Applications of thermodynamics to study the physical phenomenon of heat conduction

Thermodynamics can be understood as the discipline of the physical sciences, that studies theoretically and practically the different manifestations of energy. The study of thermodynamics is important in relation to the understanding of thermal systems in industry, as well as, supporting energetic processes in living organisms. In relation to the study of energy processes in the context of heat transfer, concepts from thermodynamics are relevant. In the present investigation, the process of heat conduction in a metal bar is analyzed by applying the heat equation and the concept of entropy variation. The first part of the research proposes a numerical method to solve the heat equation in addition to a set of finite difference equations describing the energetic behavior of the system. The numerical solution of the heat equation and the thermodynamic behavior of the system are studied by programming to demonstrate the fit of the results with the theoretical models. Finally, applications of the achieved results in engineering contexts are discussed.

Dynamics of the E-Waste Behavior Globally

Objective: To demonstrate the implications of the growth of e-waste, within the traditional conception of the Linear Economy, over time, and to deduce the potential reaction of society, by defining the model of its time of impatience. <br/> Method: For the development of the research, the logistic model of differential equations (Verhulst, 1838) and a theoretical model of finite difference equations associated with an empirical model of log-linear regression were used to analyze the growth prospects of e-waste, over time, when technological advances are estimated, as well as the potential reaction of society.<br/> Main results: The results show that there is a point of impatience in society that can be measured, as long as the specificities of each type of e-waste are known; and that the volume of e-waste grows exponentially over time, being influenced, in part, by the evolution of technology, considering the electronic products made available to society as a proxy, which is driven to consume, among other motivations, by functional obsolescence.<br/> Relevance/Originality: The results are important because they indicate that if there are no more rigid, efficient and effective regulatory measures, and if there is no paradigm shift in the production system, from extraction to final destination, there is likely to be a collapse in drainage systems, treatment and final disposal of e-waste on a global scale, with severe consequences for ecosystems, health, economic and social systems, greatly increasing our ecological footprint, thereby threatening the maintenance of life on Earth.<br/> Theoretical/methodological contributions: The study contributes to the understanding of the behavior of e-waste and the influence of technology on its growth, as well as to the logical deduction of the society's point of impatience regarding the use of the materials that generate e-waste, reinforcing the originality of the research and promoting a deeper understanding of the topic.

Direct steady-state solutions for circuit models of nonlinear electromagnetic devices

Purpose This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models. Design/methodology/approach Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only. Findings An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain. Research limitations/implications Reduction of software and hardware requirements for determining steady-states of electromagnetic. Practical implications A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form. Originality/value Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models.

Block algorithms to solve Zheng/Chen/Zhang's finite-difference equations

This paper is devoted to the design of multiblock algorithms of the FDTD-method intended for computations based on a Zheng-Chen-Zhang implicit finite-difference scheme. Special emphasis is placed on experimental research of the designed algorithms and detecting specific features of the multiblock computing based on implicit finite-difference equations. The efficiency of the proposed approaches is proved by a six-fold speed-up of computations.

Strayfield calculation for micromagnetic simulations using true periodic boundary conditions

We present methods for calculating the strayfield in finite element and finite difference micromagnetic simulations using true periodic boundary conditions. In contrast to pseudo periodic boundary conditions, which are widely used in micromagnetic codes, the presented methods eliminate the shape anisotropy originating from the outer boundary. This is a crucial feature when studying the influence of the microstructure on the performance of composite materials, which is demonstrated by hysteresis calculations of soft magnetic structures that are operated in a closed magnetic loop configuration. The applied differential formulation is perfectly suited for the application of true periodic boundary conditions. The finite difference equations can be solved by a highly efficient Fast Fourier Transform method.

On the Discrete Version of the Schwarzschild Problem

We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge lengths. This elementary length scale is defined by the Planck scale and some free parameter of such a quantum extension of the theory. Besides, Regge action was reduced to an expansion over metric variations between the tetrahedra and, in the main approximation, is a finite-difference form of the Hilbert–Einstein action. Using for the Schwarzschild problem a priori general non-spherically symmetrical ansatz, we get finite-difference equations for its discrete version. This defines a solution which at large distances is close to the continuum Schwarzschild geometry, and the metric and effective curvature at the center are cut off at the elementary length scale. Slow rotation can also be taken into account (Lense–Thirring-like metric). Thus, we get a general approach to the classical background in the quantum framework in zero order: it is an optimal starting point for the perturbative expansion of the theory, finite-difference equations are classical, and the elementary length scale has quantum origin. Singularities, if any, are resolved.

GPU COMPUTING FOR 2D WAVE EQUATION BASED ON IMPLICIT FINITE DIFFERENCE SCHEMES

In this paper we will consider the numerical implementation of the 2d wave equation which is a fundamental equation in many engineering problems. An approximate solution of a function is calculated from discrete points in spatial grid based on discrete time steps. The initial values are given by the initial value condition. First we will interpret how to transform a differential equation into an implicit finitedifference equation, respectively, a set of finite-difference equations that can be used to calculate an approximate solution. Then we will change this algorithm to parallelize this task on GPU. Special focus is on improving the performance of the parallel algorithm. In addition, we will run the implemented parallel code on the GPU and serial code the central processor, calculate the acceleration based on the execution time. We present that the parallel code that runs on a GPU gives the expected results by comparing our results to those obtained by running serial code of the same simulation on the CPU. In fact, in some cases, simulations on the GPU are found to run 22 times faster than on a CPU

Quantifying Inaccuracies in Modeling COVID-19 Pandemic within a Continuous Time Picture

Typically, mathematical simulation studies on COVID-19 pandemic forecasting are based on deterministic differential equations which assume that both the number (n) of individuals in various epidemiological classes and the time (t) on which they depend are quantities that vary continuous. This picture contrasts with the discrete representation of n and t underlying the real epidemiological data reported in terms daily numbers of infection cases, for which a description based on finite difference equations would be more adequate. Adopting a logistic growth framework, in this paper we present a quantitative analysis of the errors introduced by the continuous time description. This analysis reveals that, although the height of the epidemiological curve maximum is essentially unaffected, the position Tc1/2 obtained within the continuous time representation is systematically shifted backwards in time with respect to the position Td1/2 predicted within the discrete time representation. Rather counterintuitively, the magnitude of this temporal shift τ ≡ Tc1/2 − Td1/2 < 0 is basically insensitive to changes in infection rate κ. For a broad range of κ values deduced from COVID-19 data at extreme situations (exponential growth in time and complete lockdown), we found a rather robust estimate τ ≈ -2.65 day-1. Being obtained without any particular assumption, the present mathematical results apply to logistic growth in general without any limitation to a specific real system.

Stabilization method for the Saint-Venant equations by boundary control

In this paper, we are interested in the stabilization of the flow modeled by the Saint-Venant equations. We have solved two problems in this study. The first, we have proved that the operator associated to the Saint-Venant system has a finite number of unstable eigenvalues. Consequently, the system is not exponentially stable on the space [Formula: see text], but is exponentially stable on a subspace of the space [Formula: see text], ([Formula: see text] is a given domain). The second problem, if the advection is dominant, the natural stabilization is very slow. To solve these problems, we have used an extension method due to Russel (1974) and Fursikov (2002). Thanks to this method, we have determined a boundary Dirichlet control able to accelerate the stabilization of the flow. Also, the boundary Dirichlet control is able to kill all the unstable eigenvalues to get an exponentially stable solution on the space [Formula: see text]. Then, we extend this method to the finite difference equations analog of the continuous Saint-Venant equations. Also, in this case, we obtained similar results of stabilization. A finite difference scheme is used to compute the control and several numerical experiments are performed to illustrate the efficiency of the control.