A possible cosmological application of some thermodynamic properties of the black body radiation in n−n-dimensional Euclidean spaces

In this work we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an $n-$dimensional Euclidean space. For this case the Planck function and the Stefan-Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then no much more has been done on this subject and we believe there are some relevant aspects yet to explore. In addition to the results previously found we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arise, maxima and minima appear for the $n-d$ BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally we propose that an optimality criterion in a thermodynamic framework could have to do with the $3-d$ nature of the universe.Comment: 9 pages, 8 figure

The effect of material cyclic deformation properties on residual stress generation by laser shock processing

Laser shock processing (LSP) is a mechanical surface treatment to induce a compressive residual stress state into the near surface region of a metallic component. The effect of the cyclic deformation properties of ductile materials on the final residual stress fields obtained by LSP is analysed. Conventional modelling approaches either use simple tensile yield criteria, or isotropic hardening models if cyclic straining response is considered for the material during the peen processing. In LSP, the material is likely to be subject to cyclic loading because of reverse yielding after the initial plastic deformation. The combination of experiment and modelling shows that the incorporation of experimentally-determined cyclic stress-strain data, including mechanical hysteresis, into material deformation models is required to correctly reflect the cyclic deformation processes during LSP treatment and obtain accurate predictions of the induced residual stresses.</p

Well-posedness and stability results for the Gardner equation

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.Comment: 1 figure. Accepted for publication in Nonlin.Diff Eq.and App