Related papers: Recent topics on the O'Hara energies
The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been…
In 1962, astronomers Michel H\'enon and Carl Heiles studied orbits of stars around centers of galaxies to determine the third integral of motion in galactic dynamics. In order to do this, they reduced the system down to a 2-dimensional…
In this paper, we make a close comparison of a covariant definition of an energy/entropy in general relativity, recently proposed by a collaboration including the present authors, with existing definitions of energies such as the one from…
As noticed in Ref.[1], the Ore-Powell's classical calculation of the o-Ps -> 3 gamma decay amplitude does not fulfill Low's theorem requirements for the low energy end of the photon spectrum. We reanalyze the implications of Low's theorem…
Energy positivity is established for a class of solutions to Einstein-aether theory and the IR limit of Ho\v{r}ava gravity within a certain range of coupling parameters. The class consists of solutions where the aether 4-vector is…
A new covariant generalization of Einstein's general relativity is developed which allows the existence of a term proportional to $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory ($T_{\alpha\beta}$ is the…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
New formulae are obtained for the energy of K.N. b.h.'s that point out a gravitomagnetic energy effect. The results are valid for slowly or rapidly rotating black-holes. The expression of the energy density of Kerr-Newman back-holes in the…
Using area-preserving curve shortening flow, and a new inequality relating the potential generated by a set to its curvature, we study a non-local isoperimetric problem which arises in the study of di-block copolymer melts, also referred to…
Herein, in the context of third version of nonextensive statistical mechanics, theory generalizing the Boltzmann-Gibbs-Shannon statistics, we displayed a solution for an anomaly found by calculating the internal energy for a composite A+B,…
Variational models of phase transitions take into account double-well energies singularly perturbed by gradient terms, such as the Cahn-Hilliard free energy. The derivation by $\Gamma$-convergence of a sharp-interface limit for such energy…
I exhibit the conflicting roles of Noether's two great theorems in defining conserved quantities, especially Energy in General Relativity and its extensions: It is the breaking of coordinate invariance through boundary conditions that…
A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity. The theory explicitly breaks Lorentz…
In this paper we study the Cauchy problem for the energy-critical inhomogeneous nonlinear Schr\"odinger equation $i\partial_{t}u+\Delta u=\lambda|x|^{-\alpha}|u|^{\beta}u$ in $H^1$. The well-posedness theory in $H^1$ has been intensively…
We study some cosmological constraints on the two phenomenological models of oscillating dark energy. In these scenarios, the equation of state of dark energy varies periodically and may provide a way to unify the early acceleration…
J.Eells and L. Lemaire introduced $k$-harmonic maps, and Wang Shaobo showed the first variation formula. In this paper, we give the second variation formula of $k$-energy, and give a notion of index, nullity and weakly stable. We also study…
Recently Horava proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I consider…
The popular Hamilton-Jacobi method first proposed by Brown and York for defining quasilocal quantities such as energy for spatially bound regions assumes that the spatial boundary is orthogonal to the foliation of the spacetime. Such a…
Relevant physical phenomena are described by nonlinear Schr\"odinger equations with non-vanishing conditions at infinity. This paper investigates the respective 2D and 3D Cauchy problems. Local well-posedness in the energy space for…
We consider the semi-linear, defocusing wave equation $\partial_t^2 u - \Delta u = -|u|^{p-1} u$ in $\mathbb{R}^d$ with $1+4/(d-1)\leq p < 1+4/(d-2)$. We generalize the inward/outward energy theory and weighted Morawetz estimates in 3D to…