Numerical Analysis of Chemical Reactions by Monte Carlo Simulation

Добри Данков, Владимир Русинов, Мария Велинова, Жасмина Петрова - Изследвана е химическа реакция чрез два начина за моделиране на вероятността за химическа реакция използвайки Direct Simulation Monte Carlo метод. Изследван е порядъка на разликите при температурите и концентрациите чрез тези начини. Когато активността на химическата реакция намалява, намаляват и разликите между концентрациите и температурите получени по двата начина. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Parallel Algorithm for the Local Variations Method

Димитър С. Илиев, Станимир Д. Илиев - Актуално е изследването на поведението на течен менискус в околността на хетерогенна стена. До сега няма получено числено решение за формата на менискуса около стена, която е с хаотична хетерогенност. В настоящата статия е разработен алгоритъм за метода на локалните вариации, който може да се използва на многопроцесорни системи. С този метод е получен за първи път профила на равновесен течен менискус около вертикална стена с хаотична хетерогенност.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Comparison between Numerical and Simulation Methods for Age-dependent Branching Models with Immigration

2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

Comparison of numerical bit error rate estimation methods in 112Gbs QPSK CO-OFDM transmission

We demonstrate an accurate BER estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. Using a 112Gbs QPSK CO-OFDM transmission as an example, we show that this method offers the most accurate estimate of the system's performance in comparison with other known approaches.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

When is an image a health claim? A false-recollection method to detect implicit inferences about products' health benefits

Objective: Images on food and dietary supplement packaging might lead people to infer (appropriately or inappropriately) certain health benefits of those products. Research on this issue largely involves direct questions, which could (a) elicit inferences that would not be made unprompted, and (b) fail to capture inferences made implicitly. Using a novel memory-based method, in the present research, we explored whether packaging imagery elicits health inferences without prompting, and the extent to which these inferences are made implicitly. Method: In 3 experiments, participants saw fictional product packages accompanied by written claims. Some packages contained an image that implied a health-related function (e.g., a brain), and some contained no image. Participants studied these packages and claims, and subsequently their memory for seen and unseen claims were tested. Results: When a health image was featured on a package, participants often subsequently recognized health claims that—despite being implied by the image—were not truly presented. In Experiment 2, these recognition errors persisted despite an explicit warning against treating the images as informative. In Experiment 3, these findings were replicated in a large consumer sample from 5 European countries, and with a cued-recall test. Conclusion: These findings confirm that images can act as health claims, by leading people to infer health benefits without prompting. These inferences appear often to be implicit, and could therefore be highly pervasive. The data underscore the importance of regulating imagery on product packaging; memory-based methods represent innovative ways to measure how leading (or misleading) specific images can be. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

A method of fundamental solutions for theaxisymmetric backward heat equation

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

A method for solving LSM problems of small size in the AHP

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. It provides with ratio-scale measurements of the prioirities of elements on the various leveles of a hierarchy. These priorities are obtained through the pairwise comparisons of elements on one level with reference to each element on the immediate higher level. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM), Logarithmic Least Squares Method (LLSM), Weighted Least Squares Method (WLSM) and Chi Squares Method (X2M) are of the tools for computing the priorities of the alternatives. This paper studies a method for generating all the solutions of the LSM problems for 3 × 3 matrices. We observe non-uniqueness and rank reversals by presenting numerical results.

Solution of the Least Squares Method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.

Numerical investigation on the heat transfer enhancement using micro/nano phase-change particulate flow

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. ^ A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re = 90–600 and phase change material particle concentrations of ϵp ≤ 0.25, as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (ϵp = 50%–70%) slurry flow. By using the two newly-defined parameters, named effectiveness factor ϵeff and performance index PI, respectively, it is found that there exists an optimal relation between the channel design parameters L and D, particle volume fraction ϵp, Reynolds number Re, and the wall heat flux qw. The influence of the particle volume fraction ϵp, particle size dp, and the particle viscosity μ p, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. ^ To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed. ^

Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.

Quantifying the effects of temperature and concentration on variable-density flow in numerical modeling of groundwater systems: Implications for predictive uncertainty and data collection

Groundwater systems of different densities are often mathematically modeled to understand and predict environmental behavior such as seawater intrusion or submarine groundwater discharge. Additional data collection may be justified if it will cost-effectively aid in reducing the uncertainty of a model's prediction. The collection of salinity, as well as, temperature data could aid in reducing predictive uncertainty in a variable-density model. However, before numerical models can be created, rigorous testing of the modeling code needs to be completed. This research documents the benchmark testing of a new modeling code, SEAWAT Version 4. The benchmark problems include various combinations of density-dependent flow resulting from variations in concentration and temperature. The verified code, SEAWAT, was then applied to two different hydrological analyses to explore the capacity of a variable-density model to guide data collection. ^ The first analysis tested a linear method to guide data collection by quantifying the contribution of different data types and locations toward reducing predictive uncertainty in a nonlinear variable-density flow and transport model. The relative contributions of temperature and concentration measurements, at different locations within a simulated carbonate platform, for predicting movement of the saltwater interface were assessed. Results from the method showed that concentration data had greater worth than temperature data in reducing predictive uncertainty in this case. Results also indicated that a linear method could be used to quantify data worth in a nonlinear model. ^ The second hydrological analysis utilized a model to identify the transient response of the salinity, temperature, age, and amount of submarine groundwater discharge to changes in tidal ocean stage, seasonal temperature variations, and different types of geology. The model was compared to multiple kinds of data to (1) calibrate and verify the model, and (2) explore the potential for the model to be used to guide the collection of data using techniques such as electromagnetic resistivity, thermal imagery, and seepage meters. Results indicated that the model can be used to give insight to submarine groundwater discharge and be used to guide data collection. ^