The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Nicolas G Hadjiconstantinou - One of the best experts on this subject based on the ideXlab platform.
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extending the range of validity of fourier s law into the kinetic transport regime via Asymptotic Solution of the phonon boltzmann transport equation
Physical Review B, 2016Co-Authors: Jeanphilippe M Peraud, Nicolas G HadjiconstantinouAbstract:We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from Asymptotic Solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. However, this description does not hold within distances on the order of a few mean free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require Solution of a Boltzmann boundary-layer problem to be determined. Matching the inner, boundary layer, Solution to the outer, bulk, Solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-Solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the Asymptotic Solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials.
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extending the range of validity of fourier s law into the kinetic transport regime via Asymptotic Solution of the phonon boltzmann transport equation
Physical Review Letters, 2016Co-Authors: Nicolas G HadjiconstantinouAbstract:We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of a small but finite mean-free path from the Asymptotic Solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean-free path to the characteristic system length scale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier description. We show that, in the bulk, the traditional heat conduction equation using Fourier’s law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. However, this description does not hold within distances on the order of a few mean-free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require Solution of a Boltzmann boundary layer problem to be determined. Matching the inner, boundary layer Solution to the outer, bulk Solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-Solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and the no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the Asymptotic Solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials. All results are validated via comparisons with low-variance deviational Monte Carlo simulations.
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on the equations and boundary conditions governing phonon mediated heat transfer in the small mean free path limit an Asymptotic Solution of the boltzmann equation
ASME 2014 International Mechanical Engineering Congress and Exposition, 2014Co-Authors: Jeanphilippe M Peraud, Nicolas G HadjiconstantinouAbstract:Using an Asymptotic Solution procedure, we construct Solutions of the Boltzmann transport equation in the relaxation-time approximation in the limit of small Knudsen number, Kn << 1, to obtain continuum equations and boundary conditions governing phonon-mediated heat transfer in this limit. Our results show that, in the bulk, heat transfer is governed by the Fourier law of heat conduction, as expected. However, this description does not hold within distances on the order of a few mean free paths from the boundary; fortunately, this deviation from Fourier behavior can be captured by a universal boundary-layer Solution of the Boltzmann equation that depends only on the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Boundary conditions for the Fourier description follow from matching this inner Solution to the outer (Fourier) Solution. This procedure shows that the traditional no-jump boundary conditions are appropriate only to zeroth order in Kn. Solution to first order in Kn shows that the Fourier law needs to be complemented by jump boundary conditions with jump coefficients that depend on the material model and the phonon-boundary interaction model. In this work, we calculate these coefficients and the form of the jump conditions for an adiabatic-diffuse and a prescribed-temperature boundary in contact with a constant-relaxation-time material. Extension of this work to variable relaxation-time models is straightforward and will be discussed elsewhere. Our results are validated via comparisons with low-variance deviational Monte Carlo simulations.Copyright © 2014 by ASME
R J Marhefka - One of the best experts on this subject based on the ideXlab platform.
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a utd based Asymptotic Solution for the surface magnetic field on a source excited circular cylinder with an impedance boundary condition
IEEE Transactions on Antennas and Propagation, 2006Co-Authors: Cagatay Tokgoz, R J MarhefkaAbstract:An Asymptotic Solution based on the uniform geometrical theory of diffraction (UTD) is proposed for the canonical problem of surface field excitation on a circular cylinder with an impedance boundary condition (IBC). The radius of the cylinder and the length of the geodesic path between source and field points, both of which are located on the surface of the cylinder, are assumed to be large compared to a wavelength. Unlike the UTD based Solution pertaining to a perfect electrically conducting (PEC) circular cylinder, some higher order terms and derivatives of Fock type integrals are found to be significantly important and included in the proposed Solution. The Solution is of practical interest in the prediction of electromagnetic compatibility (EMC) and electromagnetic interference (EMI) between conformal slot antennas on a PEC cylindrical structure with a thin material coating on which boundary conditions can be approximated by an IBC. The cylindrical structure could locally model a portion of the fuselage of an aircraft or a spacecraft, or a missile. Validity and accuracy of the numerical results obtained by this Solution are demonstrated in comparison with those of an exact eigenfunction Solution.
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an Asymptotic Solution for the surface magnetic field within the paraxial region of a circular cylinder with an impedance boundary condition
IEEE Transactions on Antennas and Propagation, 2005Co-Authors: Cagatay Tokgoz, P H Pathak, R J MarhefkaAbstract:It is well-known that the high-frequency Asymptotic evaluation of surface fields by the conventional geometrical theory of diffraction (GTD) usually becomes less accurate within the paraxial (close to axial) region of a source excited electrically large circular cylinder. Uniform versions of the GTD based Solution for the surface field on a source excited perfect electrically conducting (PEC) circular cylinder were published earlier to yield better accuracy within the paraxial region of the cylinder. However, efficient and sufficiently accurate Solutions are needed for the surface field within the paraxial region of a source excited circular cylinder with an impedance boundary condition (IBC). In this work, an alternative approximate Asymptotic closed form Solution is proposed for the accurate representation of the tangential surface magnetic field within the paraxial region of a tangential magnetic current excited circular cylinder with an IBC. Similar to the treatment for the PEC case, Hankel functions are Asymptotically approximated by a two-term Debye expansion within the spectral integral representation of the relevant Green's function pertaining to the IBC case. Although one of the two integrals within the spectral representation is evaluated in an exact fashion, the other integral for which an exact analytical evaluation does not appear to be possible is evaluated Asymptotically, unlike the PEC case in which both integrals were evaluated analytically in an exact fashion. Validity of the proposed Asymptotic Solution is investigated by comparison with the exact eigenfunction Solution for the surface magnetic field.
Cagatay Tokgoz - One of the best experts on this subject based on the ideXlab platform.
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a utd based Asymptotic Solution for the surface magnetic field on a source excited circular cylinder with an impedance boundary condition
IEEE Transactions on Antennas and Propagation, 2006Co-Authors: Cagatay Tokgoz, R J MarhefkaAbstract:An Asymptotic Solution based on the uniform geometrical theory of diffraction (UTD) is proposed for the canonical problem of surface field excitation on a circular cylinder with an impedance boundary condition (IBC). The radius of the cylinder and the length of the geodesic path between source and field points, both of which are located on the surface of the cylinder, are assumed to be large compared to a wavelength. Unlike the UTD based Solution pertaining to a perfect electrically conducting (PEC) circular cylinder, some higher order terms and derivatives of Fock type integrals are found to be significantly important and included in the proposed Solution. The Solution is of practical interest in the prediction of electromagnetic compatibility (EMC) and electromagnetic interference (EMI) between conformal slot antennas on a PEC cylindrical structure with a thin material coating on which boundary conditions can be approximated by an IBC. The cylindrical structure could locally model a portion of the fuselage of an aircraft or a spacecraft, or a missile. Validity and accuracy of the numerical results obtained by this Solution are demonstrated in comparison with those of an exact eigenfunction Solution.
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an Asymptotic Solution for the surface magnetic field within the paraxial region of a circular cylinder with an impedance boundary condition
IEEE Transactions on Antennas and Propagation, 2005Co-Authors: Cagatay Tokgoz, P H Pathak, R J MarhefkaAbstract:It is well-known that the high-frequency Asymptotic evaluation of surface fields by the conventional geometrical theory of diffraction (GTD) usually becomes less accurate within the paraxial (close to axial) region of a source excited electrically large circular cylinder. Uniform versions of the GTD based Solution for the surface field on a source excited perfect electrically conducting (PEC) circular cylinder were published earlier to yield better accuracy within the paraxial region of the cylinder. However, efficient and sufficiently accurate Solutions are needed for the surface field within the paraxial region of a source excited circular cylinder with an impedance boundary condition (IBC). In this work, an alternative approximate Asymptotic closed form Solution is proposed for the accurate representation of the tangential surface magnetic field within the paraxial region of a tangential magnetic current excited circular cylinder with an IBC. Similar to the treatment for the PEC case, Hankel functions are Asymptotically approximated by a two-term Debye expansion within the spectral integral representation of the relevant Green's function pertaining to the IBC case. Although one of the two integrals within the spectral representation is evaluated in an exact fashion, the other integral for which an exact analytical evaluation does not appear to be possible is evaluated Asymptotically, unlike the PEC case in which both integrals were evaluated analytically in an exact fashion. Validity of the proposed Asymptotic Solution is investigated by comparison with the exact eigenfunction Solution for the surface magnetic field.
Wang Lianping - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Solution of population balance equation based on temom model
Chemical Engineering Science, 2013Co-Authors: Xie Mingliang, Wang LianpingAbstract:In the present study, Asymptotic Solutions for particle moment and standard deviation due to Brownian coagulation have been obtained analytically, using a specific moment-based formulation known as the Taylor-series expansion method of moment (TEMOM). The derivation is rigorous, and the accuracy of the Asymptotic Solution is fully dependent on underlying approximations in an expanded Taylor series. The accuracy has been validated by a comparison with numerical results. The Asymptotic Solutions reveal that the long-time particle moments are an explicit exponential function of time and first particle moment.
A I Shafarevich - One of the best experts on this subject based on the ideXlab platform.
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localized Asymptotic Solution of a variable velocity wave equation on the simplest decorated graph with initial conditions on a surface
Mathematical Notes, 2020Co-Authors: A V Tsvetkova, A I ShafarevichAbstract:A variable-velocity wave equation is studied on the simplest decorated graph, i.e., the topological space obtained by attaching a ray to $$\mathbb R^3$$ . The Cauchy problem with initial conditions localized on Euclidean space is considered. The leading term of an Asymptotic Solution of the problem under consideration as the parameter characterizing the size of the source tends to zero is described by using the construction of the Maslov canonical operator. It is assumed that the point on $$\mathbb R^3$$ at which the ray is attached is not a singular point of the wavefront.
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localized Asymptotic Solution of a variable velocity wave equation on the simplest decorated graph
Proceedings of the Steklov Institute of Mathematics, 2020Co-Authors: A V Tsvetkova, A I ShafarevichAbstract:We consider a variable-velocity wave equation on the simplest decorated graph obtained by gluing a ray to the three-dimensional Euclidean space, with localized initial conditions on the ray. The wave operator should be self-adjoint, which implies some boundary conditions at the gluing point. We describe the leading part of the Asymptotic Solution of the problem using the construction of the Maslov canonical operator. The result is obtained for all possible boundary conditions at the gluing point.
