Related papers: Morse theory for the Allen-Cahn functional
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 justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use…
We develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single impurity Anderson Hamiltonian. The…
We study the gradient flow of the Allen-Cahn equation with fixed boundary contact angle in Euclidean domains for initial data with bounded energy. Under general assumptions, we establish both interior and boundary convergence properties for…
This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid,…
In this work, we study a matrix-valued Allen-Cahn equation with a Saint Venant-Kirchhoff potential $F(\mathbf{A})=\frac{1}{4}\|\mathbf{A}\mathbf{A}^\top-\mathbf{I}\|^2$. Our approach employs the modulated energy method together with weak…
Let $\Gamma$ be a compact codimension-two submanifold of $\mathbb{R}^n$, and let $L$ be a nontrivial real line bundle over $X = \mathbb{R}^n \setminus \Gamma$. We study the Allen--Cahn functional, \[E_\varepsilon(u) = \int_X \varepsilon…
The total energy and action, which is stored in the flux-tube between a static quark-antiquark pair, can be compared with the potential of the pair with the help of two low energy theorems. The flux-tube and the potential are calculated in…
We consider low-energy nucleons at next-to-next-to-leading order in lattice chiral effective field theory. Three-body interactions first appear at this order, and we discuss several methods for determining three-body interaction…
A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…
The effective field theory relevant for the analysis of QCD at low energies is reviewed. The foundations of the method are discussed in some detail and a few illustrative examples are described.
This work describes the development of a third-generation charge optimized many-body (COMB3) potential for Al-C and its application to the investigation of aluminum/graphene nanostructures. In particular, the new COMB3 potential was used to…
In this paper we find solutions $u_\epsilon$ to a certain class of vector-valued parabolic Allen-Cahn equation that as $\epsilon \to 0$ develops as interface a given triod evolving under curve shortening flow.
We introduce an Allen-Cahn type functional, $\text{BE}_{\epsilon}$, that defines an energy on separating hypersurfaces, $Y$, of closed Riemannian Manifolds. We establish $\Gamma$-convergence of $\text{BE}_{\epsilon}$ to the area functional,…
Using McMahon pseudo-metrics, for any minimal semiflow admitting an invariant measure, we study the relationships between its equicontinuous structure relation, regionally proximal relation and Veech's relations; and characterize its…
Prior work using gauge/gravity duality has established the existence of a quantum critical point in the phase diagram of 3+1-dimensional gauge theories at finite charge density and background magnetic field. The critical theory, obtained by…
The Hamiltonian of electrons interacting with interface phonons in three-barrier resonant tunneling structure is established using the first principles within the models of effective mass and polarization continuum. Using the Green's…
The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the…
We introduce topological invariants of semi-decompositions (e.g. filtrations, semi-group actions, multi-valued dynamical systems, combinatorial dynamical systems) on a topological space to analyze semi-decompositions from a dynamical…
We study Abelian Maxwell-Chern-Simons theory in three-dimensional $AdS$ black hole backgrounds for both integer and non-integer Chern-Simons coupling. Such theories can be derived from various string theory constructions, which we review in…