Unified integro-differential equation for efficient dispersive FDTD simulations

2017 ◽  
Vol 36 (4) ◽  
pp. 1089-1105 ◽  
Author(s):  
Omar Ramadan
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Stability Limit ◽  
Model Parameters ◽  
Time Step ◽  
Content Type ◽  
Integro Differential Equation ◽  
Dispersive Model ◽  
Fdtd Simulations ◽  
Dispersive Models

Purpose The purpose of this paper is to derive a unified formulation for incorporating different dispersive models into the explicit and implicit finite difference time domain (FDTD) simulations. Design/methodology/approach In this paper, dispersive integro-differential equation (IDE) FDTD formulation is presented. The resultant IDE is written in the discrete time domain by applying the trapezoidal recursive convolution and central finite differences schemes. In addition, unconditionally stable implicit split-step (SS) FDTD implementation is also discussed. Findings It is found that the time step stability limit of the explicit IDE-FDTD formulation maintains the conventional Courant–Friedrichs–Lewy (CFL) constraint but with additional stability limits related to the dispersive model parameters. In addition, the CFL stability limit can be removed by incorporating the implicit SS scheme into the IDE-FDTD formulation, but this is traded for degradation in the accuracy of the formulation. Research limitations/implications The stability of the explicit FDTD scheme is bounded not only by the CFL limit but also by additional condition related to the dispersive material parameters. In addition, it is observed that implicit JE-IDE FDTD implementation decreases as the time step exceeds the CFL limit. Practical implications Based on the presented formulation, a single dispersive FDTD code can be written for implementing different dispersive models such as Debye, Drude, Lorentz, critical point and the quadratic complex rational function. Originality/value The proposed formulation not only unifies the FDTD implementation of the frequently used dispersive models with the minimal storage requirements but also can be incorporated with the implicit SS scheme to remove the CFL time step stability constraint.

scholarly journals Time domain solution of electromagnetic radiation model of the grounding system excited by pulse current

2020 ◽  
Vol 35 (1) ◽  
pp. 74-81
Author(s):  
Nedis Dautbasic ◽  
Adnan Mujezinovic
Keyword(s):  
Differential Equation ◽  
Electromagnetic Radiation ◽  
Time Domain ◽  
Gauge Condition ◽  
Pulse Excitation ◽  
Solution Technique ◽  
Grounding System ◽  
Integro Differential Equation ◽  
Transient Voltage ◽  
The Time Domain

This paper deals with an advanced electromagnetic radiation approach for analyzing the time-domain performance of grounding systems under pulse excitation currents. The model of the grounding systems presented within this paper is based on the homogeneous Pocklington integro-differential equation for the calculation of the current distribution on the grounding system and Lorentz gauge condition which is used for the grounding system transient voltage calculation. For the solution of the Pocklington integro-differential equation, the indirect boundary element method and marching on-in time method are used. Fur- thermore, the solution technique for the calculation of the grounding system transient voltage is presented. The numerical model for the calculation of the grounding system transients was verified by comparing it with onsite measurement results.

Accurate analytical/numerical solution of the heat conduction equation

2014 ◽  
Vol 24 (7) ◽  
pp. 1519-1536 ◽  
Author(s):  
Antonio Campo ◽  
Abraham J. Salazar ◽  
Diego J. Celentano ◽  
Marcos Raydan
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Time Domain ◽  
Heat Conduction Equation ◽  
Separation Of Variables ◽  
Method Of Lines ◽  
Conduction Equation ◽  
Content Type ◽  
Entire Time

Purpose – The purpose of this paper is to address a novel method for solving parabolic partial differential equations (PDEs) in general, wherein the heat conduction equation constitutes an important particular case. The new method, appropriately named the Improved Transversal Method of Lines (ITMOL), is inspired in the Transversal Method of Lines (TMOL), with strong insight from the method of separation of variables. Design/methodology/approach – The essence of ITMOL revolves around an exponential variation of the dependent variable in the parabolic PDE for the evaluation of the time derivative. As will be demonstrated later, this key step is responsible for improving the accuracy of ITMOL over its predecessor TMOL. Throughout the paper, the theoretical properties of ITMOL, such as consistency, stability, convergence and accuracy are analyzed in depth. In addition, ITMOL has proven to be unconditionally stable in the Fourier sense. Findings – In a case study, the 1-D heat conduction equation for a large plate with symmetric Dirichlet boundary conditions is transformed into a nonlinear ordinary differential equation by means of ITMOL. The numerical solution of the resulting differential equation is straightforward and brings forth a nearly zero truncation error over the entire time domain, which is practically nonexistent. Originality/value – Accurate levels of the analytical/numerical solution of the 1-D heat conduction equation by ITMOL are easily established in the entire time domain.

MFPR Model Parameters of the Athermal Irradiation-Induced Transport in Nuclear Fuels

2017 ◽  
Vol 375 ◽  
pp. 71-83 ◽  
Author(s):  
Vladimir I. Tarasov ◽  
Pavel V. Polovnikov
Keyword(s):  
Differential Equation ◽  
Molecular Dynamics ◽  
Monte Carlo ◽  
General Solution ◽  
Fission Product ◽  
Atomistic Simulations ◽  
Model Parameters ◽  
Nuclear Fuels ◽  
Integro Differential Equation ◽  
Product Release

Atomistic simulations of radiation impact due to collision cascades in oxide and nitride nuclear fuels are performed in this work using combination of Monte Carlo and molecular dynamics techniques. The key parameters of MFPR code models for the athermal self-diffusivity and irradiation-assisted fission product release from fuel are evaluated. The general solution of Olander's integro-differential equation for the knockout mechanism is developed, which allowed extension of the earlier approaches for the long-lived and stable nuclides.

Analysis of Microstrip Circuit by Using Finite Difference Time Domain (FDTD) Method

2013 ◽  
Vol 347-350 ◽  
pp. 1758-1762
Author(s):  
Lei Zhang ◽  
Tong Bin Yu ◽  
De Xin Qu ◽  
Xiao Gang Xie
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Transform Domain ◽  
Time Step ◽  
The Time Domain ◽  
Difference Time ◽  
Microstrip Circuit

The microstrip circuit is mostly analyzed in transform domain, because its equivalent circuit equation is often nonlinear differential equation, which is easily analyzed in transform domain relatively, but hardly did in time domain, so the analysis of microstrip circuit is a hard work in time domain. In this paper, the FDTD method is used to analyze the microstrip circuit in time domain, by transforming the nonlinear differential equation into time domain iterative equation, selecting suitable time step, and having an iterative computing, the time domain numerical solution can be solved. The FDTD method analyzing the microstrip circuit provides a new way of thought for analyzing microstrip circuit in time domain.

scholarly journals Formation of Escherichia coli O157:H7 Persister Cells in the Lettuce Phyllosphere and Application of Differential Equation Models To Predict Their Prevalence on Lettuce Plants in the Field

2019 ◽  
Vol 86 (2) ◽  
Author(s):  
Daniel S. Munther ◽  
Michelle Q. Carter ◽  
Claude V. Aldric ◽  
Renata Ivanek ◽  
Maria T. Brandl
Keyword(s):  
Differential Equation ◽  
Escherichia Coli ◽  
Physiological State ◽  
Model Parameters ◽  
Persister Cells ◽  
Content Type ◽  
Dormant State ◽  
Differential Equation Models ◽  
Persister Cell ◽  
Cell Fractions

ABSTRACT Escherichia coli O157:H7 (EcO157) infections have been recurrently associated with produce. The physiological state of EcO157 cells surviving the many stresses encountered on plants is poorly understood. EcO157 populations on plants in the field generally follow a biphasic decay in which small subpopulations survive over longer periods of time. We hypothesized that these subpopulations include persister cells, known as cells in a transient dormant state that arise through phenotypic variation in a clonal population. Using three experimental regimes (with growing, stationary at carrying capacity, and decaying populations), we measured the persister cell fractions in culturable EcO157 populations after inoculation onto lettuce plants in the laboratory. The greatest average persister cell fractions on the leaves within each regime were 0.015, 0.095, and 0.221%, respectively. The declining EcO157 populations on plants incubated under dry conditions showed the largest increase in the persister fraction (46.9-fold). Differential equation models were built to describe the average temporal dynamics of EcO157 normal and persister cell populations after inoculation onto plants maintained under low relative humidity, resulting in switch rates from a normal cell to a persister cell of 7.7 × 10−6 to 2.8 × 10−5 h−1. Applying our model equations from the decay regime, we estimated model parameters for four published field trials of EcO157 survival on lettuce and obtained switch rates similar to those obtained in our study. Hence, our model has relevance to the survival of this human pathogen on lettuce plants in the field. Given the low metabolic state of persister cells, which may protect them from sanitization treatments, these cells are important to consider in the microbial decontamination of produce. IMPORTANCE Despite causing outbreaks of foodborne illness linked to lettuce consumption, E. coli O157:H7 (EcO157) declines rapidly when applied onto plants in the field, and few cells survive over prolonged periods of time. We hypothesized that these cells are persisters, which are in a dormant state and which arise naturally in bacterial populations. When lettuce plants were inoculated with EcO157 in the laboratory, the greatest persister fraction in the population was observed during population decline on dry leaf surfaces. Using mathematical modeling, we calculated the switch rate from an EcO157 normal to persister cell on dry lettuce plants based on our laboratory data. The model was applied to published studies in which lettuce was inoculated with EcO157 in the field, and switch rates similar to those obtained in our study were obtained. Our results contribute important new knowledge about the physiology of this virulent pathogen on plants to be considered to enhance produce safety.

Efficient and stable generalized auxiliary differential equation FDTD implementation of graphene dispersion

2019 ◽  
Vol 38 (6) ◽  
pp. 2070-2083
Author(s):  
Omar Ramadan
Keyword(s):  
Differential Equation ◽  
Memory Storage ◽  
Complex Conjugate ◽  
Time Step ◽  
Content Type ◽  
Von Neumann ◽  
Graphene Dispersion ◽  
The Stability ◽  
Infrared Frequencies ◽  
The Given

Purpose The purpose of this paper is to present efficient and stable generalized auxiliary differential equation finite difference time domain (G-ADE-FDTD) implementation of graphene dispersion. Design/methodology/approach A generalized dispersive model is used for describing the graphene’s intraband and interband conductivities in the terahertz and infrared frequencies. In addition, the von Neumann method combined with the Routh-Hurwitz criterion are used for studying the stability of the given implementation. Findings The presented G-ADE-FDTD implementation allows modeling graphene’s dispersion using the minimal number of additional auxiliary variables, which will reduce both the CPU time and memory storage requirements. In addition, the stability of the implementation retains the standard non-dispersive Courant–Friedrichs–Lewy (CFL) constraint. Practical implications The given implementation is conveniently applicable for most commonly used dispersive models, such as Debye, Lorentz, complex-conjugate pole residue, etc. Originality/value The presented G-ADE-FDTD implementation not only unifies the implementation of both graphene’s intraband and interband conductivities, with the minimal computational requirements but also retains the standard non-dispersive CFL time step stability constraint.

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