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Propagation of Spatial Solitons with Nonlinear Kerr Effect in Thermal Medium

2007
*
Acta Physica Polonica. A
*

In this paper, the

doi:10.12693/aphyspola.112.891
fatcat:sghtrngn55e7nexq3mjpntyfzq
*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 [13] : k∇ 2 T (x, y, z) = −Q(x, y, z), (1) where Q(x, y, z) is*heat*power density due to input ...##
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Simulation of Thermoelastic Wave Propagation by Means of a Composite Wave-Propagation Algorithm

2001
*
Journal of Computational Physics
*

Elimination

doi:10.1006/jcph.2001.6697
fatcat:qxdbm74fpnbb7efzny2ranczqm
*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 ...##
###
Page 5945 of Mathematical Reviews Vol. , Issue 87j
[page]

1987
*
Mathematical Reviews
*

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. ...##
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Page 2196 of Mathematical Reviews Vol. , Issue 92d
[page]

1992
*
Mathematical Reviews
*

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. ...##
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Page 1245 of Mathematical Reviews Vol. , Issue 83c
[page]

1983
*
Mathematical Reviews
*

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. ...##
###
Asymptotic Solutions of the Equations for a Viscous Heat-Conducting Compressible Medium

2005
*
Fluid Dynamics
*

Small nonstationary perturbations in a viscous

doi:10.1007/s10697-005-0080-x
fatcat:cuakascsbvaodesr52fkif2dqm
*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. ...##
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Phototermal Spectra of Inhomogeneous Coatings

2009
*
Acta Physica Polonica. A
*

Then, we discuss the effects

doi:10.12693/aphyspola.116.535
fatcat:q6lkq7qkabfubkvqgmv2viy6dy
*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. ...##
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Energy Transfer in Pyroelectric Material
[chapter]

2011
*
Heat Conduction - Basic Research
*

Fourier

doi:10.5772/26053
fatcat:saorjtwij5g53cc6hyo2gfpmey
*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 ...##
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The Influence of Inhomogeneity Present in Layered Biological Structure on Electromagnetic Field Distribution

2011
*
Communications - Scientific Letters of the University of Zilina
*

Acknowledgment The work has been done in the framework

doi:10.26552/com.c.2011.1.37-41
fatcat:azmq2vf2wbfmtfbycjs7z5sxoy
*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. ...##
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Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method

2003
*
Applied Optics
*

With the inclusion

doi:10.1364/ao.42.002897
pmid:12790438
fatcat:gkhz76qnq5d7rgbr7xdu75s4ha
*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. ...##
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3D MATHEMATICAL MODEL CHARACTERIZING THE DYNAMICS OF THE TEMPERATURE FIELD OF A WALL STRUCTURE WITH A DOUBLE-SIDED FACING FROM A SAPROPEL-HEMP COMPOSITE MATERIAL

2021
*
Environment Technology Resources Proceedings of the International Scientific and Practical Conference
*

to the unknown velocity

doi:10.17770/etr2021vol3.6648
fatcat:xwzf6k54n5djpanmiitexdzwq4
*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. ...##
###
Page 499 of Mathematical Reviews Vol. , Issue 89A
[page]

1989
*
Mathematical Reviews
*

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 ...##
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Page 9308 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

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 ...##
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Plasma and electromagnetic effects in the ionosphere related to the dynamics of charged aerosols in the lower atmosphere

2007
*
Russian Journal of Physical Chemistry B
*

*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*. ...

##
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Longitudinal spatial inhomogeneities in intrinsic optical bistability due to induced absorption

1988
*
Journal of the Optical Society of America. B, Optical physics
*

(8) for the field

doi:10.1364/josab.5.000011
fatcat:7mmbeuki2bcsrgziqw7s3ottwq
*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. ...
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