Related papers: Vortex configurations in SO(3) \times Z(2)
Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is…
We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
We study the spontaneously broken phase of the $XY$ model in three dimensions, with boundary conditions enforcing the presence of a vortex line. Comparing Monte Carlo and field theoretic determinations of the magnetization and energy…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
In this work, we employ the $SO(2)$-rotations of a two-component, one-, two- and three-dimensional nonlinear Schr\"{o}dinger system at and near the Manakov limit, to construct vector solitons and vortex structures. This way, stable…
Tracking and forecasting the rotation of objects is fundamental in computer vision and robotics, yet SO(3) extrapolation remains challenging as (1) sensor observations can be noisy and sparse, (2) motion patterns can be governed by complex…
We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a…
We present results for the heavy quark potential computed in SU(3) from magnetic monopoles and from center vortices. The monopoles are identified after fixing SU(3) lattice configurations to the maximal abelian gauge. The center vortices…
We show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topological solitons which have only a slightly higher energy than ordinary vortices. Therefore they can be induced by…
This paper presents a spatially and temporally adaptive boundary condition to specify the volumetric flux for lattice Boltzmann methods. The approach differs from standard velocity boundary conditions because it allows the velocity to vary…
We examine the $N$-vortex problem on general domains $\Omega\subset\mathbb{R}^2$ concerning the existence of nonstationary collision-free periodic solutions. The problem in question is a first order Hamiltonian system of the form $$…
We consider a gauged $CP(2)$ theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the…
We investigate some properties of thick vortices and thick monopoles in the SU(2) lattice gauge theory by inserting operators which create these excitations. Some quantities associated with the dynamical behaviour of thick vortices and…
We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…
Our understanding of the mechanism by which topological defects are formed in symmetry breaking phase transitions has recently changed. We examine the non-equilibrium dynamics of defect formation for weakly-coupled global O(N) theories…
On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of…
The results of numerical simulation of the interaction of topological solitons (2+1)-dimensional O(3) non-linear sigma model in reversed time are presented. At the first stage, models of interactions of topological vortices are developed,…
We extend product Chern-Simons theory to develop several mixed $U(1)\times U(1)$ models where one gauge field is governed by a Chern-Simons term and the other by a Maxwell or Born-Infeld term. We show that, by choosing suitable potentials,…
We study Z(2) lattice gauge theory on triangulations of a compact 3-manifold. We reformulate the theory algebraically, describing it in terms of the structure constants of a bidimensional vector space H equipped with algebra and coalgebra…