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Purpose: Whereas, the classical Green-Naghdi Type II (GN-II) model struggles to accurately represent the thermo-mechanical behavior of thermoelectric MHD due to its inability to account for the memory effect. A new mathematical model of the GN-II theory incorporates a fractional order of heat transport to address this issue. Design/methodology/approach: The employment of the matrix exponential method, which forms the basis of the state-space approach in contemporary theory, is central to this strategy. The resulting formulation, together with the Laplace transform techniques, is applied to a variety of problems. Solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also, a problem with the distribution of heat sources is considered. The numerical technique is used to achieve the Laplace transform inversion. Findings: According to the numerical results and its graphs, the influences of the fractional order parameters, figure-of-merit factor, thermoelectric power and Peltier coefficient on the behavior of the field quantities are investigated in the new theory. Originality/value: The new modeling of thermoelectric MHD has advanced significantly as a result of this work, providing a more thorough and precise tool for forecasting the behavior of these materials under a range of thermal and magnetic conditions. [ABSTRACT FROM AUTHOR]

Abstract: The inversion method for generating non-uniformly distributed random variates is a crucial part in many applications of Monte Carlo techniques, e.g., when low discrepancy sequences or copula based models are used. Unfortunately, closed form expressions of quantile functions of important distributions are often not available. The (generalized) inverse Gaussian distribution is a prominent example. It is shown that algorithms that are based on polynomial approximation are well suited for this distribution. Their precision is close to machine precision and they are much faster than root finding methods like the bisection method that has been recently proposed. [Copyright &y& Elsevier]

A differential method is presented for recovering a function from its Laplace–Carson transform pfˆ(p) given as continuous or discrete data on a finite interval. The introduction of the variable u=1/p converts this transform into a Mellin convolution, with a transformed kernel involving the gamma function Γ. The truncation of the infinite product representation of 1/Γ leads to an approximate differential expression for the solution. The algorithm is applied to selected analytical and numerical test problems; discrete and noisy data are differentiated with the aid of Tikhonov's regularization. For the inversion of a Laplace transform, the present formula is proved to be equivalent to the Post–Widder expression. [Copyright &y& Elsevier]

An inverse problem is considered to identify the geometry of discontinuities in a conductive material Ω⊂Rd with anisotropic conductivity (I+(K−I)χD) from Cauchy data measurements taken on the boundary ∂Ω, where D⊂Ω, K is a symmetric and positive definite tensor not equal to the identity tensor and χD is the characteristic function of the domain D. As an example this models the determination of the shape, size and location of the anisotropic inner core of the Earth from measurements taken at its mantle. There are also other applications in electrical impedance tomography or in non-destructive testing of materials using infra-red scanning. We develop an integral representation of the solution and we propose an efficient boundary element method in conjunction with a least-squares constrained minimisation procedure to detect an anisotropic inclusion D, such as a circle, by a single boundary measurement. [Copyright &y& Elsevier]