In this note we show the asymptotic axisymmetry of subsonic traveling waves of finite energy to the Gross-Pitaevskii equation. In particular, using a new Hamiltonian identity, we prove that the momentum in the orthogonal directions must vanish.

In this paper generalization of the free energy perturbation identity is derived, and a computational strategy based on this result is presented. A simple example illustrates the efficiency gains that can be achieved with this method.

We study Dirac-harmonic maps from a Riemann surface to a sphere Sn. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.

— We prove the existence of infinitely many solitary waves for the nonlinear KleinGordon or Schrödinger equation ∆u− u + u = 0, in R, which have finite energy and whose maximal group of symmetry reduces to the identity.

The concept of sustainability is encouraged to preserve natural resources, social values, cultural heritage, and economic capital, which already exist to make available them for the next generations. Moreover, to enhance the level of sustainability in communities, numerous scholars indicated both individual and community identities play a crucial role. Sustainability is attainable and successfu...

Statistical mechanics provides a rigorous framework for the numerical estimation of free energy di erences in complex systems such as biomolecules. This paper presents a brief review of the statistical mechanical identities underlying a number of techniques for computing free energy di erences. Both equilibrium and nonequilibrium methods are covered.