We survey recent results related to soliton resolution.

Decisions concerning how we balance energy supply and demand should not be made by quantitative cost-benefit analyses alone. The distributions of costs and benefits among individuals, groups of individuals, nations, and generations raise questions of equity that need to be addressed forthrightly. Doing so can help rather than impede the decision-making process.

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configuratio...

We investigate linear energy preserving methods for the Volterra lattice equation as non-canonical Hamiltonian system. The averaged vector field method was applied to the Volterra lattice equation in bi-Hamiltonian form with quadratic and cubic Poisson brackets. Numerical results confirm the excellent long time preservation of the Hamiltonians and the polynomial integrals.

Equation of state parameter plays a significant role for guessing the real nature of dark energy. In the present paper polytropic equation of state p = ωρn is chosen for some of the kinematical Λ-models viz., Λ ∼ (ȧ/a), Λ ∼ ä/a and Λ ∼ ρ. Although in dust cases (ω = 0) closed form solutions show no dependency on the polytropic index n, but in non-dust situations some new possibilities are opene...

In this study, three-dimensional simulations are presented for laminar forced convection flow of a radiating gas over a backward-facing step in rectangular duct. The fluid is treated as a gray, absorbing, emitting and scattering medium. The three-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. These equations...