Related papers: Stefan's problem and beyond
We consider two implicit approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently…
We show how the Lyapunov exponents of a dynamic system can in general be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive…
By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic…
It has been shown that the criticism of Pauli as well as of Susskind and Glogover may be avoided if the standard quantum-mechanical mathematical model has been suitably extended. There is not more any reason for Einstein's citicism, either,…
The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of…
In this paper a one-phase Stefan problem with size-dependent thermal conductivity is analysed. Approximate solutions to the problem are found via perturbation and numerical methods, and compared to the Neumann solution for the equivalent…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
We prove existence and uniqueness of strong solutions to the two-phase Stefan problem with Gibbs-Thomson law where the free interface forms a ninety degree contact angle with the fixed boundary. We also discuss existence of global solutions…
A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered. An integral relationship between the temperature and the free boundary is obtained which is equivalent to the…
In this paper we consider a free boundary problem for the melting of ice where we assume that the heat is transported by conduction in both the liquid and the solid part of the material and also by radiation in the solid. Specifically, we…
We consider the one-dimensional outer stochastic Stefan problem with reflection. The problem admits maximal solutions as long as the velocity of the moving boundary remains bounded, [3,9,10]. We apply Malliavin calculus to the transformed…
We consider the interior Stefan problem under radial symmetry in two dimension. A water ball surrounded by ice undergoes melting or freezing. We construct a discrete family of global-in-time solutions, both melting and freezing scenarios.…
Recently, the authors proved [2] that the Maxwell-Stefan system with an incompressibility-like condition on the total flux can be rigorously derived from the multi-species Boltzmann equation. Similar cross-diffusion models have been widely…
In theories with higher time derivatives, the Hamiltonian analysis of Ostrogradsky predicts an instability. However, this Hamiltonian treatment does not correspond the way that these theories are treated in quantum field theory, and the…
For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer.…
In this paper we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, with periodic boundary conditions respect to the horizontal direction $x_1\in\mathbb{T}$. We prove that the system is…