The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity

This article focuses on the study of redial displacement, the carrier density, the conductive and thermodynamic temperatures and the stresses in a semiconductor medium with a spherical hole. This study deals with photo-thermoelastic interactions in a semiconductor material containing a spherical cavity. The new hyperbolic theory of two temperatures with one-time delay is used. The internal surface of the cavity is constrained and the density of carriers is photogenerated by a heat flux at the exponentially decreasing pulse boundaries. The analytical solutions by the eigenvalues approach under the Laplace transformation approaches are used to obtain the solution of the problem and the inversion of the Laplace transformations is performed numerically. Numerical results for semiconductor materials are presented graphically and discussed to show the variations of physical quantities under the present model.

Differential integral functions

The definition of differential integral functions based on Laplace transformations and the definition of differential integrals, as well as their representation on graphs and in the text, is given. An example of approximation of a function using differential integral functions is given.

Asymptotically accurate error estimates of exponential convergence for the trapezoidal rule

In many applied problems, efficient calculation of quadratures with high accuracy is required. The examples are: calculation of special functions of mathematical physics, calculation of Fourier coefficients of a given function, Fourier and Laplace transformations, numerical solution of integral equations, solution of boundary value problems for partial differential equations in integral form, etc. For grid calculation of quadratures, the trapezoidal, the mean and the Simpson methods are usually used. Commonly, the error of these methods depends quadratically on the grid step, and a large number of steps are required to obtain good accuracy. However, there are some cases when the error of the trapezoidal method depends on the step value not quadratically, but exponentially. Such cases are integral of a periodic function over the full period and the integral over the entire real axis of a function that decreases rapidly enough at infinity. If the integrand has poles of the first order on the complex plane, then the Trefethen-Weidemann majorant accuracy estimates are valid for such quadratures. In the present paper, new error estimates of exponentially converging quadratures from periodic functions over the full period are constructed. The integrand function can have an arbitrary number of poles of an integer order on the complex plane. If the grid is sufficiently detailed, i.e., it resolves the profile of the integrand function, then the proposed estimates are not majorant, but asymptotically sharp. Extrapolating, i.e., excluding this error from the numerical quadrature, it is possible to calculate the integrals of these classes with the accuracy of rounding errors already on extremely coarse grids containing only 10 steps.

Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law

The present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

Magneto-photo-thermoelastic Interactions in a Semiconductor Solid Cylinder Due to a Periodic Decaying Varying Heat

In this article, a generalized photo-thermoelastic model with relaxation time (GPTE) was introduced and applied to an infinite semiconductor body in the form of a solid cylinder. The cylinder and its adjoining vacuum are constrained exposed to periodic decaying varying heat and subjected to a uniform axial magnetic field. Analytical formulas of the physical quantities of the problem were obtained using Laplace transformations. A numerical method is used to find the inverse Laplace transforms. The effect of phase-lags, the temperature frequency on the derived expressions have been illustrated graphically and discussed.

Fast and Robust 2D Inverse Laplace Transformation of Single-Molecule Fluorescence Lifetime Data

Fluorescence spectroscopy at the single-molecule scale has been indispensable for studying conformational dynamics and rare states of biological macromolecules. Single-molecule 2D-fluorescence lifetime correlation spectroscopy (sm-2D-FLCS) is an emerging technique that holds great promise for the study of protein and nucleic acid dynamics as it 1) resolves conformational dynamics using a single chromophore, 2) measures forward and reverse transitions independently, and 3) has a dynamic window ranging from microseconds to seconds. However, the calculation of a 2D fluorescence relaxation spectrum requires an inverse Laplace transition (ILT), which is an ill-conditioned inversion that must be estimated numerically through a regularized minimization. The current methods for performing ILTs of fluorescence relaxation can be computationally inefficient, sensitive to noise corruption, and difficult to implement. Here, we adopt an approach developed for NMR spectroscopy (T1-T2 relaxometry) to perform 1D and 2D-ILTs on single-molecule fluorescence spectroscopy data using singular-valued decomposition and Tikhonov regularization. This approach provides fast, robust, and easy to implement Laplace inversions of single-molecule fluorescence data.Significance StatementInverse Laplace transformations are a powerful approach for analyzing relaxation data. The inversion computes a relaxation rate spectrum from experimentally measured temporal relaxation, circumventing the need to choose appropriate fitting functions. They are routinely performed in NMR spectroscopy and are becoming increasing used in single-molecule fluorescence experiments. However, as Laplace inversions are ill-conditioned transformations, they must be estimated from regularization algorithms that are often computationally costly and difficult to implement. In this work, we adopt an algorithm first developed for NMR relaxometry to provide fast, robust, and easy to implement 1D and 2D inverse Laplace transformations on single-molecule fluorescence data.

Copula based Measures of Repairable Parallel System with Fault Coverage

The main objective of this study is to analyse the reliability behaviour of parallel systems with three types of failure, namely unit failure, human failure and major failure. For this purpose, we apply three different statistical techniques, namely copula, coverage and copula-coverage. More precisely, this study presents a stochastic model for analysing the behaviour of a multi-state system consisting of two non-identical units by incorporating the concept of coverage factor and two types of repair facilities between failed state to a normal state. The system could be characterized as being in a failed state due to unit failures, human failure and major failures, such as catastrophic and environmental failure. All failure rates are constant and it is assumed that these are exponentially distributed whereas, repair rates follow the Gumbel-Hougaard copula distribution. The entire system is modelled as a finite-state Markov process. Time-dependent reliability measures like availability, reliability and mean time to failure (MTTF) are obtained by supplementary variable techniques and Laplace transformations. The present study provides a comparative analysis for reliability measures among the aforementioned techniques, while a discussion referring to which technique makes the system more reliable is also developed. Furthermore, numerical simulations are presented to validate the analytical results.

Oblateness Effects on Solar Sail in the Restricted Three–body Problem

In the present work, the equations of motion of the solar sail are derived in the restricted three–body system. The dimensionless coordinates are used to obtain the solution of the problem. The Laplace transformations are used to solve these systems of equations to obtain the components of the solar sail acceleration. The motion about L2, L4 and its stability are studied under obalteness effects. The results obtained are in good agreement with previous results in this field. It is remarked that this model has special importance in space-dynamics to enabling spacecraft to do some maneuvers depends on the solar sail acceleration.

Analytical Estimation of Temperature in Living Tissues Using the TPL Bioheat Model with Experimental Verification

The aim of this study is to propose the analytical method associated with Laplace transforms and experimental verification to estimate thermal damages and temperature due to laser irradiation by utilizing measurement information of skin surface. The thermal damages to the tissues are totally estimated by denatured protein ranges using the formulations of Arrhenius. By using Laplace transformations, the exact solution of all physical variables is obtained. Numerical results for the temperature and thermal damage are presented graphically. Furthermore, the comparisons between the numerical calculations with experimental verification show that the three-phase lag bioheat mathematical model is an efficient tool for estimating the bioheat transfer in skin tissue.