Related papers: Some basic facts on the system \Delta u - W_u (u) …
A free-energy minimization approach is used to address the secular & dynamical instabilities & the bifurcations along sequences of rotating, self-gravitating fluid and stellar systems. Our approach stems from the Landau-Ginzburg theory of…
We introduce a generic, parallel Wang-Landau method that is naturally suited to implementation on massively parallel, petaflop supercomputers. The approach introduces a replica-exchange framework in which densities of states for overlapping…
A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their…
A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``positive" and ``negative") set of flows. Special solutions…
We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\to 0$, the ground state at general rational filling fraction is a crystal with a gap--a Tao-Thouless state. For filling fractions…
In this paper, first we study carefully the positive solutions to $\Delta u+\lambda_{1}u\ln u +\lambda_{2}u^{b+1}=0$ defined on a complete noncompact Riemannian manifold $(M, g)$ with $Ric(g)\geq -Kg$, which can be regarded as…
We derive constraints on the form of the renormalized stress tensor for states on Kerr space-time based on general physical principles: symmetry, the conservation equations, the trace anomaly and regularity on (sections of) the event…
We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features.…
We describe the asymptotic behavior of critical points of $\int_{\Omega} [(1/2)|\nabla u|^2+W(u)/\varepsilon^2]$ when $\varepsilon\to 0$. Here, $W$ is a Ginzburg-Landau type potential, vanishing on a simple closed curve $\Gamma$. Unlike the…
Given a field $\{B(x)\}_{x\in\mathbf{Z}^d}$ of independent standard Brownian motions, indexed by $\mathbf{Z}^d$, the generator of a suitable Markov process on $\mathbf{Z}^d,\,\,\mathcal{G},$ and sufficiently nice function…
The basic Landau model for the incommensurate-commensurate transition to the uniform or dimerized uniaxial ordering is critically reexamined. The previous analyses identified only sinusoidal and homogeneous solutions as thermodynamically…
Ginzburg-Landau theory describes phase transitions as the competition between energy and entropy: The ordered phase has lower energy, while the disordered phase has larger entropy. When heating the system, ordering is reduced entropically…
We investigate, on a bounded domain $\Omega$ of $\R^2$ with fixed $S^1$-valued boundary condition $g$ of degree $d>0$, the asymptotic behaviour of solutions $u_{\varepsilon,\delta}$ of a class of Ginzburg-Landau equations driven by two…
Let $x$ be a cyclic sequence of $n$ elements of the finite field $\mathbb{F}_q$ (the first element immediately follows the $n$-th one). Let us define the operation $\Delta$ as the transition from $x$ to the sequence of differences of the…
For $n\ge 3$ and $0<\epsilon\le 1$, let $\Omega\subset\mathbb R^n$ be a bounded smooth domain and $u_\epsilon:\Omega \subset\R^n\to \mathbb R^2$ solve the Ginzburg-Landau equation under the weak anchoring boundary condition: $$\begin{cases}…
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…
The Ginzburg-Landau-Wilson theory that describes the disordered Fermi liquid - d-wave superconductor phase transition at zero temperature is derived at weak coupling. The theory represents an interacting dissipative system of bosonic Cooper…
Spontaneous scalarization phenomenon in scalar-tensor gravity is known to be a form of phase transition, and it was recently shown that the order of this transition changes depending on the parameters of the theory. There exists a…
We consider the 4$d$ mass-energy double critical NLS \[ (i\partial_t+\Delta)u = -|u|^2 u + |u| u. \] In Luo (2024) and Cheng--Miao--Zhao (2016), the authors established a scattering/blowup dichotomy for solutions satisfying the energy…
We study a massless Dirac particle with PT symmetric non-Hermitian Rashba interaction in the background of Dirac oscillator potential to show the PT phase transition in a (2+1) dimensional relativistic system analytically. PT phase…