相关论文: The Phase Transition in 5 Point Energy Minimizatio…

We study systems of $n$ points in the Euclidean space of dimension $d \ge 1$ interacting via a Riesz kernel $|x|^{-s}$ and confined by an external potential, in the regime where $d-2\le s<d$. We also treat the case of logarithmic…

The effective potential at finite temperature is constructed within the minimal standard model when a real Higgs singlet is added on. We find that a region of parameter space exists for which one can find a first order transition strong…

For physical systems described by smooth, finite-range and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that unless the equipotential…

We study the thermodynamics and the chemical potential for a five-dimensional charged AdS black hole by treating the cosmological constant as the number of colors $N$ in the boundary gauge theory and its conjugate quantity as the associated…

We analyze transition potentials $(V(r) \stackrel{r\sim 0}{\rightarrow} {\alpha r^{-2}})$ in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range $-1/4 < \alpha < 3/4$, the eigenvalue problem becomes…

We consider the problem of rigorously computing periodic minimizers to the Ohta-Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the…

We study point configurations on the torus $\mathbb T^d$ that minimize interaction energies with tensor product structure which arise naturally in the context of discrepancy theory and quasi-Monte Carlo integration. Permutation sets on…

The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equation has been solved as an unconstrained minimization…

This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…

We study the phase transitions in the simplicial Ising model on hypergraphs, in which the energy within each hyperedge (group) is lowered only when all the member spins are unanimously aligned. The Hamiltonian of the model is equivalent to…

We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical constraint that their union is the subgraph of a function, whose…

Unlike the situation for the 1d Dirac delta derivative Schrodinger pseudo potential (SPP) and the 2d Dirac delta SPP, where the indeterminacy originates from a lack of scale in the first and both a lack of scale as well as the wave function…

We compute the equilibrium measure in dimension d=s+4 associated to a Riesz s-kernel interaction with an external field given by a power of the Euclidean norm. Our study reveals that the equilibrium measure can be a mixture of a continuous…

We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain $\Omega$ with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational…

We consider electrogeodesics on which the energy $E<0$ in the Reissner-Nordstr\"{o}m metric. It is shown that outside the horizon there is exactly one turning point inside the ergoregion for such particles. This entails that such a particle…

In the minimal supersymmetric standard model (MSSM) the one-loop finite-temperature corrections from the squark-Higgs bosons sector are calculated, the effective two-Higgs-doublet potential is reconstructed and possibilities of the…

We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold.…

We prove that a local minimizer of the Ginzburg-Landau energy in ${\mathbb R}^3$ satisfying the condition $\liminf_{R\to\infty}E(u;B_R)/RlnR < 2\pi$ must be constant. The main tool is a new sharp eta-ellipticity result for minimizers in…

The paper deals with minimum energy problems in the presence of external fields with respect to the Riesz kernels $|x-y|^{\alpha-n}$, $0<\alpha<n$, on $\mathbb R^n$, $n\geqslant2$. For quite a general (not necessarily lower semicontinuous)…

Using the delta correction to the standard free energy \cite{bc} in the elastic setting with a quadratic foundation term and some parameters, we introduce a one dimension only model for strong segregation in diblock copolymers, whose sharp…