Academic literature on the topic 'Numerical analysis'

Entanglement has recently been one of the most essential elements in the development of various quantum technologies. In fact, a swapping protocol was introduced to create a long-distance entanglement from multiple shorter ones. Extending the previous work, this paper provides a more detailed numerical analysis to help create long-distance entanglement out of the two non-maximal three-level states. Specifically, it shows that while the protocol does not always yield optimal results, namely, the weaker link, there is a substantial number of states that yield an optimal result. Moreover, we discuss the numerical approach in showing the existence of states that provide a result close to the optimal outcome, which may be useful in realizing the long-distance entanglement used in quantum technology.

Lo scavo di gallerie rappresenta sicuramente una tra le sfide più impegnative che un ingegnere civile possa affrontare. Ciò è dovuto principalmente alla natura tridimensionale di questo problema di interazione terreno-struttura ma anche alle numerose incertezze che possono entrare in gioco nella progettazione. Recentemente, le tecniche di calcolo numeriche, che permettono una più ampia comprensione del problema, hanno subito un notevole sviluppo, diventando una risorsa fondamentale per la progettazione di scavi in sotterraneo. Tuttavia, solo ingegneri con una buona preparazione numerica sono in grado di gestire la modellazione di problemi di interazione terreno-struttura così complessi. Inoltre, tali modelli richiedono una attenta calibrazione dei parametri e una costante validazione con dati di monitoraggio. Lo scopo di questa tesi è quello di analizzare alcune delle principali problematiche legate alla progettazione di gallerie superficiali scavate in tradizionale. Il vantaggio principale dello scavo in traditionale rispetto a quello meccanizzato è legato alla maggiore flessibilità nella scelta dei rivestimenti e delle techniche di rinforzo del cavo e del fronte della galleria. Tuttavia, una maggiore flessibilità progettuale è necessariamente legata ad una profonda conoscenza del comportamento deformativo dell’ammasso, nonché ad un utilizzo consapevole delle tecniche modellazione numerica. Il presente lavoro è principalmente incentrato sulle seguenti tematiche riguardanti la progettazione di gallerie superficiali: - la stabilità di fronti di scavo rinforzati e non rinforzati; - l’applicabilità degli Eurocodici ad una progettazione condotta mediante tecniche di modellazione numerica; - la calibrazione dei parametri del modello numerico e la sua validazione attraverso dati di monitoraggio.
Among the problems that civil engineers have to face, the design and verification of an underground construction is one of the most challenging. A tunnel engineer has to tackle with a complex three-dimensional soil-structure interaction problem where many factors and uncertainties come into play. This is the reason why professional experience and engineering judgment usually play a crucial role. In recent years, numerical calculation techniques, which can provide an important basis for a better understanding of the problem, have strongly improved. They have become a fundamental resource for underground construction design, but they also entail some drawbacks: - only engineers with a strong numerical background can handle complex soil-structure interaction problems; - numerical calculations, especially if 3D, can be very time-consuming; - material parameters should be carefully evaluated, according to the particular problem and adopted constitutive law; - numerical models need to be validated with field monitoring data. The goal of this thesis is to investigate the main issues regarding the applicability of numerical analyses to the design and verification of traditionally excavated shallow tunnels. Despite, the remarkable technological improvement in mechanised tunnelling, traditional techniques still represent, in some cases, the most suitable and convenient solution. The principal advantage of traditional techniques is the high flexibility in the choice of supports and reinforcement measures. However, design flexibility implies a deep understanding of the ground response to underground openings as well as a conscious use of numerical models. This work provides a contribution to the numerical design of shallow tunnels by focusing on three principal issues: - stability of reinforced and unreinforced excavation faces; - Eurocodes applicability to a numerically-based design; - parameters calibration and numerical validation through comparison with monitoring data.

This thesis is on the topic of numerical thermal analysis, specically of the SmallExplorer for Advanced Missions SEAM. SEAM is a 3 unit Cubesat, which isgoing to be launched in a sun-synchronous orbit to measure the magnetic sphere.It makes use of a boom deployment system to remove the sensors from themagnetic eld inuences of the body. The goal of this thesis is to study thethermal behaviour of the satellite, specically the internal components and thethermal deformation of the boom structure. The numerical simulations makeuse of the Monte Carlo Ray-tracing method. Furthermore thermal vacuumcycle tests have been compared to the thermal model as a form of validation.Additionally the thesis also serves as a nal thermal analysis of the satellite, tocheck if all components operate within their specied thermal operating range.
Detta examensarbete handlar om numerisk termisk analys av SEAM (SmallExplorer for Advanced Missions) satellit. SEAM är en 3U CubeSat, som skaskickas upp i solsynkron bana kring jorden för att utföra magnetfältmätningar.Satelliten använder sig av en utfällbar bom för att separera magnetsensorer frånmagnetiska störningar från satellitens elektronik. Examensarbetet syftar tillatt studera termiska beteende av satelliten, specifikt temperaturområden i bananför interna komponenter samt termisk deformation av den utfällbara bomstrukturen.Numeriska simuleringar av strålningsöverföring av värme använderMonte-Carlo metod för att följa strålar. Experimentella resultat från termiskvakuum testning av satelliten har jämförts med termiska modellen för att valideraden. Examensarbetet utgör den slutliga termiska analysen av satelliten, föratt säkerställa att alla komponenter används inom deras specificerade temperaturområde.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Esta pesquisa tem como objetivo a implementação de uma ferramenta numérica que contabiliza as inclusões horizontais e subhorizontais na parcela de solo devidamente discretizada por elementos finitos. Este modelo implementa a análise de esforços axiais e cisalhantes solicitados nas interfaces grampo/nata, nata/solo e no próprio aço (grampo) e, também, esforços fletores de um material “equivalente” formado pela combinação das rigidezes do grampo e da nata. Este objetivo é alcançado através da implementação de mais um “pacote” de subrotinas, denominado grampo, no programa DYNREL, desenvolvido no Departamento de Engenharia Civil da PUC-Rio (Figueiredo, 1991). A formulação proposta para contabilizar o efeito das inclusões considera, além dos deslocamentos nodais horizontal e vertical, a influência das rotações no sistema de forças envolvido. A parcela reativa do grampo é calculada iterativamente em função das variáveis primárias obtidas no programa principal para o meio discretizado sem reforço e, assim, acrescida ao vetor de forças internas contrárias. Logo o novo vetor de forças desbalanceadas do sistema incorpora o efeito das inclusões passivas (grampo). O presente trabalho apresenta detalhes da técnica de estruturas grampeadas, do modelo numérico de análise implementado, de exemplos de validação do comportamento das estruturas grampeadas e de exemplos ilustrativos destas estruturas.
The present research has as its main objective the development of a numerical tool capable of simulating the introduction of long structural inclusions in a soil mass discretized by finite elements. Models of the behaviour of the nail/grout system and its interaction with the soil mass were implemented. These models take into account the normal and shear loads transferred at the nail-grout and grout-soil interfaces besides the axial loads and moments acting in the nail itself. The models are able to consider both elastic and inelastic behaviour both at the interfaces and the nail. The proposed models , consisting on a set of subroutines, were implemented in the program DYNREL, developped at the Civil Engineering Department of PUC Rio (Figueiredo,1991). DYNREL is a finite element program which uses dynamic relaxation as the solution algorithm for the equilibrium equations. In the implementation carried out, it is considered that the soil mass is discretized without taking into account the nail. The reactions of the nails are calculated at each time step from the displacements of the elements intercepted by the nails. These displacements are used in the developped subroutines to generate the force reactions from the nails which in turn are transferred back to the finite element mesh for the following time step calculations. The present work presents detais of the implemented models as well as validation and illustrative examples. Conclusions are drawn relative to the numerical implementation carried out and to the results obtained on the analysis of hypothetical nailed retaining structure.
Esta investigación tiene como objetivo principal, el desarrollo de una herramienta numérica capaz de simular la introducción de refuerzos en una masa de suelo discretizada por elementos finitos. Fueron implementados modelos de comportamiento del sistema clavo/nata y sus interacciones con el suelo. Estos modelos consideran las cargas normales y cisallantes que actúan en las interfaces clavo - nata y nata - suelo debido a la acción de momentos y cargas axiales. Los modelos consideran tanto el comportamiento inelástico como el elástico en las interfaces y los clavos. Los modelos propuestos, que consisten en una serie de subrutinas, fueron implementados en el programa DYNREL, desarrollado en el Departamento de Ingeniería Civil de la PUC-Rio (Figueiredo, 1991). O DYNREL es un programa en elementos finitos que utiliza del Relajamiento Dinámico como algoritmo de solución para las ecuaciones de equilibrio. En la implementación se considera una masa de suelo discretizada sin llevar en cuenta el clavo. Las reacciones de los clavos se calculan en cada instante de tiempo por los desplazamientos de los elementos interceptados por los clavos. Estos desplazamientos se utilizan en las subrutinas desarrolladas para generar las fuerzas de reacción de los clavos, que son transferidos nuevamente para la red de elementos finitos para los cálculos en el instante de tiempo siguiente. Este trabajo presenta detalles de los modelos implementados, así como ejemplos de evaluación y aplicación. Se arriban a conclusiones relativas a la implementación numérica y a los resultados obtenidos del análisis de extructuras de contención clavadas hipotéticas.

Magnetic nanoparticles (NPs) with sizes ranging from 2 to 20 nm in diameter represent an important class of artificial nanostructured materials, since the NP size is comparable to the size of a magnetic domain. They have potential applications in data storage, catalysis, permanent magnetic nanocomposites, and biomedicine. To begin with, a brief overview on the background of Fe-based bimetallic NPs and their applications for data-storage and catalysis was presented in Chapter 1. In Chapter 2, L10-ordered FePt NPs with high coercivity were directly prepared from a novel bimetallic acetylenic alternating copolymer P3 by a one-step pyrolysis method without post-thermal annealing. The chemical ordering, morphology and magnetic properties were studied. Magnetic measurements showed that a record coercivity of 3.6 T (1 T = 10 kOe) was obtained in FePt NPs. By comparison of the resultant FePt NPs synthesized under Ar and Ar/H2, the characterization proved that the incorporation of H2 would affect the nucleation and promote the growth of FePt NPs. The L10 FePt NPs were also successfully patterned on Si substrate by nanoimprinting lihthography (NIL). The highly ordered ferromagnetic arrays on a desired substrate for bit-patterned media (BPM) were studied and promised bright prospects for the progress of data-storage. Furthermore, we also reported a new FePt-containing metallopolymer P4 as the single-source precursor for metal alloy NPs synthesis, where the metal fractions were on the side chain and the ratio could be easily controlled. This polymer was synthesized from random copolymer poly(styrene-4-ethynylstyrene) PES-PS and bimetallic precursor TPy-FePt ([Pt(4’-ferrocenyl-(N^N^N))Cl]Cl) by Sonogashira coupling reaction. After pyrolysis of P4, the stoichiometry of Fe and Pt atoms in the synthesized NPs (NPs) is nearly close to 1:1, which is more precise than using TPy-FePt as precursor. Polymer P4 was also more favorable for patterning by high throughout NIL as compared to TPy-FePt. Ferromagnetic nanolines, potentially as bit-patterned magnetic recording media, were successfully fabricated from P4 and fully characterized. In Chapter 3, a novel organometallic compound TPy-FePd-1 [4’-ferrocenyl-(N^N^N)PdOCOCH3] was synthesized and structurally characterized, whose crystal structure showed a coplanar Pd center and Pd-Pd distance (3.17 Å). Two metals Fe and Pd were evenly embedded in the molecular dimension and remained tightly coupled between each other benefiting to the metalmetal (Pd-Pd) and ligand ππ stacking interactions, all of which made it facilitate the nucleation without sintering during preparing the FePd NPs. Ferromagnetic FePd NPs of ca. 16.2 nm in diameter were synthesized by one-pot pyrolysis of the single-source precursor TPy-FePd-1 under getter gas with metal-ion reduction and minimal nanoparticle coalescence, which have a nearly equal atomic ratio (Fe/Pd = 49/51) and exhibited coercivity of 4.9 kOe at 300 K. By imprinting the mixed chloroform solution of TPy-FePd-1 and polystyrene (PS) on Si, reproducible patterning of nanochains was formed due to the excellent self-assembly properties and the incompatibility between TPy-FePd-1 and PS under the slow evaporation of the solvents. The FePd nanochains with average length of ca. 260 nm were evenly dispersed around the PS nanosphere by self-assembly of TPy-FePd-1. In addition, the orientation of the FePd nanochains could also be controlled by tuning the morphology of PS, and the length was shorter in confined space of PS. Orgnic skeleton in TPy-FePd-1 and PS were carbonized and removed by pyrolysis under Ar/H2 (5 wt%) and only magnetic FePd alloy nanochains with domain structure were left. Besides, a bimetallic complex TPy-FePd-2 was prepared and used as a single-source precursor to synthesize ferromagnetic FePd NPs by one-pot pyrolysis. The resultant FePd NPs have a mean size of 19.8 nm and show the coercivity of 1.02 kOe. In addition, the functional group (-NCMe) in TPy-FePd-2 was easily substituted by a pyridyl group. A random copolymer PS-P4VP was used to coordinate with TPy-FePd-2, and the as-synthesized polymer made the metal fraction disperse evenly along the flexible chain. Fabrication of FePd NPs from the polymers was also investigated, and the size could be easily controlled by tuning the metal fraction in polymer. FePd NPs with the mean size of 10.9, 14.2 and 17.9 nm were prepared from the metallopolymer with 5 wt%, 10 wt% and 20wt% of metal fractions, respectively. In Chapter 4, molybdenum disulfide (MoS2) monolayers decorated with ferromagnetic FeCo NPs on the edges were synthesized through a one-step pyrolysis of precursor molecules in an argon atmosphere. The FeCo precursor was spin coated on the MoS2 monolayer grown on Si/SiO2 substrate. Highly-ordered body-centered cubic (bcc) FeCo NPs were revealed under optimized pyrolysis conditions, possessing coercivity up to 1000 Oe at room temperature. The FeCo NPs were well-positioned along the edge sites of MoS2 monolayers. The vibration modes of Mo and S atoms were confined after FeCo NPs decoration, as characterized by Raman shift spectroscopy. These MoS2 monolayers decorated with ferromagnetic FeCo NPs can be used for novel catalytic materials with magnetic recycling capabilities. The sizes of NPs grown on MoS2 monolayers are more uniform than from other preparation routines. Finally, the optimized pyrolysis temperature and conditions provide receipts for decorating related noble catalytic materials. Finally, Chapters 5 and 6 present the concluding remarks and the experimental details of the work described in Chapters 2-4.

Multitud de problemas en ciencia e ingeniería se plantean como ecuaciones en derivadas parciales (EDPs). Si la frontera del recinto donde esas ecuaciones han de satisfacerse se desconoce a priori, se habla de "Problemas de frontera libre", propios de sistemas estacionarios no dependientes del tiempo, o bien de "Problemas de frontera móvil", asociados a problemas de evolución temporal, donde la frontera cambia con el tiempo. La solución a dichos problemas viene dada por la expresión de la(s) variable(s) dependiente(s) de la(s) EDP(s) junto con la función que determina la posición de la frontera. Dado que este tipo de problemas carece en la mayoría de los casos de solución analítica conocida, se hace preciso recurrir a métodos numéricos que permitan obtener una solución lo suficientemente aproximada, y que además mantenga propiedades cualitativas de la solución del modelo continuo de EDP(s). En este trabajo se ha abordado el estudio numérico de algunos problemas de frontera móvil provenientes de diversas disciplinas. La metodología aplicada consta de dos pasos sucesivos: aplicación de la transformación de Landau o "Front-fixing transformation" al modelo en EDP(s) con el fin de mantener inmóvil la frontera del dominio, y posterior discretización a través de un esquema en diferencias finitas. De ahí se obtienen esquemas numéricos que se implementan por medio de la herramienta MATLAB. Mediante un exhaustivo análisis numérico, se estudian propiedades del esquema y de la solución numérica (positividad, estabilidad, consistencia, monotonía, etc.). En el primer capítulo de este trabajo se revisa el estado del arte del campo objeto de estudio, se justifica la necesidad de disponer de métodos numéricos adaptados a este tipo de problemas y se describe brevemente la metodología empleada en nuestro enfoque. El Capítulo 2 se dedica a un problema perteneciente a la Biología Matemática y que consiste en determinar la evolución de la población de una especie invasora que se propaga en un hábitat. Este modelo consiste en una ecuación de difusión-reacción unida a una condición tipo Stefan. Los resultados del análisis numérico confirman la existencia de una dicotomía propagación-extinción en la evolución a largo plazo de la densidad de población de la especie invasora. En particular, se ha podido precisar el valor del coeficiente de la condición de Stefan que separa el comportamiento de propagación del de extinción. Los Capítulos 3 y 4 se centran en un problema de Química del Hormigón con interés en Ingeniería Civil: el proceso de carbonatación del hormigón, fenómeno evolutivo que lleva consigo la degradación progresiva de la estructura afectada y finalmente su ruina, si no se toman medidas preventivas. En el Capítulo 3 se considera un sistema de dos EDPs de tipo parabólico con dos incógnitas. Para su resolución, hay que considerar además las condiciones iniciales, las de contorno y las de tipo Stefan en la frontera. Los resultados numéricos confirman la tendencia de la ley de evolución de la frontera móvil hacia una función del tipo "raíz cuadrada del tiempo". En el Capítulo 4 se considera un modelo más general que el anterior, en el que intervienen seis especies químicas que se encuentran tanto en la zona carbonatada como en la no carbonatada. En el Capítulo 5 se aborda un problema de transmisión de calor que aparece en diversos procesos industriales; en este caso, en el enfriamiento durante la colada de metal fundido, donde la fase sólida avanza y la líquida se va extinguiendo. La frontera móvil (frente de solidificación) separa ambas fases, siendo su posición en cada instante la variable a determinar, junto con las temperaturas en cada fase. Después de la adecuada transformación y discretización, se implementa un esquema en diferencias finitas, subdividiendo el proceso en tres estadios temporales, a fin de tratar las singularidades asociadas a posicione
Many problems in science and engineering are formulated as partial differential equations (PDEs). If the boundary of the domain where these equations are to be solved is not known a priori, we face "Free-boundary problems", which are characteristic of non-time dependent stationary systems; besides, we have "Moving-boundary problems" in temporal evolution processes, where the border changes over time. The solution to these problems is given by the expression of the dependent variable(s) of PDE(s), together with the function that determines the position of the boundary. Since the analytical solution of this type of problems is lacked in most cases, it is necessary to resort to numerical methods that allow an accurate enough solution to be obtained, and which also maintain the qualitative properties of the solution(s) of the continuous model. This work approaches the numerical study of some moving-boundary problems that arise in different disciplines. The applied methodology consists of two successive steps: firstly, the so-called Landau transformation, or "Front-fixing transformation", which is used in the PDE(s) model to maintain the boundary of the domain immobile; later, we proceed to its discretization with a finite difference scheme. Different numerical schemes are obtained and implemented through the MATLAB computational tool. Properties of the scheme and the numerical solution (positivity, stability, consistency, monotonicity, etc.) are studied by an exhaustive numerical analysis. The first chapter of this work reports the state of the art of the field under study, justifies the need to adapt numerical methods to this type of problem, and briefly describes the methodology used in our approach. Chapter 2 presents a problem in Mathematical Biology that consists in determining over time the evolution of an invasive species population that spreads in a habitat. This problem is modelled by a diffusion-reaction equation linked to a Stefan-type condition. The results of the numerical analysis confirm the existence of a spreading-vanishing dichotomy in the long-term evolution of the population density of the invasive species. In particular, it is possible to determine the value of the coefficient of the Stefan condition that separates the propagation behaviour from extinction. Chapters 3 and 4 focus on a problem of Concrete Chemistry with an interest in Civil Engineering: the carbonation of concrete, an evolutionary phenomenon that leads to the progressive degradation of the affected structure and its eventual ruin if preventive measures are not taken. Chapter 3 considers a system of two parabolic type PDEs with two unknowns. For its resolution, the initial and boundary conditions have to be considered together with the Stefan conditions on the carbonation front. The numerical analysis results agree with those obtained in a previous theoretical study. The dynamics of the concentrations and the moving boundary confirm the long-term behaviour of the evolution law for the moving boundary as a "square root of time". Chapter 4 considers a more general model than the previous one, which includes six chemical species, defined in both the carbonated and non-carbonated zones, whose concentrations have to be found. Chapter 5 addresses a heat transfer problem that appears in various industrial processes; in this case, the solidification of metals in casting processes, where the solid phase advances and liquid reduces until it is depleted. The moving boundary (the solidification front) separates both phases. Its position in each instant is the variable to be determined together with the temperature profiles in both phases. After suitable transformation, discretization is carried out to obtain a finite difference scheme to be implemented. The process was subdivided into three temporal stages to deal with the singularities associated with the moving boundary position in the initialisation and depletion stages.
Multitud de problemes en ciència i enginyeria es plantegen com a equacions en derivades parcials (EDPs). Si la frontera del recinte on eixes equacions han de satisfer-se es desconeix a priori, es parla de "Problemas de frontera lliure", propis de sistemes estacionaris no dependents del temps, o bé de "Problemas de frontera mòbil", associats a problemes d'evolució temporal, on la frontera canvia amb el temps. Atés que este tipus de problemes manca en la majoria dels casos de solució analítica coneguda, es fa precís recórrer a mètodes numèrics que permeten obtindre una solució prou aproximada a l'exacta, i que a més mantinga propietats qualitatives de la solució del model continu d'EDP(s). En aquest treball s'ha abordat l'estudi numèric d'alguns problemes de frontera mòbil provinents de diverses disciplines. La metodologia aplicada consta de dos passos successius: en primer lloc, s'aplica l'anomenada transformació de Landau o "Front-fixing transformation" al model en EDP(s) a fi de mantindre immòbil la frontera del domini; posteriorment, es procedix a la seva discretització a través d'un esquema en diferències finites. D'ací s'obtenen esquemes numèrics que s'implementen per mitjà de la ferramenta informàtica MATLAB. Per mitjà d'una exhaustiva anàlisi numèrica, s'estudien propietats de l'esquema i de la solució numèrica (positivitat, estabilitat, consistència, monotonia, etc.). En el primer capítol d'aquest treball es revisa l'estat de l'art del camp objecte d'estudi, es justifica la necessitat de disposar de mètodes numèrics adaptats a aquest tipus de problemes i es descriu breument la metodologia emprada en el nostre enfocament. El Capítol 2 es dedica a un problema pertanyent a la Biologia Matemàtica i que consistix a determinar l'evolució en el temps de la distribució de la població d'una espècie invasora que es propaga en un hàbitat. Este model consistix en una equació de difusió-reacció unida a una condició tipus Stefan, que relaciona les funcions solució i frontera mòbil a determinar. Els resultats de l'anàlisi numèrica confirmen l'existència d'una dicotomia propagació-extinció en l'evolució a llarg termini de la densitat de població de l'espècie invasora. En particular, s'ha pogut precisar el valor del coeficient de la condició de Stefan que separa el comportament de propagació del d'extinció. Els Capítols 3 i 4 se centren en un problema de Química del Formigó amb interés en Enginyeria Civil: el procés de carbonatació del formigó, fenomen evolutiu que comporta la degradació progressiva de l'estructura afectada i finalment la seua ruïna, si no es prenen mesures preventives. En el Capítol 3 es considera un sistema de dos EDPs de tipus parabòlic amb dos incògnites. Per a la seua resolució, cal considerar a més, les condicions inicials, les de contorn i les de tipus Stefan en la frontera. Els resultats de l'anàlisi numèrica s'ajusten als obtinguts en un estudi teòric previ. S'han dut a terme experiments numèrics, comprovant la tendència de la llei d'evolució de la frontera mòbil cap a una funció del tipus "arrel quadrada del temps". En el Capítol 4 es considera un model més general, en el que intervenen sis espècies químiques les concentracions de les quals cal trobar, i que es troben tant en la zona carbonatada com en la no carbonatada. En el Capítol 5 s'aborda un problema de transmissió de calor que apareix en diversos processos industrials; en aquest cas, en el refredament durant la bugada de metall fos, on la fase sòlida avança i la líquida es va extingint. La frontera mòbil (front de solidificació) separa ambdues fases, sent la seua posició en cada instant la variable a determinar, junt amb les temperatures en cada una de les dos fases. Després de l'adequada transformació i discretització, s'implementa un esquema en diferències finites, subdividint el procés en tres estadis temporals, per tal de tractar les singularitats asso
Piqueras García, MÁ. (2018). Numerical Methods for Multidisciplinary Free Boundary Problems: Numerical Analysis and Computing [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/107948
TESIS