scholarly journals On Exact Series Solution of Strongly Coupled Mixed Parabolic Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
M. V. Ferrer ◽  
J. Camacho
Keyword(s):  
Exact Solution ◽  
Series Solution ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Problems ◽  
Strongly Coupled ◽  
Stable Matrix

This paper studies the construction of the exact solution for parabolic coupled systems of the type , , , , , and , where , , , and are arbitrary matrices for which the block matrix is nonsingular, and is a positive stable matrix.

scholarly journals On Exact Series Solution for Strongly Coupled Mixed Parabolic Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
José Antonio Verdoy
Keyword(s):  
Exact Solution ◽  
Boundary Value Problems ◽  
Series Solution ◽  
Boundary Value ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Boundary ◽  
Strongly Coupled ◽  
Parabolic Boundary Value Problems ◽  
Stable Matrix

This paper continues with the construction of the exact solution for parabolic coupled systems of the typeut=Auxx,A1u(0,t)+B1ux(0,t)=0,A2u(l,t)+B2ux(l,t)=0,0<x<1,t>0, andu(x,0)=f(x), whereA1,A2,B1, andB2are arbitrary matrices for which the block matrix(A1B1A2B2)is nonsingular, andAis a positive stable matrix. Although this problem has been solved in the literature (Soler et al., 2013), in this work we are using completely new conditions.

scholarly journals On the Exact Series Solution for Nonhomogeneous Strongly Coupled Mixed Parabolic Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
Roberto Capilla ◽  
José Antonio Verdoy
Keyword(s):  
Boundary Value Problems ◽  
Series Solution ◽  
Boundary Value ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Boundary ◽  
Strongly Coupled ◽  
Parabolic Boundary Value Problems ◽  
Stable Matrix

An exact series solution for nonhomogeneous parabolic coupled systems of the typeut-Auxx=Gx, t, A1u0, t+B1ux0, t=0, A2ul, t+B2uxl, t=0, 0<x<1, t>0, ux, 0=fx, whereA1, A2, B1, andB2are arbitrary matrices for which the block matrix is nonsingular, andAis a positive stable matrix, is constructed.

scholarly journals On the exact solution of a class of homogeneous strongly coupled mixed parabolic problems

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 897-915
Author(s):  
Emilio Defez ◽  
Vicente Soler ◽  
Sergio Romero-Vivó ◽  
José Verdoy
Keyword(s):  
Exact Solution ◽  
Projection Method ◽  
Series Solution ◽  
Coupled Systems ◽  
Parabolic Problems ◽  
Strongly Coupled

In this paper an exact series solution for homogeneous parabolic coupled systems is constructed using a projection method. An illustrative example is given.

scholarly journals Exact and analytic-numerical solutions of strongly coupled mixed diffusion problems

2000 ◽  
Vol 43 (2) ◽  
pp. 269-293 ◽  
Author(s):  
L. Jódar ◽  
E. Navarro ◽  
J. A. Martin
Keyword(s):  
Approximate Solution ◽  
Error Bounds ◽  
Series Solution ◽  
Numerical Solutions ◽  
Strongly Coupled ◽  
Stable Matrix ◽  
Diffusion Problems ◽  
Admissible Error

AbstractThis paper deals with the construction of exact and analytical-numerical solutions with a priori error bounds for systems of the type ut = Auxx, A1u(0, t) + B1ux (0, t) = 0, A2u (1, t) + B2ux (1, t) = 0, 0 < x < 1, t > 0, u(x, 0) = f(x), where A1, A2, B1 and B2 are matrices for which no simultaneous diagonalizable hypothesis is assumed, and A is a positive stable matrix. Given an admissible error ε and a bounded subdomain D, an approximate solution whose error with respect to an exact series solution is less than ε uniformly in D is constructed.

scholarly journals Fundamental limitations of the mode temperature concept in strongly coupled systems

2020 ◽  
Vol 75 (8) ◽  
pp. 803-807
Author(s):  
Svend-Age Biehs ◽  
Achim Kittel ◽  
Philippe Ben-Abdallah
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Strong Coupling ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Strong Coupling Limit ◽  
Strongly Coupled ◽  
Fundamental Limitations ◽  
Temperature Concept ◽  
Vacuum Gap

AbstractWe theoretically analyze heat exchange between two quantum systems in interaction with external thermostats. We show that in the strong coupling limit the widely used concept of mode temperatures loses its thermodynamic foundation and therefore cannot be employed to make a valid statement on cooling and heating in such systems; instead, the incorrectly applied concept may result in a severe misinterpretation of the underlying physics. We illustrate these general conclusions by discussing recent experimental results reported on the nanoscale heat transfer through quantum fluctuations between two nanomechanical membranes separated by a vacuum gap.

Article

1999 ◽  
Vol 77 (11) ◽  
pp. 1810-1812 ◽  
Author(s):  
Alex D Bain
Keyword(s):  
Spin System ◽  
Coupled System ◽  
Coupled Systems ◽  
Physical Reason ◽  
Strongly Coupled ◽  
System Combination ◽  
First Order ◽  
Weakly Coupled ◽  
Quantum Transitions ◽  
Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

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