The Mullins effect is a common name for family of intriguing inelastic responses various solid materials, in particular filled rubbers. Given the importance effect, there have been many attempts to develop mathematical models describing effect. However, most available focus exclusively on mechanical response and are restricted idealized isothermal setting. We lift restriction processes, we prop...

Abstract High-energy and high-intensity lasers are essential for pushing the boundaries of science. Their development has allowed leaps forward in basic research areas, including laser–plasma interaction, high-energy density science, metrology, biology medical technology. The Helmholtz International Beamline Extreme Fields user consortium contributes operates two high-peak-power optical using h...

We study the effect of nonfactorizable background geometry on thermodynamics clustering galaxies. A canonical partition function is derived for gravitating system galaxies treated as point particles contained in cells appropriate dimensions. Various thermodynamic equations state, like Helmholtz free energy and entropy, among others, are also obtained. estimate corrected Newton law distribution ...

The Monte Carlo method based on two-dimensional entropic sampling within the Wang-Landau (WL) algorithm is applied to simulation of a continuous model of a polyelectrolyte between membrane surfaces. Membranes are presented by parallel plane surfaces holding either fixed or mobile dipoles (representing lipid headgroups). A strongly charged polyion accompanied by neutralizing counterions is place...

I IN THE last two decades historians of science have shown increasing interest in the emergence of the doctrine of the conservation of energy. A particular aspect of this topic has been the contribution made to nineteenth-century discussions on force and power by men working in physiology: Hermann Helmholtz (1821-1894) and Julius Robert Mayer (1814-1878) are probably the best known. The seminal...

We present an elementary proof of the Helmholtz decomposition on whole R based on the minimization principle of the calculus of variations and some basic results of real analysis and Sobolev spaces. We also use the elementary and self-contained proofs to provide some representation results on the curl-free fields and the divergence-free fields in L(R) in terms of local functions.

This paper deals with the Helmholtz-Hodge decomposition of a vector field in bounded domain. We present a practical algorithm to compute this decomposition in the context of divergence-free and curl-free wavelets satisfying suitable boundary conditions. The method requires the inversion of divergence-free and curl-free wavelet Gram matrices. We propose an optimal preconditioning which allows to...