deterministic models
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2022 ◽  
Vol 22 (1) ◽  
pp. 201-222
Éverton Souza Ramos ◽  
Rogério Carrazedo

Abstract This paper presents a numerical study about the effects of chloride-induced corrosion on the service life of structures. A two-dimensional geometrically nonlinear mechanical model based on Finite Element Method (FEM) was developed for reinforced concrete structures. The corrosion initiation stage was evaluated by Fick's diffusion laws. The corrosion propagation was carried out by deterministic models based on Faraday's law. Pitting corrosion was simulated in the reinforcements by pit elements, distributed longitudinally on the steel rebars, which degrade the physical properties over time. The service life was determined by the crack width.Two parametric analyses were performed. In the first analysis, five models were created with a variablecover thickness and water/cement ratio (w/c). In the second analysis, the reduction in yield stress due to corrosion was considered.The results showed that the concrete cover thicknessand the w/c ratio significantly influence the service life. The reduction of the cover thickness from 30 mm to 25 mm resulted in 21.26% reduction in service life, whilethe increase in the w/c ratio from 0.50 to 0.55 caused 32.98% reduction in service life of the structural element analyzed.

2021 ◽  
pp. 143-154
Martin Wight

This essay focuses on the various motives of decision-makers responsible for state policy. While smaller and weaker powers often choose to capitulate to threats, states prepared to use force have been inspired by distinct combinations of motives. These have included winning independence, imposing domination, promoting allegiance to an ideology, gaining economic advantages, and resisting the rise to supremacy of a political-military competitor. Fear of the loss of security and autonomy may lead to preventive war or intervention to maintain a favourable balance of power. While leaders as prominent as Napoleon and Bismarck have referred to deterministic models of causation in some circumstances, ‘the motive of mutual fear’ may predominate. Compared to their important role in medieval litigation, irredentist wars intended to settle legal and territorial claims have become vestigial, but they may be regarded as modern versions of wars for rights.

2021 ◽  
Vol 17 (12) ◽  
pp. e1009713
Jesse Kreger ◽  
Natalia L. Komarova ◽  
Dominik Wodarz

To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, as well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.

Membranes ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 989
Tuan Minh Hoang-Trong ◽  
Aman Ullah ◽  
William Jonathan Lederer ◽  
Mohsin Saleet Jafri

Calcium (Ca2+) plays a central role in the excitation and contraction of cardiac myocytes. Experiments have indicated that calcium release is stochastic and regulated locally suggesting the possibility of spatially heterogeneous calcium levels in the cells. This spatial heterogeneity might be important in mediating different signaling pathways. During more than 50 years of computational cell biology, the computational models have been advanced to incorporate more ionic currents, going from deterministic models to stochastic models. While periodic increases in cytoplasmic Ca2+ concentration drive cardiac contraction, aberrant Ca2+ release can underly cardiac arrhythmia. However, the study of the spatial role of calcium ions has been limited due to the computational expense of using a three-dimensional stochastic computational model. In this paper, we introduce a three-dimensional stochastic computational model for rat ventricular myocytes at the whole-cell level that incorporate detailed calcium dynamics, with (1) non-uniform release site placement, (2) non-uniform membrane ionic currents and membrane buffers, (3) stochastic calcium-leak dynamics and (4) non-junctional or rogue ryanodine receptors. The model simulates spark-induced spark activation and spark-induced Ca2+ wave initiation and propagation that occur under conditions of calcium overload at the closed-cell condition, but not when Ca2+ levels are normal. This is considered important since the presence of Ca2+ waves contribute to the activation of arrhythmogenic currents.

2021 ◽  
Vol 48 (2) ◽  
pp. 257-272

ABSTRACT. The paper presents a state-of-art review of different objective techniques available for tropical cyclone track prediction. A brief description of current theories of tropical cyclone motion is given. Deterministic models with statistical and dynamical methods have been discussed. Recent advances in the understanding of cyclone structure and motion aspects have led to improved prediction of tropical cyclones. There has been considerable progress in the field of prediction by dynamical methods. High resolution Limited Area Models (LAM) as well as Global Circulation Models (GCM) are now being used extensively by most of the leading operational numerical weather prediction (NWP) centres in the world The major achievements towards improvement of such models have come from improved horizontal resolution of the models, inclusion of physical processes, use of synthetic and other non-conventional data in the data assimilation schemes and nudging method for initial matching of analysed cyclone centres with corresponding observations. A brief description of further improvement in deterministic approach for prediction of tropical cyclone tracks is outlined.  

2021 ◽  
Vol 24 (4) ◽  
pp. 382-390
Roshmi Das ◽  
Ashis Kumar Sarkar

We have proposed here two deterministic models of Jatropha Curcas plant and Whitefly that simulate the dynamics of interaction between them where the distribution of Whitefly on plant follows Poisson distribution.In the first model growth rate of the plant is assumed to be in logistic form whereas in the second model it is taken as exponential form. The attack pattern and the growth of the whitefly are assumed as Holling type II function.The first model results a globally stable state and in the second one we find a globally attracting steady state for some parameter values,and a stable limit cycle for some other parameter values. It is also shown that there exist Hopf bifurcation with respect to some parameter values. The paper also discusses the question about persistence and permanence of the model. It is found that the specific growth rate of both the population and attack pattern of the whitefly governs the dynamics of both the models.

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3122
Shah Hussain ◽  
Elissa Nadia Madi ◽  
Hasib Khan ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  

In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ1,σ2 and β1,β2, and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19.

2021 ◽  
Vol 68 (4) ◽  
pp. 699-712
R. RAKHI ◽  

Forecasting of heavy rainfall events is still a challenge even for the most advanced state-of-art high resolution NWP modelling systems. Very often the models fail to accurately predict the track and movement of the low pressure systems leading to large spatial errors in the predicted rain. Quantification of errors in forecast rainfall location and amounts is important for forecasters (to choose a forecast and interpret) and modelers for monitoring the impact of changes and improvements in model physics and dynamics configurations. This study aims to quantify and summarize errors in rainfall forecast for heavy rains associated with a Bay of Bengal (BOB) low pressure systems. The verification analysis is based on three heavy rain events during June to September (JJAS) 2015. The performance of the three deterministic models, NCMRWF’s Global Forecast Systems (NGFS), NCMRWF’s Unified Model (NCUM) and Australian Community Climate and Earth-System Simulator – Global (ACCESS-G) in predicting these heavy rainfall events has been analysed. In addition to standard verification metrics like RMSE, ETS, POD and HK Score, this paper also uses new family of scores like EDS (Extreme Dependency Score), EDI (Extremal Dependence Index) and Symmetric EDI with special emphasis on verification of extreme rainfall to bring out the relative performance of the models for these three rainfall events. The results indicate that Unified modeling framework in NCUM and ACCESS-G by and large performs better than NGFS in rainfall forecasts over India specially at higher lead times. Relatively improved skill in NCUM forecasts can be attributed to (i) improved resolution (~17 km) and (ii) END Game dynamics of NCUM.

2021 ◽  
Vol 11 (1) ◽  
Sigurd Einum ◽  
Claus Bech ◽  
Øystein Nordeide Kielland

AbstractIn ectotherms, adult body size commonly declines with increasing environmental temperature, a pattern known as the temperature-size rule. One influential hypothesis explaining this observation is that the challenge of obtaining sufficient oxygen to support metabolism becomes greater with increasing body size, and more so at high temperatures. Yet, previous models based on this hypothesis do not account for phenotypic plasticity in the physiology of organisms that counteracts oxygen limitation at high temperature. Here, we model the predicted strength of the temperature-size response using estimates of how both the oxygen supply and demand is affected by temperature when allowing for phenotypic plasticity in the aquatic ectotherm Daphnia magna. Our predictions remain highly inconsistent with empirical temperature-size responses, with the prior being close to one order of magnitude stronger than the latter. These results fail to provide quantitative support for the hypothesis that oxygen limitation drives temperature-size clines in aquatic ectotherms. Future studies into the role of oxygen limitation should address how the strength of the temperature-size response may be shaped by evolution under fluctuating temperature regimes. Finally, our results caution against applying deterministic models based on the oxygen limitation hypothesis when predicting future changes in ectotherm size distributions under climate change.

2021 ◽  
Vol 7 (167) ◽  
pp. 14-17
V. Kostyuk

The article considers the method of modeling and factor analysis of the final production result of the enterprise – the volume of production. It is proposed to use deterministic models in the factor analysis of this indicator, which contain the set of factors that reflect the size and efficiency of use of the production areas of the enterprise. The article emphasizes that in the market economy, factor analysis is the important and effective basis for justifying management decisions. The main task of such analysis is the systematic and comprehensive study of the production activities of the enterprise in order to objectively assess the achieved results and establish real ways to further improve its efficiency. Taking this into account, the study of theoretical approaches to the performance of the factor analysis of the efficiency of using the production areas of the enterprise, that is, determining the quantitative influence of factors on the volume of production, is gaining relevance. To study the impact of these factors on the change of this indicator, it is proposed to conduct the step-by-step factor analysis, the essence of which is that the calculation of the impact on the change of the analyzed indicator is first two factors, then three and so on. This allows in each case to calculate the impact on the change of the studied indicator only the factors that are currently the most significant and relevant. The method of factor analysis of production volume given in the article gives the chance to define influence on its change of the most important factors reflecting the sizes and efficiency of use of the industrial areas occupied by the enterprise, to investigate patterns of such influence, to use this information at substantiation of administrative decisions.

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