Related papers: Irregular traces of multiple SLE(0) systems with m…
We develop a theory of multiple radial SLE(0) -- a smooth system of curves in a simply connected domain $\Omega$ with marked boundary points $z_1, \ldots, z_n \in \partial \Omega$ and a marked interior point $q$ -- arising as the…
We consider multiple radial SLE curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by…
We develop a theory for the multiple radial $\mathrm{SLE}(\kappa)$ systems with parameter $\kappa > 0$ -- a family of random multi-curve systems in a simply connected domain $\Omega$, with marked boundary points $z_1, \ldots, z_n \in…
Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…
We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
In this paper we answer positively a question of whether it is possible for a circle diffeomorphism with breaks to be smoothly conjugate to a rigid rotation in the case when its breaks are lying on pairwise distinct trajectories. An example…
Tracking of rotation and translation of medical instruments plays a substantial role in many modern interventions. Traditional external optical tracking systems are often subject to line-of-sight issues, in particular when the region of…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The…
The two-point function of the conserved traceless spin-$\ell$ currents which are constructed from the scalar field $\sigma(z)$ is evaluated and renormalized by a dimensional regularization procedure. The anomaly is managed to arise only in…
The spectrum of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their…
We numerically study trajectories of spiral-wave-cores in excitable systems modulated proportionally to the integral of the activity on the straight line, several or dozens of equi-spaced measuring points on the straight line, the…
We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational function lead to explicit formulas for the dynamical system…
We investigate spatial reflection and associated nonlocal order in spin chain quantum systems. The proposed string order parameters, e.g., reflected via operations of the spatial reflection or combinations of it with spin reflection, are…
The spin-orbital polarization of superconducting excitations in momentum space is shown to provide distinctive marks of unconventional pairing in the presence of inversion symmetry breaking.Taking the prototypical example of an electronic…
Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which these patterns…
Using one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low energy dynamics in the gapless phase through bosonization and…
We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…
In this paper the collective dynamics of $N$-coupled piecewise linear (PWL) systems with different number of scrolls and coupled in a master-slave sequence configuration is studied, i.e. a ring connection with unidirectional links.…