Related papers: Conformal maps and edge mode attenuation on imperf…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
This paper studies the theoretical construction and analytic error estimation of complex Bessel function-based conformal mappings in regions with randomly perturbed boundaries. First, we construct a conformal mapping applicable to such…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…
The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require…
We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites,…
I investigate the scattering properties of transformation devices as the traditional impedance matching criteria are altered. This is demonstrated using simple theory and augmented by numerical simulations that investigate the role of…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
Critical systems are described by conformal field theories, whose dynamics can be exactly solved in two dimensions. In the presence of a boundary, with the so-called method of images it is possible to study the surface critical behaviour of…
Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires…
Motivated by the recent theoretical and experimental progress in implementing topological orders with photons, we analyze photonic systems with different topologies and present a scheme to probe their topological features. Specifically, we…
We study dynamics of the one-dimensional Ising model in the presence of static symmetry-breaking boundary field via the two-time autocorrelation function of the boundary spin. We find that the correlations decay as a power law. We uncover a…
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is…
A two-dimensional water wave model based on conformal mapping is presented. The model is exact in the sense that it does not rely on truncated series expansions, nor suffer any numerical diffusion. Additionally, it is computationally highly…