed at gaining a physical understanding of the unsteady aerodynamics of the reverse flow region. The current work contributes phase-averaged, three-component velocity field measurements collected on a rotor at high advance ratios. Stereoscopic particle image velocitmetry (PIV) was performed on a Mach-scale rotor across three advance ratios (0:6 ≤ μ ≤ 0:8), three radial stations (0:3 ≤ r/R ≤ 0:6), and one collective (θ0 = 10°). The present analysis focuses on how the reverse flow dynamic stall vortex, which results from flow separation about the sharp geometric trailing edge of a rotor blade in reverse flow, evolves over time in three dimensions. For a constant advance ratio, the size of the reverse flow dynamic stall vortex increases with decreasing radial station, creating a gradient in vorticity along the blade span. Tip-to-root radial flow, the amount of which increases for inboard radial stations, was also associated with the development of the reverse flow dynamic stall vortex. The current work postulates that due to an increase in radial flow, inboard radial stations are subject to a greater radial transport of vorticity than outboard sections and, in turn, produce less dimensional vorticity than outboard sections at the same convective time. Coupled with previous experimental models of reverse flow, the current work represents an important step in identifying the dominant unsteady characteristics of the reverse flow region and is designed to inform a low order model of rotors at high advance ratio.

The unsteady aerodynamics of low pressure turbine vibrating airfoils in flap mode is studied in detail using a frequency domain linearized Navier-Stokes solver. Both the travelling-wave and influence coefficient formulations of the problem are used to highlight key aspects of the physics and understand different trends such as the effect of reduced frequency and Mach number. The study is focused in the low-reduced frequency regime which is of paramount relevance for the design of aeronautical low-pressure turbines and compressors. It is concluded that the effect of the Mach number on the unsteady pressure phase can be neglected in first approximation and that the unsteadiness of the vibrating and adjacent airfoils is driven by vortex shedding mechanisms. Finally a simple model to estimate the work-per-cycle as a function of the reduced frequency and Mach Number is provided. The edge-wise and torsion modes are presented in less detail but it is shown that acoustic waves are essential to explain its behaviour. The non-dimensional work-per-cycle of the edge-wise mode shows a large dependence with the Mach number while in the torsion mode a large number of airfoils is needed to reconstruct the work-per-cycle departing from the influence coefficients.

Abstract With increasing exit Mach number through the transonic regime, increased losses in a turbine can be incurred due to the increase in shock losses. The transonic regime is specifically of interest as it exhibits both a loss bucket behavior as well as the potential for unique trailing edge shedding modes at midspan. As for the endwall secondary flows, there can be increased losses due to the increase in shock interactions with endwall secondary vortices. In this second part of the two part series, the variation in exit isentropic Mach number varied up to 1.15 where the endwall secondary flow development is compared between numerical predictions and experimental results for a low aspect ratio turbine (AR = 0.66 and Zw = 1.0). Experimental results are produced via testing in the SLU linear turbine cascade and include results of airfoil static pressures. Numerical analysis is completed using Cadence Fine/Turbo (RANS modeling with the SST k-omega turbulence closure model) and validated via the experimental data. Numerical predictions include airfoil static pressure loading, passage secondary flow development, shock interactions within the passage, as well as downstream mixing loss characterization. Results show the impact of the exit isentropic Mach number on the shock-vortex and shock-boundary layer interactions affecting the endwall secondary flow development. With increased exit isentropic Mach number, the flow exhibits a transition in the passage shock behavior having a direct impact on the endwall secondary flow development and shock-induced vortices within the passage. However, this work also shows the presence of a shock-vortex interaction with the passage vortex. As a result, the downstream mixing losses are then compared at six downstream planes (0.2 to 3.0Cx) where numerically predicted energy loss is assessed showing the increased rate of production at higher exit isentropic Mach number. The results of this part show evidence and support for a secondary flow model which details the endwall secondary flow development for an oblique shock structure within the transonic regime.

An analysis of laser Doppler velocimeter (LDV) data for the axial velocity flowfield in the rotor of the Mach 2 inlet flow supersonic throughflow fan (SSTF) is presented in this paper. The paper starts with a short description of the SSTF test package to highlight the specifics of the SSTF operation. It is followed by a detailed description of a dedicated LDV system for measurement in a supersonic throughflow fan and the experience gained. Most of the experimental data presented were acquired in a low supersonic throughflow regime (inlet Mach number of 1.4). The results and conclusions presented are based mainly on the experimental data only. A limited amount of computational fluid dynamics (CFD) predictions were used for comparison with the experimental results. The CFD methods, however, are not discussed in this paper. As shown in this paper, a reasonably good agreement between the LDV data and the CFD predictions was found for the low supersonic throughflow regime. The design point data (inlet Mach number of 2.0) exhibited an unexpectedly high noise in the velocity data in comparison with the data for low supersonic throughflow operating conditions. For the off-design supersonic regime (shock in rotor), substantial differences exist between the experimental and computational data.

Optical fiber ring resonators using directional couplers as signal tapping elements are called to play an important role in the future all-optical communication and sensor networks. The possibility of obtaining a wide range of strutures capable of performing wide-band signal processing operations in a guided-wave format has attracted the interest of several research groups. Initial effort focused on structures operating under linear regime showing and demonstrating potential applications as fiber sensors [1], all-fiber lasers [2], Fabry-Perot and Mach-Zehnder interferometers [3], [4], and optical filters for WDM and OFDM [5].

Las previsiones de retroceso económico y social en América Latina y el Caribe son alarmantes. La COVID-19 golpea con fuerza la región marcada que tendrá que afrontar una contracción del 9,4%, una de las más severas en todo el planeta. La desigualdad, la informalidad y la insuficiente dotación sanitaria lastran las posibilidades de hacer frente a la pandemia. Pero son los más vulnerables quienes asumen el costo, hasta 52 millones de personas que podrían caer en la pobreza y 40 millones podrían perder sus empleos, un retroceso de 15 años para la región. Pero la COVID-19 no afecta a todos por igual, una élite se mantiene inmune al contagio de la crisis económica. Desde el principio de los confinamientos, hay 8 nuevos milmillonarios en América Latina y el Caribe, personas con un patrimonio superior a los mil millones de dólares. Las personas más ricas han aumentado su fortuna en US$ 48 200 millones desde marzo 2020, lo que equivale a un tercio del total de los paquetes de estímulo de todos los países de la región. Para hacer frente a esta crisis tan profunda, Oxfam propone una serie de reformas que recaigan sobre quienes más tienen y menos han sufrido la pandemia. Entre otros un impuesto sobre el patrimonio neto de las personas más ricas con el que se podría recaudar al menos US$ 14 260 millones, 50 veces más de lo que ahora se estaría recaudando sobre esta élite de grandes fortunas. In the context of the COVID-19 pandemic, forecasts for economic and social decline in Latin America and the Caribbean are alarming. The region will face a 9.4% contraction in its economy, among the most severe in the world. Coping with the pandemic is hindered by inequality, weak and insufficient social protection and limited public health capabilities. Up to 52 million people could fall into poverty and 40 million could lose their jobs – a 15-year setback for the region. Yet, an elite remains ‘immune’ to the contagion of the economic crisis. Since the beginning of the pandemic, there have been 8 new billionaires in LAC: 1 every 2 weeks since the lockdowns began. The richest people have increased their fortune by $48.2bn since March 2020, equivalent to a third of the total stimulus packages of all countries in the region. In this paper, Oxfam proposes a series of reforms targeting those who have being less affected by the pandemic. They include a net wealth tax that could potentially generate $14.3bn, 50 times more than billionaires in the region pay now in theory, under current tax systems.

The Federal Reserve Bank of Cleveland's Community Issues Survey (CIS) collects information semiannually from direct service providers to monitor economic conditions and identify issues impacting low- and moderate-income (LMI) households in the Fourth District—a region that includes Ohio, western Pennsylvania, eastern Kentucky, and the northern panhandle of West Virginia. In March 2023, we surveyed more than 600 service providers who directly serve LMI individuals and communities across our District and received 95 responses (15 percent response rate). The results of this survey, summarized here, provide insights into how organizations and the households they serve are faring as they continue to navigate the impacts of inflation.

The Federal Reserve Bank of Cleveland's Community Issues Survey (CIS) collects information semiannually from direct service providers to monitor economic conditions and identify issues impacting low- and moderate-income (LMI) households in the Fourth District, a region that includes Ohio, western Pennsylvania, eastern Kentucky, and the northern panhandle of West Virginia. In March 2024, we surveyed nearly 600 organizations that directly serve LMI individuals and communities across our District and received 100 responses (17 percent response rate). The results of this survey are summarized here and provide insights into how organizations and the households they serve are faring as they continue to navigate the impacts of inflation.

El turismo en Colombia, es un sector importante en la economía; el departamento del Huila posee un potencial alto de desarrollo en este sector; este trabajo se realizó en el municipio de La Plata, en un ámbito de desarrollo turístico sostenible; entendiendo esto como el equilibrio entre el sector privado, publico, académico y la comunidad. El objetivo del presente trabajo fue estructurar el plan estratégico y prospectivo del municipio de La Plata Huila para convertirlo como eje regional de desarrollo en el turismo sostenible 2020 – 2030. Para esto se utilizaron los métodos de prospectiva estratégica planteados por Mojica (2010); se desarrolló el análisis del sector, a través de estudios bibliométricos, patentometría, vigilancia tecnológica, aplicaciones como Mic-Mac, Mactor y ábaco de Regniere. También se realizó la estructuración de variables estratégicas, el análisis morfológico de los escenarios, la postulación de estos escenarios en los ejes de Peter Schwartz y la determinación del grado de gobernabilidad de las acciones a desarrollar. Los resultados mostraron que el desarrollo del sector turístico en el mundo, ha tenido como eje fundamental el turismo sostenible integrado con el ámbito rural. El escenario “La Plata Ciudad Región” fue elegido como reto, y en este se aprovecharon los potenciales del turismo rural y cultural, permitiendo que los turistas hicieran una inmersión en las actividades y los ambientes tradicionales. Además, presenta alianzas entre el estado y la empresa privada para potencializar estos cambios; en este escenario el turista disfruta de un parque automotor acondicionado, pensando en la comodidad y la seguridad.

Banco de la República is celebrating its 100th anniversary in 2023. This is a very significant anniversary and one that provides an opportunity to highlight the contribution the Bank has made to the country’s development. Its track record as guarantor of monetary stability has established it as the one independent state institution that generates the greatest confidence among Colombians due to its transparency, management capabilities, and effective compliance with the central banking and cultural responsibilities entrusted to it by the Constitution and the Law. On a date as important as this, the Board of Directors of Banco de la República (BDBR) pays tribute to the generations of governors and officers whose commitment and dedication have contributed to the growth of this institution.1 Banco de la República’s mandate was confirmed in the National Constitutional Assembly of 1991 where the citizens had the opportunity to elect the seventy people who would have the task of drafting a new constitution. The leaders of the three political movements with the most votes were elected as chairs to the Assembly, and this tripartite presidency reflected the plurality and the need for consensus among the different political groups to move the reform forward. Among the issues considered, the National Constitutional Assembly gave special importance to monetary stability. That is why they decided to include central banking and to provide Banco de la República with the necessary autonomy to use the instruments for which they are responsible without interference from other authorities. The constituent members understood that ensuring price stability is a state duty and that the entity responsible for this task must be enshrined in the Constitution and have the technical capability and institutional autonomy necessary to adopt the decisions they deem appropriate to achieve this fundamental objective in coordination with the general economic policy. In particular, Article 373 established that “the State, through Banco de la República, shall ensure the maintenance of the purchasing power of the currency,” a provision that coincided with the central banking system adopted by countries that have been successful in controlling inflation. In 1999, in Ruling 481, the Constitutional Court stated that “the duty to maintain the purchasing power of the currency applies to not only the monetary, credit, and exchange authority, i.e., the Board of Banco de la República, but also those who have responsibilities in the formulation and implementation of the general economic policy of the country” and that “the basic constitutional purpose of Banco de la República is the protection of a sound currency. However, this authority must take the other economic objectives of state intervention such as full employment into consideration in their decisions since these functions must be coordinated with the general economic policy.” The reforms to Banco de la República agreed upon in the Constitutional Assembly of 1991 and in Act 31/1992 can be summarized in the following aspects: i) the Bank was assigned a specific mandate: to maintain the purchasing power of the currency in coordination with the general economic policy; ii) the BDBR was designatedas the monetary, foreign exchange, and credit authority; iii) the Bank and its Board of Directors were granted a significant degree of independence from the government; iv) the Bank was prohibited from granting credit to the private sector except in the case of the financial sector; v) established that in order to grant credit to the government, the unanimous vote of its Board of Directors was required except in the case of open market transactions; vi) determined that the legislature may, in no case, order credit quotas in favor of the State or individuals; vii) Congress was appointed, on behalf of society, as the main addressee of the Bank’s reporting exercise; and viii) the responsibility for inspection, surveillance, and control over Banco de la República was delegated to the President of the Republic. The members of the National Constitutional Assembly clearly understood that the benefits of low and stable inflation extend to the whole of society and contribute mto the smooth functioning of the economic system. Among the most important of these is that low inflation promotes the efficient use of productive resources by allowing relative prices to better guide the allocation of resources since this promotes economic growth and increases the welfare of the population. Likewise, low inflation reduces uncertainty about the expected return on investment and future asset prices. This increases the confidence of economic agents, facilitates long-term financing, and stimulates investment. Since the low-income population is unable to protect itself from inflation by diversifying its assets, and a high proportion of its income is concentrated in the purchase of food and other basic goods that are generally the most affected by inflationary shocks, low inflation avoids arbitrary redistribution of income and wealth.2 Moreover, low inflation facilitates wage negotiations, creates a good labor climate, and reduces the volatility of employment levels. Finally, low inflation helps to make the tax system more transparent and equitable by avoiding the distortions that inflation introduces into the value of assets and income that make up the tax base. From the monetary authority’s point of view, one of the most relevant benefits of low inflation is the credibility that economic agents acquire in inflation targeting, which turns it into an effective nominal anchor on price levels. Upon receiving its mandate, and using its autonomy, Banco de la República began to announce specific annual inflation targets as of 1992. Although the proposed inflation targets were not met precisely during this first stage, a downward trend in inflation was achieved that took it from 32.4% in 1990 to 16.7% in 1998. At that time, the exchange rate was kept within a band. This limited the effectiveness of monetary policy, which simultaneously sought to meet an inflation target and an exchange rate target. The Asian crisis spread to emerging economies and significantly affected the Colombian economy. The exchange rate came under strong pressure to depreciate as access to foreign financing was cut off under conditions of a high foreign imbalance. This, together with the lack of exchange rate flexibility, prevented a countercyclical monetary policy and led to a 4.2% contraction in GDP that year. In this context of economic slowdown, annual inflation fell to 9.2% at the end of 1999, thus falling below the 15% target set for that year. This episode fully revealed how costly it could be, in terms of economic activity, to have inflation and exchange rate targets simultaneously. Towards the end of 1999, Banco de la República announced the adoption of a new monetary policy regime called the Inflation Targeting Plan. This regime, known internationally as ‘Inflation Targeting,’ has been gaining increasing acceptance in developed countries, having been adopted in 1991 by New Zealand, Canada, and England, among others, and has achieved significant advances in the management of inflation without incurring costs in terms of economic activity. In Latin America, Brazil and Chile also adopted it in 1999. In the case of Colombia, the last remaining requirement to be fulfilled in order to adopt said policy was exchange rate flexibility. This was realized around September 1999, when the BDBR decided to abandon the exchange-rate bands to allow the exchange rate to be freely determined in the market.Consistent with the constitutional mandate, the fundamental objective of this new policy approach was “the achievement of an inflation target that contributes to maintaining output growth around its potential.”3 This potential capacity was understood as the GDP growth that the economy can obtain if it fully utilizes its productive resources. To meet this objective, monetary policy must of necessity play a countercyclical role in the economy. This is because when economic activity is below its potential and there are idle resources, the monetary authority can reduce the interest rate in the absence of inflationary pressure to stimulate the economy and, when output exceeds its potential capacity, raise it. This policy principle, which is immersed in the models for guiding the monetary policy stance, makes the following two objectives fully compatible in the medium term: meeting the inflation target and achieving a level of economic activity that is consistent with its productive capacity. To achieve this purpose, the inflation targeting system uses the money market interest rate (at which the central bank supplies primary liquidity to commercial banks) as the primary policy instrument. This replaced the quantity of money as an intermediate monetary policy target that Banco de la República, like several other central banks, had used for a long time. In the case of Colombia, the objective of the new monetary policy approach implied, in practical terms, that the recovery of the economy after the 1999 contraction should be achieved while complying with the decreasing inflation targets established by the BDBR. The accomplishment of this purpose was remarkable. In the first half of the first decade of the 2000s, economic activity recovered significantly and reached a growth rate of 6.8% in 2006. Meanwhile, inflation gradually declined in line with inflation targets. That was how the inflation rate went from 9.2% in 1999 to 4.5% in 2006, thus meeting the inflation target established for that year while GDP reached its potential level. After this balance was achieved in 2006, inflation rebounded to 5.7% in 2007, above the 4.0% target for that year due to the fact that the 7.5% GDP growth exceeded the potential capacity of the economy.4 After proving the effectiveness of the inflation targeting system in its first years of operation, this policy regime continued to consolidate as the BDBR and the technical staff gained experience in its management and state-of-the-art economic models were incorporated to diagnose the present and future state of the economy and to assess the persistence of inflation deviations and expectations with respect to the inflation target. Beginning in 2010, the BDBR established the long-term 3.0% annual inflation target, which remains in effect today. Lower inflation has contributed to making the macroeconomic environment more stable, and this has favored sustained economic growth, financial stability, capital market development, and the functioning of payment systems. As a result, reductions in the inflationary risk premia and lower TES and credit interest rates were achieved. At the same time, the duration of public domestic debt increased significantly going from 2.27 years in December 2002 to 5.86 years in December 2022, and financial deepening, measured as the level of the portfolio as a percentage of GDP, went from around 20% in the mid-1990s to values above 45% in recent years in a healthy context for credit institutions.Having been granted autonomy by the Constitution to fulfill the mandate of preserving the purchasing power of the currency, the tangible achievements made by Banco de la República in managing inflation together with the significant benefits derived from the process of bringing inflation to its long-term target, make the BDBR’s current challenge to return inflation to the 3.0% target even more demanding and pressing. As is well known, starting in 2021, and especially in 2022, inflation in Colombia once again became a serious economic problem with high welfare costs. The inflationary phenomenon has not been exclusive to Colombia and many other developed and emerging countries have seen their inflation rates move away from the targets proposed by their central banks.5 The reasons for this phenomenon have been analyzed in recent Reports to Congress, and this new edition delves deeper into the subject with updated information. The solid institutional and technical base that supports the inflation targeting approach under which the monetary policy strategy operates gives the BDBR the necessary elements to face this difficult challenge with confidence. In this regard, the BDBR reiterated its commitment to the 3.0% inflation target in its November 25 communiqué and expects it to be reached by the end of 2024.6 Monetary policy will continue to focus on meeting this objective while ensuring the sustainability of economic activity, as mandated by the Constitution. Analyst surveys done in March showed a significant increase (from 32.3% in January to 48.5% in March) in the percentage of responses placing inflation expectations two years or more ahead in a range between 3.0% and 4.0%. This is a clear indication of the recovery of credibility in the medium-term inflation target and is consistent with the BDBR’s announcement made in November 2022. The moderation of the upward trend in inflation seen in January, and especially in February, will help to reinforce this revision of inflation expectations and will help to meet the proposed targets. After reaching 5.6% at the end of 2021, inflation maintained an upward trend throughout 2022 due to inflationary pressures from both external sources, associated with the aftermath of the pandemic and the consequences of the war in Ukraine, and domestic sources, resulting from: strengthening of local demand; price indexation processes stimulated by the increase in inflation expectations; the impact on food production caused by the mid-2021 strike; and the pass-through of depreciation to prices. The 10% increase in the minimum wage in 2021 and the 16% increase in 2022, both of which exceeded the actual inflation and the increase in productivity, accentuated the indexation processes by establishing a high nominal adjustment benchmark. Thus, total inflation went to 13.1% by the end of 2022. The annual change in food prices, which went from 17.2% to 27.8% between those two years, was the most influential factor in the surge in the Consumer Price Index (CPI). Another segment that contributed significantly to price increases was regulated products, which saw the annual change go from 7.1% in December 2021 to 11.8% by the end of 2022. The measure of core inflation excluding food and regulated items, in turn, went from 2.5% to 9.5% between the end of 2021 and the end of 2022. The substantial increase in core inflation shows that inflationary pressure has spread to most of the items in the household basket, which is characteristic of inflationary processes with generalized price indexation as is the case in Colombia. Monetary policy began to react early to this inflationary pressure. Thus, starting with its September 2021 session, the BDBR began a progressive change in the monetary policy stance moving away from the historical low of a 1.75% policy rate that had intended to stimulate the recovery of the economy. This adjustment process continued without interruption throughout 2022 and into the beginning of 2023 when the monetary policy rate reached 12.75% last January, thus accumulating an increase of 11 percentage points (pp). The public and the markets have been surprised that inflation continued to rise despite significant interest rate increases. However, as the BDBR has explained in its various communiqués, monetary policy works with a lag. Just as in 2022 economic activity recovered to a level above the pre-pandemic level, driven, along with other factors, by the monetary stimulus granted during the pandemic period and subsequent months, so too the effects of the current restrictive monetary policy will gradually take effect. This will allow us to expect the inflation rate to converge to 3.0% by the end of 2024 as is the BDBR’s purpose.Inflation results for January and February of this year showed declining marginal increases (13 bp and 3 bp respectively) compared to the change seen in December (59 bp). This suggests that a turning point in the inflation trend is approaching. In other Latin American countries such as Chile, Brazil, Perú, and Mexico, inflation has peaked and has begun to decline slowly, albeit with some ups and downs. It is to be expected that a similar process will take place in Colombia in the coming months. The expected decline in inflation in 2023 will be due, along with other factors, to lower cost pressure from abroad as a result of the gradual normalization of supply chains, the overcoming of supply shocks caused by the weather, and road blockades in previous years. This will be reflected in lower adjustments in food prices, as has already been seen in the first two months of the year and, of course, the lagged effect of monetary policy. The process of inflation convergence to the target will be gradual and will extend beyond 2023. This process will be facilitated if devaluation pressure is reversed. To this end, it is essential to continue consolidating fiscal sustainability and avoid messages on different public policy fronts that generate uncertainty and distrust. 1 This Report to Congress includes Box 1, which summarizes the trajectory of Banco de la República over the past 100 years. In addition, under the Bank’s auspices, several books that delve into various aspects of the history of this institution have been published in recent years. See, for example: Historia del Banco de la República 1923-2015; Tres banqueros centrales; Junta Directiva del Banco de la República: grandes episodios en 30 años de historia; Banco de la República: 90 años de la banca central en Colombia. 2 This is why lower inflation has been reflected in a reduction of income inequality as measured by the Gini coefficient that went from 58.7 in 1998 to 51.3 in the year prior to the pandemic. 3 See Gómez Javier, Uribe José Darío, Vargas Hernando (2002). “The Implementation of Inflation Targeting in Colombia”. Borradores de Economía, No. 202, March, available at: https://repositorio.banrep.gov.co/handle/20.500.12134/5220 4 See López-Enciso Enrique A.; Vargas-Herrera Hernando and Rodríguez-Niño Norberto (2016). “The inflation targeting strategy in Colombia. An historical view.” Borradores de Economía, No. 952. https://repositorio.banrep.gov.co/handle/20.500.12134/6263 5 According to the IMF, the percentage change in consumer prices between 2021 and 2022 went from 3.1% to 7.3% for advanced economies, and from 5.9% to 9.9% for emerging market and developing economies. 6 https://www.banrep.gov.co/es/noticias/junta-directiva-banco-republica-reitera-meta-inflacion-3

The Jurisprudence of Equality project (JEP) trains judges and other judicial actors on the applicability of international women's rights law in domestic courts, thus enhancing their ability to treat cases of violence against women and ensuring greater protection for women's rights in the region. The purpose of this report is to distill the findings and conclusions from the JEP evaluation in Argentina, Brazil, Chile and Uruguay. This evaluation was meant to find out to which extent the project is being implemented as planned, identifying any difficulties during implementation, and ways to overcome them. It has also assessed the effect that project activities are having in achieving the project goal. Apart from document review and interviews in Washington and in the four countries visited in March-April 2000 with relevant stakeholders, the evaluation relies on two main instruments for each country: (a) a survey, applied to trainers and seminar participants. The questionnaires were designed with the close cooperation of the Washington IWJF director and the education director, as well as in consultation with other stakeholders in the field, and the IDB in Washington and Country Offices; (b) a series of focus groups carried out separately with trainers and seminar participants.

This brief sets out key considerations for risk communications and community engagement (RCCE) to promote adherence to COVID-19 preventive measures in greater Kampala, Uganda. It looks at adherence to COVID-19 preventive measures, assesses the challenges to their adoption and outlines key considerations for partners working in RCCE and the wider COVID-19 emergency response. The brief responds to concern (as of March 2022) about COVID-19 transmission in informal urban areas in Uganda due to their high population density, limited sanitary infrastructure, and reported low uptake of vaccination. Ensuring effective communication and engagement with a series of preventative measures is essential in limiting the spread of COVID-19. The Ministry of Health and response partners have been proactive, however interventions and guidance for COVID-19 have taken limited account of social science research about the perceptions and practices related to COVID-19 regulations. This brief aims to address this gap so these data may be used to inform more effective and practicable guidance for vulnerable groups. This brief draws primarily on an analysis of existing scientific and grey literature. Additional primary data was collected through consultation with six social science and RCCE experts who focus on this geographical area. The brief was requested by UNICEF Uganda in consultation with the Uganda Ministry of Health (MoH) RCCE subcommittee and the RCCE technical working group for the Eastern and South Africa region (ESAR). It was developed for SSHAP by Theresa Jones (Anthrologica) and supported by Elizabeth Storer (London School of Economics), with contributions and reviews by colleagues at Anthrologica, the Institute of Development Studies (IDS), UNICEF ESARO and Uganda, Makerere University, the London School of Hygiene and Tropical Medicine (LSHTM), Dreamline Products and the IFRC.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.