Related papers: Phase transitions with bounded index: Parallels to…
We show that the sum of the Morse index and the nullity of Willmore immersions of bounded energy is lower semi-continuous without assuming that the limiting immersion and the bubbles are free of branch points. Our proof is based on a…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
The coexistent physics of de Rham-Gabada-dze-Tolley (dRGT) massive black holes and holographic massive black holes is investigated in the extended phase space where the cosmological constant is viewed as pressure. Van der Waals like phase…
We establish the lower semi continuity of the Morse index and the upper continuity of the Morse Index plus nullity of sequences of critical points of the Sacks-Uhlenbeck type relaxation of the Yang-Mills Energy in 4 dimension. The result is…
This paper is concerned with the existence and uniqueness of transition fronts of a general reaction-diffusion-advection equation in domains with multiple branches. In this paper, every branch in the domain is not necessary to be straight…
We present a general recipe to describe topological phase transitions in condensed matter systems with interactions. We show that topological invariants in the presence of interactions can be efficiently calculated by means of a…
We study stable solutions to the fractional Allen-Cahn equation \linebreak $(-\Delta)^{s/2} u = u-u^3$, $|u|<1$ in $\mathbb{R}^n$. For every $s\in (0,1)$ and dimension $n\geq 2$, we establish sharp energy estimates, density estimates, and…
In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and…
In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to the definition of Morse index when allowing for a contact…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
We study solutions of the 2D Ginzburg-Landau equation -\Delta u+\frac{1}{\ve^2}u(|u|^2-1)=0 subject to "semi-stiff" boundary conditions: the Dirichlet condition for the modulus, |u|=1, and the homogeneous Neumann condition for the phase.…
Is it possible to obtain unbounded minimal surfaces in certain asymptotically flat 3-manifolds as a limit of solutions to a natural mountain pass problem with diverging boundaries? In this work, we give evidence that this might be true by…
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle…
We prove lower bounds for energy in the Gaussian core model, in which point particles interact via a Gaussian potential. Under the potential function $t \mapsto e^{-\alpha t^2}$ with $0 < \alpha < 4\pi/e$, we show that no point…
We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the…
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one…
We study a solution of the Einstein's equations generated by a self-gravitating, anisotropic, static, non-singular matter fluid. The resulting Schwarzschild like solution is regular and accounts for smearing effects of noncommutative…
We show that if two 4-dimensional metrics of arbitrary signature on one manifold are geodesically equivalent (i.e., have the same geodesics considered as unparameterized curves) and are solutions of the Einstein field equation with the same…
A key question in the study of N=2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound…
In the current work we revisit the pair-potential recently proposed by Wang et al. (Phys. Chem. Chem. Phys. 10624, 22, 2020) as a well defined finite-range alternative to the widely used Lennard-Jones interaction model. The advantage of…