Related papers: Incompressible topological solitons
We identify infinite classes of potentials for which the Coleman instantons do not exist. For these potentials, the decay of a false vacuum must be described by the new instantons introduced in [7,8].
This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior…
We discuss phenomenology of quantum vacuum. Phenomenology of macroscopic systems has three sources: thermodynamics, topology and symmetry. Thermodynamics of the self-sustained vacuum allows us to treat the problems related to the vacuum…
Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such…
A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes…
We study soliton solutions in 1+1 dimensional gauged sigma models, obtained by dimensional reduction from its 2+1 dimensional counterparts. We show that the Bogomol'nyi bound of these models can be expressed in terms of two conserved…
We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in $R^n$, n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in…
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
We construct a family of smooth charged bubbling solitons in $\mathbb{M}^4 \times$T$^2$, four-dimensional Minkowski with a two-torus. The solitons are characterized by a degeneration pattern of the torus along a line in $\mathbb{M}^4$…
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
The evolution of a pair of point vortices in whole space, subject to the inviscid Euler equations for incompressible fluid flow, is solved exactly for rotationally symmetric initial conditions. This exact solution shows that the vortex…
In this letter the nontopological scalar solitons with a self-interaction potential are investigated in a static de Sitter spacetime and their field equations are derived. In particular, with series expansion we prove analytically the…
Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the…
We consider two types of "dimension bubbles", which are viewed as 4d nontopological solitons that emerge from a 5d theory with a compact extra dimension. The size of the extra dimension varies rapidly within the domain wall of the soliton.…
We show that in tilting perfect fluid cosmological models with an ultra-radiative equation of state, generically the tilt becomes extreme at late times and, as the tilt instability sets in, observers moving with the tilting fluid will…
We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible…
We construct topological soliton solutions describing baryonic tubes and layers with modulation in the $SU(2)$ non-linear sigma model coupled with $\omega$-mesons in $3+1$ dimensions. Using appropriate As\"antze for the pionic matter field…
We study the scattering properties of topological solitons on obstructions in the form of holes and barriers. We use the 'new baby Skyrme' model in (2+1) dimensions and we model the obstructions by making the coefficient of the baby skyrme…
We derive a precise estimate on the volume growth of the level set of a potential function on a complete noncompact Riemannian manifold. As applications, we obtain the volume growth rate of a complete noncompact self-shrinker and a gradient…
In this paper, we study the lifespan and continuation criteria of several two-dimensional incompressible fluid models. Motivated by a novel energy-vorticity formulation, combining linear transport estimate and a bootstrap argument, we are…