Related papers: Long-range phase coexistence models: recent progre…
We propose a possible nonlocal approximation of the Willmore functional, in the sense of Gamma-convergence, based on the first variation ot the fractional Allen-Cahn energies, and we prove the corresponding $\Gamma$-limsup estimate. Our…
A Cahn-Hilliard-Allen-Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem w.r.t. the inverse of temperature, we proposed and…
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…
We present approximation methods which lead to law of large numbers and fluctuation results for functionals of $\Lambda$-coalescents, both in the dust-free case and in the case with a dust component. Our focus is on the tree length (or…
This paper deals with existence of solutions to the following fractional $p$-Laplacian system of equations \begin{equation*} %\tag{$\mathcal P$}\label{MAT1} \begin{cases} (-\Delta_p)^s u =|u|^{p^*_s-2}u+…
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore…
The Allen--Cahn equation is one of fundamental equations of phase-field models, while the logarithmic Flory--Huggins potential is one of the most useful energy potentials in various phase-field models. In this paper, we consider numerical…
In this paper we obtain sharp weighted estimates for solutions of the $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p ({\Omega},$\delta$ $\gamma$), $\delta$ being the…
We consider numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computational…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
We give an outlook on the future of coherence theory and many-body quantum dynamics as experiments develop in the arena of ultra-cold atoms. Novel results on quantum heating of center-of-mass temperature in evaporative cooling and…
In the first part of the document I describe in a general way the $\gamma / \phi_3$ extraction and compare the experimental environments. I then switch to the available results from the CDF experiment. In the third part I present early…
In this paper, we study the existence of solutions of the equation $(-\Delta)_1^s u=f$ in a bounded open set with Lipschitz boundary $\Omega\subset \Rn$, vanishing on $\Co \Omega$, for some given $s\in (0,1)$, and asymptotics as $p\to 1$ of…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
The fractional differential equation $L^\beta u = f$ posed on a compact metric graph is considered, where $\beta>0$ and $L = \kappa^2 - \nabla(a\nabla)$ is a second-order elliptic operator equipped with certain vertex conditions and…
We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain $\Omega$ we study solutions to the eigenfunction equation \[ (- \Delta)^s u = \lambda(u- \gamma)_+ \] with $u \equiv 0$ on…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel technique is proposed to estimate the minimum eigenvalue of…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…
In this study, a phase-field lattice Boltzmann model based on the Allen-Cahn equation with a filtered collision operator and high-order corrections in the equilibrium distribution functions is presented. Here we show that in addition to…