Related papers: On $\infty$-Ground States in the Plane
Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is…
The gravity-capillary problem with inclined walls is a problem that describes an open fluid flowing over an angled wall. It has broad applications in science and engineering. In this paper, we study the steady states of the two-dimensional…
We study the behavior of a probability measure near the bottom of its support in terms of time averaged quotients of its Laplace transform. We discuss how our results are connected to both rank-one perturbation theory as well as renewal…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
Filtration of real gases described by Peng-Robinson equations of state in 3-dimensional space is studied. Thermodynamic states are considered as either Legendrian submanifolds in contact space, or Lagrangian submanifolds in symplectic…
In the landscape, if there is to be any prospect of scientific prediction, it is crucial that there be states which are distinguished in some way. The obvious candidates are states which exhibit symmetries. Here we focus on states which…
Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by…
We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.
Geometry and topology play a fundamental role in determining pattern formation on 2D surfaces in condensed matter physics. For example, local positive Gaussian curvature of a 2D surface attracts positive topological defects in a liquid…
We examine the formation of localized states on a generalized nonlinear impurity located at, or near the surface of a semi-infinite 2D square lattice. Using the formalism of lattice Green functions, we obtain in closed form the number of…
We study closed smooth convex plane curves $\Gamma$ enjoying the following property: a pair of points $x,y$ can traverse $\Gamma$ so that the distances between $x$ and $y$ along the curve and in the ambient plane do not change; such curves…
To our best knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex…
We consider gravitational perturbation around maximally symmetric background of a theory of gravity involving quadratic curvature correction. This leads to a decoupled model of the standard transverse, traceless graviton mode and an…
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative…
The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in…
A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the…
The distance conjecture diagnoses viable low-energy effective realisation of consistent theories of quantum gravity by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in…
In this work, the behavior of test particles near a domain wall of a stable false vacuum bubble is studied. It is shown that matter is naturally trapped in the vicinity of a static domain wall, and also, that there is a discontinuity in the…