scholarly journals Uncertainty quantification for phase-space boundary integral models of ray propagation

Wave Motion ◽  
2019 ◽  
Vol 87 ◽  
pp. 151-165 ◽  
Author(s):  
David J. Chappell ◽  
Gregor Tanner
Keyword(s):  
Phase Space ◽  
Uncertainty Quantification ◽  
Boundary Integral ◽  
Space Boundary

Duality predictions on the ISR data of pp → pX near the phase-space boundary

1972 ◽  
Vol 38 (5) ◽  
pp. 317-320 ◽  
Author(s):  
J. Dias De Deus ◽  
W.S. Lam
Keyword(s):  
Phase Space ◽  
Space Boundary

scholarly journals EDUCING THE VOLUME OUT OF THE PHASE-SPACE BOUNDARY

2006 ◽  
Vol 21 (19n20) ◽  
pp. 3967-3988
Author(s):  
MANUEL A. COBAS ◽  
M. A. R. OSORIO ◽  
MARÍA SUÁREZ
Keyword(s):  
Phase Space ◽  
Finite Volume ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Surface Boundary ◽  
Duality Symmetry ◽  
Volume Dependence ◽  
Volume Limit ◽  
Space Boundary ◽  
Space Volume

We explicitly show that, in a system with T-duality symmetry, the configuration space volume degrees of freedom may hide on the surface boundary of the region of accessible states with energy lower than a fixed value. This means that, when taking the decompactification limit (big volume limit), a number of accessible states proportional to the volume is recovered even if no volume dependence appears when energy is high enough. All this behavior is contained in the exact way of computing sums by making integrals. We will also show how the decompactification limit for the gas of strings can be defined from a microcanonical description at finite volume.

scholarly journals Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities

2019 ◽  
Vol 13 (4) ◽  
pp. 238-244
Author(s):  
Heorhiy Sulym ◽  
Iaroslav Pasternak ◽  
Mariia Smal ◽  
Andrii Vasylyshyn
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Integral Formula ◽  
Boundary Integral ◽  
Cauchy Integral Formula ◽  
Cauchy Integral ◽  
Plemelj Formula ◽  
Space Boundary

Abstract The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.

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