Academic literature on the topic 'Half-wave potential'

A method of potentials is presented for the derivation of the dynamic response of an elastic half-space to an arbitrary, time-harmonic, finite, buried source. The development includes a set of transformed stress-potential and displacement-potential relations which are apt to be useful in a variety of wave propagation problems. Specific results for an embedded source of uniform distributions are also included.

An improved version of the generalized density-dependent cluster model is presented to describe an α particle tunneling through a microscopic potential barrier. The microscopic potential is numerically constructed in the double folding model for both the Coulomb potential and the nuclear potential. The decay width is computed using the integral of the quasibound state wave function, the scattering state wave function, and the difference of potentials. We perform a systematic calculation of α-decay half-lives for even-even, odd-A, and odd-odd nuclei ranging from N = 84 to N = 126. The calculated α-decay half-lives are found to be in good agreement with the experimental values.

We find that the RMS wave height (square root of the potential energy) rather than peak-to-peak wave height is a better experimental and analytic criterion for determining when a regular, two-dimensional deep-water wave will break. A spectral algorithm for two-dimensional potential flow is developed and used to compare breaking onset criteria for energy input from (i) converging sidewalls, (ii) a submerged disturbance, and (iii) wave focusing. We also find that wave-breaking criteria (potential energy or the more classical peak-to-peak wave height) are a function of the rate of energy input. Large plunging waves occur when energy input rates are large. As energy input rates become smaller there is a smooth transition to smaller spilling waves. The various energy input methods show similar breaking trends in the limit as the energy input rate becomes small - waves break when the potential energy becomes approximately 52 % of the energy for the most energetic Stokes wave, with the formation of a singularity immediately before the crest. The effects of wave modulation and reflection are briefly discussed and shown not to affect the potential energy breaking criterion significantly. The experimental scatter of the RMS wave height is shown to be half that of wave steepness during incipient breaking in wave packets.

Master's thesis deals with new methods of preparing catalytic materials for positive electrode of an oxygen-hydrogen fuel cell and the influence of potassium permanganate or doping agent molar mass change on theirs attributes. Further it studies the use of proper measuring methods designed to qualify theirs attributes and the presentation of achieved results. In particular methods of linear sweep and cyclic voltammetry and the processing of data using Koutecky-Levich and Tafel plot and wave log analysis. Values of half-wave and onset potential and kinetic coefficient have been measured and calculated.

AbstractThe ‘blue economy’ embraces more than five million jobs and the gross added value in the second decade of this century is surpassing EUR half a trillion a year. Now when this growth even accelerates in many more sub-sectors the process goes driven in two ways. On one side, a wave of smart specialization strategies at regional and urban level is under way, in many cases incorporating the restorative economy elements. On the other side, changes just happened even without the respective strategies in the blue economy structure and challenge the established sectors. The purpose of this chapter of the book is to identify the main challenges of the smart specialization strategies at urban and regional level incorporating the blue growth elements that are met towards the restorative economy frames. The methods used are a literature and key policy documents review and some secondary data analysis over performed by the European Commission contractor investigation with reference to a project performed in the sector. As a conclusion the recommendation for sectoral specialization of the coastal areas and its cities’ economy in accordance with the innovative potential for blue growth was outlined, with the understanding it might be fragile due to the unsustainable economic activities in the seas.

In this paper, the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 3-D full- and half-space domains will be discussed. First, the fast multipole BEM formulations will be presented and then improvements to the formulations and algorithms will be discussed. Examples with large-scale acoustic BEM models, with the DOFs above 2 millions and solved on desktop PCs, will be presented to demonstrate the potential of the fast multipole BEM for modeling large-scale structural acoustic problems.

Abstract Analytical solutions are formulated for the displacement, stress, and electric potential in piezoelectric actuator and receiver on an elastic half-space. The surface wave is taken into account when the piezoelectric actuator is subjected to the harmonic electric excitation. The derived analytical formulas are used to compute the output potential of piezoelectric receiver. Experiment measurements are performed and compared with numerical results in good agreement. The influence of excitation frequency, material property and dimension of the piezoelectric material is presented.

Ensuring pipeline stability is a fundamental aspect of subsea pipeline design and can contribute a significant proportion of project costs in regions with large diameter trunklines, shallow water and severe geotechnical and metocean conditions [1]. Reducing the conservatism and simplifications of existing pipeline stabilisation design methods therefore offers economic benefits to hydrocarbon producers necessary to ensure the ongoing viability of projects in these regions. To realise this potential and reduce the conservatism of the existing design methods, a more accurate understanding of the hydrodynamic loads exerted by waves and currents is required. This paper investigates one of the inherent assumptions incorporated into the existing design methods through the arrangement of previous experimental investigations to determine whether rectilinear motion provides a reasonable approximation to simulate the near seabed orbital particle paths in wind-generated waves. This assumption is based on the flattening of particle paths to ellipsoids with depth and ignores the small vertical velocity components near the seabed. Based on the hydrodynamic forces calculated numerically using a validated Computational Fluid Dynamics (CFD) model for rectilinear and orbital wave modelling it is concluded that pipeline stabilisation requirements calculated in accordance with the DNV-RP-F109 absolute lateral static stability design method and rectilinear wave motion assumption are conservative. It is also concluded that the hydrodynamic force asymmetry in favour of the reverse half wave cycle caused by the vertical velocity components in orbital wave conditions requires further consideration to determine the implication for dynamic lateral stability design methods.

Wave breaking has different physics from the potential flow wave motion. The roller model introduced by Svendsen [1] illustrates the separation of the wave motion and the roller. The roller propagation speed, therefore, is a very important factor for the energy calculation of the bore. The wave celerity data collected at the wave tank displays that the maximum roller propagation speed occurs when the wave has already decayed due to the breaking. This fact clearly displays that the bore energy cannot be calculated only from the wave height as it is done for non-breaking waves. It is certain that most the energy is dissipated through the roller formation in the outer surfzone, but a certain amount of energy is transferred to the roller at the same time and it accelerates the bore speed. Slow decay of the roller propagation speed indicates that the excess energy left in the roller dissipates in the inner surfzone at much slower rate than in the outer surfzone. Therefore, these two zones have to be clearly separated, but the amount of energy transferred into the roller is unknown. In this paper, we focus on the examination of the peak roller propagation speed that appears at the border of the outer and the inner surfzone by using the experimental data collected at the wave tank. In that way, the initial condition of roller propagation speed can be determined for the inner surfzone. The energy conservation between the wave motion and the roller kinetic energy derives an equation to calculate the roller propagation speed. The energy transfer rate is estimated by adjusting the value given by the full energy conversion with the observed roller propagation speed. It is found that about half of the energy is transferred into the roller. The model successfully illustrates the peak bore propagation speed which existing formulae cannot explain.

This paper reports on analytical and experimental studies of transient effects in electroosmotic (EO) micropumps, focusing on an EO micropump operational paradigm of practical importance: the use of variable-duty-cycle square wave driving voltages. Models of transient effects in EO micropumps are evaluated and developed, and load inertia as well as thermal and diffusion effects are considered. Detailed models, based on solutions for electroosmotic flow between infinite parallel plates, are presented for slit capillary array EO micropumps with slit half-width on the order of one micron. Driving typical microfluidic system loads, analysis by analogy to Stokes' second problem predicts pseudosteady electroosmotic flow in these micropumps for input frequencies up to 100 Hz, with attenuation of high-frequency components of square-wave inputs due to load inertial effects. In experiments with slit capillary array electroosmotic micropumps driven by 10 Hz square waves, micropump output is observed to be generally nonlinear with duty cycle, with significant flow rate enhancement relative to constant-voltage operation at duty cycles above 40%. Lateral diffusion during temporary zero-field conditions may lead to a slight increase in time-averaged zeta potential for square-wave-driven EO micropumps.

Marine construction technologies could be designed to offer power generation in addition to their sea defence and coastal erosion prevention function. This paper aims to evaluate and optimize the performance of an Overtopping Wave Energy Converter (OWEC) as part of a hybrid generation system integrated into an offshore wind turbine. For that purpose, two configurations have been investigated. A 100kW OWEC was combined with a micro-gas turbine of 80kW at the first configuration and the same OWEC with a wind turbine (WT) of 200kW at the second. The preliminary design of an integrated offshore OWEC/WT is presented. The findings of the present investigation have been applied to a specific test case of a small, off–grid island, in the Aegean archipelago. Regarding its power requirement, Donoussa island currently relies exclusively on fossil fuel. At the same time, a high wave and wind power potential is available. A representative set of wind data have been obtained and numerically analyzed. A wave simulation, overtopping prediction and power output has been carried out. Moreover, a techno-economic and environmental assessment of the proposed offshore integrated design is presented. The stand alone coastal OWEC, and a single offshore wind turbine have been evaluated versus the proposed offshore hybrid power generation scheme. The OWEC is expected to generate 320MWh per year, thus covering half of the island’s estimated power demand. Using both wave and wind power generation, energy autonomy of the island could be achieved. In order to cover the requirements of extreme cases, a micro gas-turbine power generation unit has been considered, in parallel to the existing fossil fuel power generation unit. From the techno-economic assessment point of view, the coastal OWEC construction has a shorter return on investment time of 11 years as compared to 13 years of the proposed integrated design but lower profitable investment. Besides providing sufficient electrical power for the island, the additional environmental benefit of the proposed system is that it can be used to counter coastal erosion. The integrated offshore OWEC/WT design could potentially double the power output of each and every offshore wind turbine installation. This result could therefore be interpreted either as halving of the required number of offshore wind turbines erections or as doubling of the power output of an offshore wind park.

Floating fish cages provide the main production utilities for salmon farming. However, despite their pivotal role in production safety as well as in protection of the environment, there is still much room for improvement in relation to verified structural design procedures and computerized tools for structural analysis. To a large extent they can be regarded as not being in accordance with the state-of-the-art of structural analysis and design for more traditional types of marine structures. In this paper a study of fatigue design for floating fish farms is presented. The study is based on a structure which is being applied by the Norwegian fish farming industry today. The floater is made of steel cylinders which are configured as a square. The formulation for the wave loading is based on a combination of potential theory and horizontal drag forces on the floater. Horizontal and vertical drag forces on the netpen are also accounted for. A fatigue design procedure for floating fish farms in steel is suggested. The procedure is based on a time domain analysis of the structure in irregular waves. For each seastate half an hour (real time) analysis is performed and the stress history for an assumed critical location is computed. Based on the stress histories, the fatigue damage is estimated by application of rain flow counting and a given SN curve. The scatter diagram for the seastates at a given location is generated from the associated wind speed distribution.

Abstract The paper introduces a parameterization of the DNV GL storm profile for developing an analytical model for calculations of the return period of a storm whose peak exceeds a given threshold. The DNV GL storm evolution is represented via an isosceles trapezoidal shape in which the minor base represents the storm peak duration, the major base the total storm duration and the height is half of the highest significant wave height in the actual storm. In this representation, the storm duration is not related to the storm intensity and it is fixed constant and equal to 42 hours, while the peak duration is assumed to be 6 hours. The parameterization proposed in the paper consists in expressing the peak duration as a fraction of the total storm duration allowing to investigate the effects of storm peak duration on long term estimates. The analytical solution for the return period is derived by following the classical approach of Equivalent Storm Models that is referring to the equivalent storm sequence, with the only difference that all the Trapezoidal Storm durations are identical whatever the storm intensity is. This assumption leads to significant simplification on the model development and potential employment as well. Further, a closed form solution is achieved for the return period which is also a generalization of the triangular shape. Finally, data analysis with NDBC buoys data is carried out for validating the model and elucidating analogies and differences with respect to classical Equivalent Storm approach. Results have shown that the Trapezoidal Model can be thought as a triangular one with a prudential factor on the storm peak duration which results in a reasonable overestimation of maximum expected wave height and return values.

Concrete railroad ties have been used in increasing numbers in the U.S., particularly in high-speed rail, heavy-haul freight lines, and new track construction because of their reduced deflections, durability, and competitive cost. In-track assessment of concrete railroad ties can be a challenge, however because many exterior tie surfaces are covered by tie pads and rail or ballast. This damage may include concrete section wear from abrasion, cracking, or crumbling, or other types of defects. Damage internal to the concrete can also not be seen visually. The time and cost needed to inspect these tie surfaces means that it is not routinely performed. Non-destructive testing offers promise as a way to assess concrete tie integrity without having to remove ballast, however more information is needed to know how well non-destructive techniques work in detecting damage. Two of the most promising techniques for investigating the integrity of concrete non-destructively are ultrasonic pulse velocity and impact-echo. Ultrasonic pulse velocity (UPV) and Impact-echo (IE) were applied to investigate the uniformity of concrete railroad tie and its cavities, cracks and defects for concrete ties taken from track after service. This paper evaluated the variability of the test results in UPV and IE testing condition in which two concrete railroad ties with same manufacture and load history condition were tested in both methods. Two additional concrete ties with the same manufacture and load history as each other with visible longitudinal cracks were also examined to see how the damage affected the variability measured. For this purpose, wave pulse for every full length tie from full top, half top, longitude and two sides were measured using ultrasonic pulse (ASTM C597). Also, thickness of concrete ties on both sides, including rail seat location and the middle were assessed by standard tests method for measuring the p-wave speed and the thickness of concrete using the impact-echo method (ASTM C1383). Advice is given on how to interpret ultrasonic pulse velocity and impact-echo measurements and given the variability of the test method how to flag ties for potential deterioration given that most ties in service will not have initial measurements taken before damage for comparison.

Abstract Hydrogen has great potential as an alternative fuel for internal combustion engines (ICE) because of its high energy density by mass, high specific heat ratio, free of CO2 and PM emission, and ultra-low NOx emission. In the present paper, a premixed spark-ignition engine fueled by hydrogen was simulated. 3D combustion CFD was employed to simulate and optimize the engine combustion. Parametric studies of equivalence ratio were conducted to identify the appropriate range for practical operation. It was found that higher equivalence ratio in H2ICE is not feasible since it exhibits very high pressure rise rate and strong pressure oscillations. It is due to its much fast flame speed and detonabiltiy. Frequency analysis was conducted on the predicted pressure trace. The dominant frequencies were compared with the first four drum mode. It was found that the dominant resonance frequency corresponds to the drum mode of (0,1). This is due to the fact that the pressure wave originates from the center of combustion chamber. With an equivalence ratio of 0.4, the engine produces similar pressure trace as the baseline gasoline engine, while its close-cycle work is less than half of the gasoline engine, due to low equivalence ratio and hydrogen’s low energy density per unit volume. NOx emission is two order of magnitude lower than the stoichiometric gasoline engine. However, for lean burn PFI H2ICE, N2O emission is much higher than stoichiometric gasoline engine, which needs special attention in the future. Spark timing was swept for the equivalence ratio 0.4 case to further optimize the engine. The mechanisms of NO and N2O formation at different operating conditions are compared and discussed. It was found that NO emission is sensitive to spark timing, while N2O emission is not. The engine-out N2O emission is about one order of magnitude lower than the engine-out NO emission.

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%.