The Experts below are selected from a list of 1086 Experts worldwide ranked by ideXlab platform
L K Bieniasz - One of the best experts on this subject based on the ideXlab platform.
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a new theory of potential step chronoamperometry at hemispheroidal electrodes complete explicit semi analytical formulae for the faradaic current density and the faradaic current
2017Co-Authors: L K BieniaszAbstract:Abstract The recently described theory of potential step chronoamperometry at inlaid microdisk electrodes [L. K. Bieniasz, Electrochim. Acta 199(2016)1] is extended to hemispheroidal electrodes, assuming diffusional transport under limiting current conditions. Both oblate and prolate hemispheroids are discussed. The theory provides previously unknown, rigorous, complete, and explicit expressions for the concentration, the Faradaic current density, and the Faradaic current. The expressions are in the form of Inverse Laplace Transforms of infinite series involving spheroidal wave functions. Numerical Laplace transform inversion, applied to the series, yields highly accurate solution values. Hence, the present solutions are advantageous over formerly used low-accurate and/or heuristic approximations, for the purposes of experimental data analysis, and for testing of modelling/simulation techniques.
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theory of potential step chronoamperometry at a microband electrode complete explicit semi analytical formulae for the faradaic current density and the faradaic current
2015Co-Authors: L K BieniaszAbstract:Abstract Theory of potential step chronoamperometry under limiting current conditions and for purely diffusional transport at a microband electrode has been a subject of several studies. However, no complete and explicit expressions for the Faradaic current density and the Faradaic current have been reported thus far. In the present study such expressions are derived using a novel theoretical approach. The microband is considered as a limiting case of an elliptic cylinder, when the length of the smallest diameter of the elliptic cross-section tends to zero. Solution to the problem of heat conduction around an elliptic cylinder, due to Tranter [Quart. J. Mech. Appl. Math. 4 (1951) 461], is utilised. Following Tranter, the method of separation of variables in the Laplace space is used, resulting in two Mathieu differential equations. The concentration of the depolarizer, the Faradaic current density, and the Faradaic current, are then expressed as Inverse Laplace Transforms of certain infinite series involving appropriate Mathieu functions. The series are amenable to further analytical examinations. In particular, it is proven that a quasi-steady state develops at large time. It is also demonstrated how the popular idea, of an hemicylinder electrode “equivalent” to a microband, has to be understood to be correct. Numerical evaluation of the series provides unprecedentedly highly accurate solution values. Hence, the present solutions should be preferred over formerly used low-accurate formulae, for the purposes of experimental data analysis, and for the testing of modelling/simulation techniques.
Loyal Durand - One of the best experts on this subject based on the ideXlab platform.
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a new numerical method for Inverse Laplace Transforms used to obtain gluon distributions from the proton structure function
2011Co-Authors: M M Block, Loyal DurandAbstract:We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace Transforms needed to obtain gluon distributions from the proton structure function \(F_{2}^{\gamma p}(x,Q^{2})\). We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/sβ for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power vβ−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10−6 obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q2=5 GeV2 down to the lower virtuality Q2=1.69 GeV2. For devolution, β is negative, giving rise to Inverse Laplace Transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.
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a new numerical method for Inverse Laplace Transforms used to obtain gluon distributions from the proton structure function
2011Co-Authors: M M Block, Loyal DurandAbstract:We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace Transforms needed to obtain gluon distributions from the proton structure function $F_2^{\gamma p}(x,Q^2)$. We numerically inverted the function $g(s)$, $s$ being the variable in Laplace space, to $G(v)$, where $v$ is the variable in ordinary space. We have since discovered that the algorithm does not work if $g(s)\rightarrow 0$ less rapidly than $1/s$ as $s\rightarrow\infty$, e.g., as $1/s^\beta$ for $0<\beta<1$. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of $\beta$. The new algorithm is {\em exact} if the original function $G(v)$ is given by the product of a power $v^{\beta-1}$ and a polynomial in $v$. We test the algorithm numerically for very small positive $\beta$, $\beta=10^{-6}$ obtaining numerical results that imitate the Dirac delta function $\delta(v)$. We also devolve the published MSTW2008LO gluon distribution at virtuality $Q^2=5$ GeV$^2$ down to the lower virtuality $Q^2=1.69$ GeV$^2$. For devolution, $ \beta$ is negative, giving rise to Inverse Laplace Transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.
M M Block - One of the best experts on this subject based on the ideXlab platform.
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a new numerical method for Inverse Laplace Transforms used to obtain gluon distributions from the proton structure function
2011Co-Authors: M M Block, Loyal DurandAbstract:We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace Transforms needed to obtain gluon distributions from the proton structure function \(F_{2}^{\gamma p}(x,Q^{2})\). We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/sβ for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power vβ−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10−6 obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q2=5 GeV2 down to the lower virtuality Q2=1.69 GeV2. For devolution, β is negative, giving rise to Inverse Laplace Transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.
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a new numerical method for Inverse Laplace Transforms used to obtain gluon distributions from the proton structure function
2011Co-Authors: M M Block, Loyal DurandAbstract:We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace Transforms needed to obtain gluon distributions from the proton structure function $F_2^{\gamma p}(x,Q^2)$. We numerically inverted the function $g(s)$, $s$ being the variable in Laplace space, to $G(v)$, where $v$ is the variable in ordinary space. We have since discovered that the algorithm does not work if $g(s)\rightarrow 0$ less rapidly than $1/s$ as $s\rightarrow\infty$, e.g., as $1/s^\beta$ for $0<\beta<1$. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of $\beta$. The new algorithm is {\em exact} if the original function $G(v)$ is given by the product of a power $v^{\beta-1}$ and a polynomial in $v$. We test the algorithm numerically for very small positive $\beta$, $\beta=10^{-6}$ obtaining numerical results that imitate the Dirac delta function $\delta(v)$. We also devolve the published MSTW2008LO gluon distribution at virtuality $Q^2=5$ GeV$^2$ down to the lower virtuality $Q^2=1.69$ GeV$^2$. For devolution, $ \beta$ is negative, giving rise to Inverse Laplace Transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.
Hamdy M Youssef - One of the best experts on this subject based on the ideXlab platform.
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two dimensional thermal shock problem of fractional order generalized thermoelasticity
2012Co-Authors: Hamdy M YoussefAbstract:In this study, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the fractional order generalized thermoelasticity theory. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution is applied to a specific problem of a half-space subjected to thermal shock. The Inverse Fourier Transforms are obtained analytically, while the Inverse Laplace Transforms are computed numerically. Some comparisons have been shown in figures to estimate the effect of the fractional order on all the studied fields.
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two dimensional problem of a two temperature generalized thermoelastic half space subjected to ramp type heating
2008Co-Authors: Hamdy M YoussefAbstract:In this work, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the theory of two-temperature generalized thermoelasticity. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating. The Inverse Fourier Transforms are obtained analytically while the Inverse Laplace Transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating.
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state space approach of two temperature generalized thermoelasticity of one dimensional problem
2007Co-Authors: Hamdy M Youssef, Eman A N AllehaibiAbstract:Abstract In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory [Youssef, H., 2005a. The dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, J. Appl. Math. Mech., 26(4), 4827; Youssef, H., 2005b. Theory of two-temperature generalized thermoelasticity, IMA J. Appl. Math., 1–8]. The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to thermal shock and traction free. The Inverse Laplace Transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature parameter.
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state space approach of two temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading
2007Co-Authors: Hamdy M Youssef, Amnah H AlharbyAbstract:In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The Inverse Laplace Transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.
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two dimensional generalized thermoelasticity problem for a half space subjected to ramp type heating
2006Co-Authors: Hamdy M YoussefAbstract:In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating. The Inverse Fourier Transforms are obtained analytically while the Inverse Laplace Transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating with different theories of thermoelasticity.
A. Tovbis - One of the best experts on this subject based on the ideXlab platform.
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Asymptotics beyond all orders and analytic properties of Inverse Laplace Transforms of solutions
1994Co-Authors: A. TovbisAbstract:A number of modern mathematical and physical problems require the study of delicate asymptotic properties lying “beyond” the power series asymptotics. In this paper we suggest a link between these asymptotic problems and some analytic properties of Inverse Laplace Transforms of the corresponding solutions. The main result claims that these Inverse Transforms are holomorphic in an appropriately cut complex plane. A direct consequence of this is the nonexistence of solutions to the class of “asymptotics beyond all orders” problems, such as regular shocks of the Kuramoto-Sivashinsky equaiton ([Gr]), needle crystal solutions of the simple geometrical model of crystal growth ([KS]), solitary wave solutions to a class of the fifth-order Kortveg-de Vries equations ([KO, Sect.8], [GJ]), homoclinic orbits of some singularly perturbed mappings ([Ec, HM]) and others.
