We consider Nonlinear Equilibrium (NE) for the optimal allocation of limited resources. The NE is a generalization of Walras-Wald equilibrium, which is equivalent to J. Nash equilibrium in n-person concave games. Finding NE is equivalent to solving a variational inequality (VI) with a monotone and smooth operator on Ω = R+ ⊗ R+ . Projection on Ω is a very simple procedure; therefore, our main f...

We consider an assignment market with one seller who owns several indivisible heterogeneous goods and many buyers each willing to buy up to a given capacity. Our aim is to study the relationship between the core of the game and the set of competitive equilibria. The core is non-empty and it has a lattice structure which contains the allocation in which every buyer gets his marginal contribution...

The non equilibrium Green’s function method used in density functional theory based methods for computing electron transport at nano scale requires repeated inversions of a large block tridiagonal matrix. This calculation constitutes a substantial part of the total execution time, and therefore an efficient special method for the block tridiagonal matrix inversion was developed recently. This p...

We investigate the applicability of the path integral of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with a thermal noise and a fiber-bundle model with a decay of fibers are considered. Initially, we develop an analogy with the Gibbs formalism of non-equilibrium states. Later, we switch from the approach of non-equilibrium state...

The use of equilibrium-based and mass transfer-based leaching tests has been proposed to provide an integrated assessment of leaching processes from solid wastes. The objectives of the research presented here are to (i) validate this assessment approach for contaminated soils and cement-based matrices, (ii) evaluate the use of diffusion and coupled dissolution-diffusion models for estimating co...

The electron spin relaxation times measured in ESR spectroscopy are physically distinct from the electron spin relaxation times which appear in the theory of NMR Paramagnetic Relaxation Enhancement ~NMR-PRE!. ESR involves decay of a perturbed spin density matrix toward thermal equilibrium, while in NMR-PRE measurements, the electron spin density matrix remains at thermal equilibrium throughout ...

the clay crosslinked hydrogel nanocomposites were synthesized by graft copolymerization of acrylamide and itaconic acid in the presence of different amounts of laponite using ammonium persulfate and n,n,n',n'-tetramethylethylene diamine  )temed) as a free radical initiator and catalyst, respectively. the xrd patterns of nanocomposites showed that the clay layers are completely exfolia...

The phase behavior of a binary symmetric fluid in thermal equilibrium with a porous matrix has been studied with the optimized random phase approximation and grand canonical Monte Carlo simulations. Depending on the matrix properties and the matrix-fluid and fluid-fluid interactions we find three types of phase diagram characterized by a tricritical point, a tricritical point with a triple poin...