Academic literature on the topic 'Entropy production rate'

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

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As leis de balanço expressam de uma maneira mais geral as leis de conservação e, portanto, é natural que coincidam em algumas definições ou resultados que vamos mostrar aqui. Um sistema de leis de conservação estritamente hiperbólico numa dimensão espacial sob certas condições é um sistema simetrizável, portanto, possui uma entropia convexa. Isto induz a definiroparentropia-fluxodeentropiaeaproduçãodeentropia,ingredientesmínimospara usar o critério de admissibilidade da taxa de entropia e conferir se a solução do problema de Riemann respectivo é ótimo. A taxa de entropia definida aqui em termos da entropia é um funcional que pode ser minimizada nos leques de ondas com estados constantes do problema de Riemann, usando as equações de Euler-Lagrange. Primeiramente, mostramos que as soluções do problema de Riemann são funções de variação limitada, resultando num método variacional para resolver o problema. Neste trabalho será mostrado que a solução obtida pelo método variacional, coincide com a solução obtida pelo método das curvas caraterísticas.
The balance laws express in a more general way the conservation laws and therefore it is naturalthattheycoincideinsomedefinitionsorresultsthatwewillshowhere. Thestrictly hyperbolic systems of conservation laws in a spatial dimension under certain conditions is a symmetrizable system, therefore it has a convex entropy. This induces to define the entropy-entropy flux pair and the entropy production, minimum ingredients to use the Entropy rate admissibility criterion and check whether the solution of the respective Riemann problem is optimal. The entropy rate defined here in terms of entropy is a functional that can be minimized in the wave fans with constant states of the Riemann problem using the Euler-Lagrange equations, we show that the solutions of the Riemann problem are functions of bounded variation, resulting in a variational method to solve the respective problem. In this work it will be shown that the solution obtained by the variational method, coincides with the solution obtained by the method of characteristics.

In questa tesi tratteremo il problema di costruire una teoria termodinamica per trasformazioni su un sistema passante per stati di non-equilibrio. Cercando di generalizzare a sistemi che non sono all’equilibrio, rilasseremo la richiesta che siano in equilibrio globalmente. Lo stato termodinamico sarà univocamente determinato da un insieme di parametri termodinamici definiti localmente, della stessa natura e significato fisico dei parametri usati nella termodinamica classica. Le molteplici assunzioni necessarie al fine di avere una teoria mesoscopica comunque predittiva verranno giustificate a posteriori, quando possibile, in base alle predizioni che da tale modello nasceranno. In particolare ci concentreremo sugli effetti termoelettrici di Thompson, Seebeck e Peltier, esempi storici di grande rilevanza nel campo della termodinamica del non-equilibrio.

This thesis consists of three parts: The first and second parts focus on long-time asymptotics of macroscopic and kinetic models respectively, while in the third part we connect these regimes using different scaling approaches. (1) Keller–Segel-type aggregation-diffusion equations: We study a Keller–Segel-type model with non-linear power-law diffusion and non-local particle interaction: Does the system admit equilibria? If yes, are they unique? Which solutions converge to them? Can we determine an explicit rate of convergence? To answer these questions, we make use of the special gradient flow structure of the equation and its associated free energy functional for which the overall convexity properties are not known. Special cases of this family of models have been investigated in previous works, and this part of the thesis represents a contribution towards a complete characterisation of the asymptotic behaviour of solutions. (2) Hypocoercivity techniques for a fibre lay-down model: We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in non-woven textile production. Further, we prove convergence to equilibrium with an explicit rate. This part of the thesis is an extension of previous work which considered the case of a stationary conveyor belt. Adding the movement of the belt, the global equilibrium state is not known explicitly and a more general hypocoercivity estimate is needed. Although we focus here on a particular application, this approach can be used for any equation with a similar structure as long as it can be understood as a certain perturbation of a system for which the global Gibbs state is known. (3) Scaling approaches for collective animal behaviour models: We study the multi-scale aspects of self-organised biological aggregations using various scaling techniques. Not many previous studies investigate how the dynamics of the initial models are preserved via these scalings. Firstly, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local kinetic 1D and 2D models to simpler models existing in the literature. Secondly, we investigate how some of the kinetic spatio-temporal patterns are preserved via these scalings using asymptotic preserving numerical methods.

In this thesis, we aim to create a framework for the derivation of thermodynamically consistent anisotropic viscoelastic models. As an example we propose simple models extending the isotropic Oldroyd-B and Giesekus models to illustrate the models' behavior and the process of finding the correct equations. We show what behavior in sheer we can expect and continue with a 3D simulation inspired by the experiment on a real liquid crystal mixture. Finally, we compare the simulation and the experiment to find similarities and possible further research topics.

A situation of turbulent peace is defined as an ambiguous transition from direct violence (which ends by means a fragile and incomplete peace agreement among enemies) to an indirect and subtle violence euphemistically denominated as progress. Indeed, a big rate of economic growth implies growing prosperity, incremented consumption, and increasing investment in the present but, sadly, the consequence of this material progress will be the suffering of future generations because the exhaustion and deterioration of nature in a world where the entropy is worsened by the rapacity of actual generations. The depletion and contamination of natural resources is the inherent cost of material progress and development of “productive” forces. The ideological, coercive and economic power of some organized minorities, and the acquiescence of a big majority of human beings constitutes the root of this problem. The antidote against this power is the critical examination of values by active citizens and the guide of ethics. In the long run this problem can be solved promoting a nonviolent economy.

The work is devoted to the study of the influence of changes in the acid-base state on the indices of mineral metabolism in the body of cadmium sulphate-poisoned 6 months age-rats. It is known that the entry of cadmium salts into the body causes disorders of protein, lipid, carbohydrate, and mineral metabolism. As well-known, the endotoxicants affect cellular structures and activate lysosomal enzymes, block mitochondrial oxidation and ribosomal synthesis, initiate free radical processes, that are accompanied by disturbance of rheology and blood coagulation, micro- and macro-circulation, water-electrolyte balance. Such caused alterations in macro- and microelement composition of poisoned animals’ organisms disrupt the course of numerous metabolic processes. The research was conducted on the basis of the Department of Biochemistry and Vivarium of the National University of Life and Environmental Sciences of Ukraine using adult 6 months-age outbred rats breeding of the Research and Production Center of Laboratory Animal Husbandry of Educational and Scientific Institute of Veterinary Medicine and Quality and Safety of Livestock Products. Biological models of introduction of rats into the state of experimental metabolic acidosis and alkalosis before and after cadmium sulphate poisoning have been developed, as well as indices of acid-base status and mineral metabolism of the developed experimental models have been studied. The influence of the changes of parameters of acid-base state of the body on the content in the blood of poisoned rats of macronutrients (sodium, potassium, calcium, magnesium, inorganic phosphorus) and trace elements (copper, zinc, and iron). At compare of the changes in parameters of acid-base status of the blood of cadmium sulfate-poisoned animals, it was noted that the state of experimental metabolic acidosis is more expressed than alkalosis, that is more effective for correction and normalization of mineral metabolism in poisoned rats.

Viruses are obligate intracellular pathogens that utilize many of the host metabolic machineries for reproduction. Unlike the binary fission of bacteria, the replication process of viruses is more like a production line with a final assembly process to produce their progenies. Any agents used to prevent viral replication must be specific to the virus and cause as little problem for the host as possible. The rate of virus replication can also cause problems. In rapidly reproducing viruses, the high replication rate generates mutants that could be selected for resistance to antivirals. On the other hand, viruses could remain latent with little metabolic activity. None of the current antivirals are effective against latent viruses. The life cycle of a typical virus goes through the following stages: ● Attachment; ● Entry and uncoating; ● Replication of viral nucleic acid; ● Establishing latency or persistent infection (in some viruses); ● Translation of viral protein and post-translational modifications; ● Secretion and assembly of viral particles; and ● Release from host cells. Each of these steps can be used as antiviral targets. The most common strategy is to use a nucleoside analogue as a false substrate. However, such a false substrate can also be taken up by host polymerase and could result in toxicity, e.g. mitochondrial toxicity in some of the earlier antiretroviral drugs. The most successful example to circumvent this problem is aciclovir, which is the prodrug of the active agent aciclovir tri-phosphate. Aciclovir is a substrate for the viral enzyme thymidine kinase carried by the herpes simplex virus (HSV) and varicella-zoster virus (VZV), which converts it into aciclovir monophosphate. As this only happens inside cells infected by HSV or VZV, it is concentrated only in infected cells. Host enzymes then add further phosphates to form the active agent aciclovir triphosphate, which has a higher affinity to viral polymerase than host polymerase. It acts as a false substrate for the viral polymerase and results in premature termination of nucleic acid replication. A similar mechanism is utilized in ganciclovir against cytomegalovirus (CMV). The viral phosphate kinase involved in the case of CMV is the UL97 protein.

Postoperative complications in the anterior chamber can affect both glaucoma progression and vision. Preoperative considerations and surgical technique are important to reduce and prevent these complications. A flat anterior chamber is one of the most common complications following tube shunt surgery, occurring at a rate of 3.5%– 27%. Although often associated with hypotony and choroidal effusions and usually due to increased outflow after surgery, it may also be related to decreased aqueous production, especially in eyes with previous ciliary body ablation. Increased outflow could result from leakage around the tube or overfiltration either before fibrous capsule formation over the plate or through tube fenestrations. Diagnosis of the cause of hypotony can be made with a careful slit-lamp examination. Leakage around the tube can be viewed internally by gonioscopy, though a flat or shallow anterior chamber can make seeing potential leakage difficult. The location of overfiltration can be determined by looking at areas of conjunctival elevation. Conjunctival bleb formation at the limbus could help identify leakage around the tube at its scleral tunnel insertion. Early elevation of a bleb over the reservoir of a tube shunt is also seen with incomplete occlusion in the nonvalved (or sometimes valved) tube. Elevation near the tube-plate junction could also indicate overflow at a fenestration but is unusual. Intracameral irrigation of fluorescein can help identify the source of leakage. A flat anterior chamber associated with hypotony can have serious sequelae, including corneal edema, cataract, and failure of the procedure. Medical treatment to deepen the anterior chamber with cycloplegics and reduction of wound healing inhibitors should be tried first but is often insufficient, as this treatment will not quickly eliminate the source of leakage. More aggressive intervention will be needed if there is central flattening (Grade 2 or 3 flat chamber). Identifying the source of leakage is important in determining management. If there is leakage at the site of the tube’s entry into the sclera, viscoelastic may be needed to fill the anterior chamber. Air injection is an alternative that allows for continued visualization of the leak if desired.

Scene 1: Entry to a classroom building. With a deafening noise he revved up the two-cycle engine on a blower preparing to clean the leaves, paper, and cigarette butts that had accumulated in the entryway. He made considerable progress herding the debris away from the building and down the sidewalk until cigarette butts lodged in the seams in the concrete. Turning, he blasted the miscreant trash at right angles, but this only blew the debris onto the grass, posing still greater difficulties. Moving cigarette butts and bits of paper in an orderly fashion through grass is a challenge, even for a machine capable of generating gale-force winds. Then the apparatus stalled out—“down time,” it’s called. In that moment of sweet silence, I walked over and inquired whether he thought a broom or rake might do as well. “What’d you say?” he responded. “Can’t hear anything, my ears are still ringing!” I repeated the question. “S’pose so,” he said, “but they think I’m more productive with this piece of *&!@.” Perhaps he is more productive. I do not know how experts calculate efficiency in complex cases like this. If, however, the goal is to disrupt public serenity, burn scarce fossil fuels, create a large amount of blue smoke, damage lung tissue, purchase expensive and failureprone equipment, frazzle nerves, interrupt conversations, and improve the market for hearing aids, rakes and brooms cannot compete. When the technology and the task at hand are poorly matched, however, there is no real efficiency. In such cases the result, in Amory Lovins’s telling phrase, is rather like “cutting butter with a chain saw.” Scene 2: Committee meeting. I once served on what is called with some extravagance the Educational Plans and Policies Committee. It is a committee to which one is elected, or sentenced, depending on your view. In one meeting we were casually asked to pronounce our blessing on a plan to link the entire campus so that everyone would be able to communicate with everyone else via computer, 24 hours a day, without leaving dormitory rooms or offices. This, we were told, was what our competitor colleges were doing. We were assured that this was the future.

In order to study analytically the nature of the size separation in granular mixture, we present the maximum entropy production principle based on kinetic temperature of granular mixture. For simplicity we apply this principle to size separation of a sphere binary mixture in vibrated bed, and we find a new thermodynamic mechanism of size separation phenomenon. With the irreversible processes such as elastic collisions and frictions, the kinetic energy is dissipated rapidly in system, which induces the entropy production. By the fact that the entropy production rate always has the absolute maximum at the stable state of granular mixture, we find the crossover from “Brazil Nut Effect” to its reverse by changing particles size and density, and our result is about satisfied with Schnautz’s experiment.

In this paper hot wire measurements of the boundary layer velocity profiles at discrete locations along the suction surface of a turbine blade profile are presented. The measured aerodynamic data is transformed into thermodynamic data by way of the entropy function for the investigated Reynolds numbers of 76,000, 120,000 and 185,000 based on inlet velocity and chord length. The measurements are compared with predictions obtained from a commercially available computational fluid dynamics code and a prediction technique based on semi-empirical correlations. Interestingly the accuracy of the relatively simple semi-empirical technique, in respect to entropy production, is found to be comparable to that of the time consuming CFD code over the range of Reynolds numbers tested.

A numerical model is developed to examine the flow conditions of multiphase heat transfer and entropy production during hydrate formation in subsea pipelines. The temperature and pressure gradients of the oil and gas flow in subsea pipelines lead to entropy generation. This paper examines the impacts and effects of thermodynamic irreversibilities on the nucleation and growth processes of hydrate crystals in the pipeline flows. The effects of heat transfer ratio, internal diameter of the pipe, molar gas density, and environment temperature on entropy production in subsea pipelines are predicted and discussed in this paper. The numerical model accounts for the temperature distribution along the axial length of the pipe, reaction kinetics, and mass transfer between the solid and fluid layer. The kinetic energy of the hydrate particles during the coagulation process is analyzed in the numerical model. The results indicate that entropy production is highest at the beginning of the nucleation process. Pipelines with smaller internal radii have a lower rate of hydrate formation in subsea pipelines. The results from the numerical model are verified by comparison with experimental results for structure type II natural gas hydrates.

A T-junction structure is common in nuclear reactor systems, and plays an essential role in safety operation. An accurate estimation of the resistance characteristics of a T-junction is important for both energy conservation and engineering design. In the current study, the concept of the head loss coefficient K for a local structure was proposed, and its thermodynamic definition is extended to laminar flow within a T-junction by an entropy production approach, which was initially for turbulent flows. Specific numbers of K was determined by integration of the entropy generation rate obtained from a numerical simulation. In addition, the correlation between K and Re of combining and dividing flows was also derived.

In the present work, an analytical expression for entropy generation production for mono-dispersed stream of droplets impacted on the upward heated surface at critical heat flux regime was found. The expression involving the relevant parameters for entropy production contributed to the heat transfer and the entropy flux due to the phase change and the spreading process. The influence of impact velocity and flow rate on entropy generation was explored.

The principle of minimum entropy production has played an important role in the development of non-equilibrium thermodynamics. Inspired by this principle, Bejan derived the expression of the local entropy production rate for heat convection and established the entropy production minimization approach for the heat exchanger optimization design. Although one can obtain the entropy production distribution in the heat exchanger numerically, it can not directly been employed to examine the heat exchanger performance. Tondeur and Kvaalen found that the entropy production uniformity is closely related to the heat exchanger performance. In the present work, based on Tondear and Kvaalen’s work, an entropy production uniformity factor is defined, which quantifies the uniformity of the local entropy generation distribution in heat exchanger. Numerical results of the heat transfer in a rectangular channel show that the larger entropy production uniformity factor implies less irreversible loses. Therefore, this factor can serve as a thermodynamic figure of merit for assessing the heat exchanger performance.

An investigation of the transient entropy property term, entropy storage, for a desalination device was performed. It was illustrated that entropy production rates provide a means of comparing alternative energy solutions and a measure of their sustainability. To satisfy these objectives one needs accurate calculation of entropy production rates. It was confirmed that neglecting the exergy storage term is not a valid approximation for the hourly and daily averaged values of the second law analysis. For a solar desalination system neglecting the exergy storage terms introduced a maximum difference in the entropy production rate of 7.4% and a difference of 7.3% in the daily average. In the solar desalination process with heat recovery the second law performance is greater than that for the reverse osmosis process, the chief competitor, when the exergy storage terms are correctly included in the analysis. The results demonstrate that for variable energy sources such as renewable energy systems, the second law analysis provides a measure of the sustainability of competing system and that the exergy storage terms should be included in the analysis.

The problem of determining the optimal configuration of a cooled gas-turbine blade is approached by an entropy minimization technique proposed in previous works by the same authors. The present paper describes the application of the same line of thought to a more complex (and realistic) pseudo-optimization procedure, in which the objective function is again the global entropy generation rate, but two integral constraints are added to the original formulation: the maximum blade temperature (weak constraint) and the overall enthalpy drop of the working fluid in the blade passage (strong constraint). The discontinuous optimization procedure is presented here in an application which resembles a trial-and-error technique, but can be rigorously and formally described and implemented [12]. As a “zero configuration”, a realistic 2-D geometry is considered, and the thermo-fluiddynamic field around it is computed via a standard finite-element code. Then, the entropy generation rates in the blade/fluid system are calculated, and the value of the overall enthalpy drop of the gas as well as the value and location of the maximum blade temperature are recorded. Keeping all other parameters fixed (in particular, maintaining the same cooling air flowrate), the geometry of the blade is slightly “perturbed”, by introducing arbitrary modifications in the blade profile, the number and location of cooling holes, etc. Again, the velocity and temperature fields are computed, and inlet conditions are tuned so that the overall enthalpy drop remains approximately constant and the blade maximum temperature does not exceed a certain assigned value. An “optimal” configuration is found, which is affected by the minimal entropy generation rate, while abiding to the imposed constraints. The procedure is demonstrated on a realistic blade profile, and is shown to produce a better performing cascade, at least in this 2-D simulation. The extension to 3-D problems is — in principle — straightforward (but see Section 3 for further comments).

The principle of minimum entropy production is applied to the analysis of the formation of a solid structure in the course of the eutectic solidification. It is assumed that the liquid and solid phases are divided by the plane boundary and the solidification rate is constant. At these conditions solidification results in the development of the lamellar structure in the solid and the process is defined by the lamellar spacing and the rate of the motion of the liquid-solid interface. The variational equation describing system evolution is modified to describe the process in question. A solution of this equation determines the relationship between the solidification rate and the lamellar spacing. The obtained results complies with experimental data.

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%.