Related papers: Relaxing the Geodesic Rule in Defect Formation Alg…
We examine the basic assumptions underlying a scenario due to Kibble that is widely used to estimate the production of topological defects. We argue that one of the crucial assumptions, namely the geodesic rule, although completely valid…
In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in arXiv:1209.5461. We intend to make the construction…
We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum $P(k) \propto k^n$, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over…
The phenomenon of sediment pattern formation in a channel flow is numerically investigated by performing simulations which resolve all the relevant scales of the problem. The numerical approach employed and the flow configuration considered…
We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…
We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the…
The paper presents the first rigorous error analysis of an unfitted finite element method for a linear parabolic problem posed on an evolving domain $\Omega(t)$ that may undergo a topological change, such as, for example, a domain…
We study the geodesic motion of test particles in the space-time of two Abelian-Higgs strings interacting via their magnetic fields. These bound states of cosmic strings constitute a field theoretical realization of p-q-strings which are…
Making use of the wealth of new observational data coming from the sky it is possible to constrain particle physics theories beyond the Standard Model. One way to do this is illustrated in this article: a subset of theories admits cosmic…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
We carry out three-dimensional numerical simulations to investigate the formation rate of semilocal strings. We find that the back-reaction of the gauge fields on the scalar field evolution is substantial, and leads to a significant…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from…
Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. The…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
In this note, we study the deformation of the topological string by $\bar\Omega$. Namely, adopting the perturbative string amplitudes approach, we identify the $\bar\Omega$-deformation in terms of a physical state in the sting spectrum. We…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness; computing shortest paths or geodesics yields measures of network connectivity that can…