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In this paper, the propagation and behavior of spatial solitons of inhomogeneous nonlinear Schrödinger equation in thermal medium will be investigated analytically. ... The theoretical model is established by considering the change of refractive index of medium due to heat deposition of entrance beam. The soliton like solution in such thermal medium was derived. ... Thermal lensing model The steady state heat conducting equation in the medium with thermal conductivity k is  : k∇ 2 T (x, y, z) = −Q(x, y, z), (1) where Q(x, y, z) is heat power density due to input ...doi:10.12693/aphyspola.112.891 fatcat:sghtrngn55e7nexq3mjpntyfzq
Elimination of source terms is made following the method of balancing source terms after independent solution of the heat conduction equation. ... in inhomogeneous media. ... THERMOELASTIC WAVES In the thermoelastic case, the equation for the temperature in two dimensions, is solved by means of a simple algorithm for the heat conductivity equation in an inhomogeneous medium ...doi:10.1006/jcph.2001.6697 fatcat:qxdbm74fpnbb7efzny2ranczqm
Our models exhibit different propagation regimes tuned by the strength of the inhomogeneity.” 87}:78037 CLASSICAL THERMODYNAMICS, HEAT TRANSFER 87j:80002 Kernévez, Jean-Pierre (F-COMP); 87j:78038 Trubuil ... This path-integral-Riemann-space (PIRS) approach recovers the exact solutions of the heat conduction and the corresponding electromagnetic wedge problems. ...
Methods Partial Differential Equations 5 (1989), no. 4, 363-399. The authors consider the inhomogeneous heat-conduction equation in two space variables on a finite strip. ... Methods Partial Differential Equations 6 (1990), no. 4, 343-369. The authors consider the inhomogeneous heat-conduction equa- tion in two space variables on a finite strip. ...
This work is concerned with the propagation of a nonlinear thermal wave in an inhomogeneous medium. ... K. 83c:80008 Heat conduction in a truncated wedge of semi-infinite height with circular boundaries. (Spanish summary) Rev. Técn. Fac. Ingr. Univ. Zulia 4 (1981), no. 1-2, 59-80. ...
Small nonstationary perturbations in a viscous heat-conducting compressible medium are analyzed on the basis of the linearization of the complete system of hydrodynamic equations for small Knudsen numbers ... It is shown that the density and temperature perturbations (elastic perturbations) satisfy the same wave equation which is an asymptotic limit of the hydrodynamic equations far from the inhomogeneity regions ... A linearized equation, the asymptotic limit of the initial hydrodynamic equations for a viscous heat-conducting compressible medium, is derived. ...doi:10.1007/s10697-005-0080-x fatcat:cuakascsbvaodesr52fkif2dqm
Then, we discuss the effects of inhomogeneous thermal properties in photothermal amplitude and phase spectra of coatings. ... Finally, a method for quantitative depth profiling that makes use of prior knowledge about the type of profile existing in a sample to reduce the instabilities associated with the mathematically ill conditioned ... The main problem arises from the impossibility of solving the inhomogeneous heat conduction equation in a general case. ...doi:10.12693/aphyspola.116.535 fatcat:q6lkq7qkabfubkvqgmv2viy6dy
Heat Conduction - Basic Research
Fourier heat conduction equation. ... Unlike propagation angle θ, γ has its boundary to guarantee the waves are of attenuation. ... The content of this book covers several up-to-date approaches in the heat conduction theory such as inverse heat conduction problems, non-linear and non-classic heat conduction equations, coupled thermal ...doi:10.5772/26053 fatcat:saorjtwij5g53cc6hyo2gfpmey
Acknowledgment The work has been done in the framework of Grant VEGA 1/0761/08 "Design of Microwave Methods for Materials Nondestructive Testing" of the Ministry of Education of the Slovak Republic and ... The first term on the right-hand side of this equation represents the current that produces a loss (heat) in the material through movement of free charges and bound charges. ... Wave propagation in biological materials If material conductivity does not equal zero value a material is lossy. ...doi:10.26552/com.c.2011.1.37-41 fatcat:azmq2vf2wbfmtfbycjs7z5sxoy
With the inclusion of a small inhomogeneity, such a value will change in line with the property of the embedded inhomogeneity. ... Reflectivity at the tissue-air interface is calculated by use of Snell's law and the Fresnel equation. ... radiation-transfer equations ͑RTEs͒ because the effect of time-dependent light propagation is negligible in traditional heat-transfer problems. ...doi:10.1364/ao.42.002897 pmid:12790438 fatcat:gkhz76qnq5d7rgbr7xdu75s4ha
to the unknown velocity of heat propagation along the thickness dimension of the composite sapropel-hemp slab. ... The proposed model consists of a system of three initial-boundary value problems with respect to the temperature function for each layer, respectively, and one initial-boundary value problem with respect ... ACKNOWLEDGEMENTS This work is dedicated to the blessed memory of Professor Janis S. Rimshans, Liepaja University. ...doi:10.17770/etr2021vol3.6648 fatcat:xwzf6k54n5djpanmiitexdzwq4
Summary (translated from the Russian): “We consider the exterior boundary value problem for the Helmholtz equation with respect to a spherical surface with a boundary condition of impedance type with a ... Summary: “An inverse scattering method to reconstruct simulta- neously the permittivity profile and the conductivity profile of a one-dimensional inhomogeneous medium which makes use of the transverse ...
An innovative feature of the theory is not requiring a boundary condition of zero tangential electric field at the conducting surface, but requiring explicitly that the bulk conductivity be taken into ... Summary: “In a waveguide filled with an inhomogeneous non- stationary medium and of a cross-section with piecewise smooth boundary we single out a system of not monochromatic mode fields generalizing the ...
of atmospheric conductivity. ... The ionosphere is subject to actions of the conduction electric current flowing in the atmosphere-ionosphere circuit. ... Equation (5.7) can be used to estimate the order of magnitude of the amplitude of plasma inhomogeneities caused by the perturbation of E ionosphere level conductivity. ...doi:10.1134/s199079310702008x fatcat:jyveillsdveetdqqnr57zfceyq
(8) for the field equation-, %,% heat-conductivity equation, Eqs. (2) and (3) , together with Eqs. (7) , do not cause bistability. ... I I I 0 X L o5 04 ated primarily with the output-side heat-conductivity 0 3 boundary conditions. ... Englund, "Longitudinal conductivity boundary conditions. ...doi:10.1364/josab.5.000011 fatcat:7mmbeuki2bcsrgziqw7s3ottwq
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