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Motivated by the theoretical observation that isotropic chirality can exist even in completely random systems, we design a dielectric metamaterial consisting of a random colloid of meta-atoms, which exhibits unprecedentedly high isotropic…
We consider generalized $\alpha$-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincar\'e disk $\mathbb{D}$, such surfaces include the hyperbolic…
The multipole expansion has found limited applicability for optical dielectric resonators in inhomogeneous environment, such as on the surface of substrates. Here, we generalize the method of images to multipole analysis for light…
The existence of generalised global supersolutions with a control upon the total mass is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that…
The bulk spectrum of a possible Chern insulator on a quasicrystalline lattice is examined. The effect of being a 2D insulator seems to override any fractal properties in the spectrum. We compute that the spectrum is either two continuous…
A three-dimensional integrable generalization of the St\"ackel systems is proposed. The classification of such systems is obtained which results in two families. The first one is the direct sum of the two-dimensional case which is…
We review some known results on the superintegrability of monopole systems in the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT spaces. We show that these results can be extended to certain curved backgrounds…
Polar dielectrics with low crystal symmetry and sharp phonon resonances can support hyperbolic shear polaritons - highly confined surface modes with frequency-dependent optical axes and asymmetric dissipation features. So far, these modes…
We develop a time-domain numerical framework for global scalar wave scattering in Minkowski spacetime. The main contribution is an exact conformal matching of three compactified regions: a past hyperboloidal domain attached to $\mathscr…
The generalized deformed oscillator schemes introduced as unified frameworks of various deformed oscillators are proved to be equivalent, their unified representation leading to a correspondence between the deformed oscillator and the N=2…
Considered is a worldsheet supersymmetric generalization of the D=3 Ferber--Schirafuji twistor--superparticle action.
The analytical solutions for the general-four-wave-mixing hyperpolarizabilities $\chi^{(3)}(-(w_1+w_2+w_3);w_1,w_2,w_3)$ on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained…
We propose quasiperiodic heterostructures associated with the tessellations of the unit disk by regular hyperbolic triangles. We present explicit construction rules and explore some of the properties exhibited by these geometric-based…
We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up…
Quasi-two-dimensional (2D) systems, such as an electron gas confined in a quantum well, are important model systems for many-body theories. Earlier studies of the crossover from 3D to 2D in ground-state density-functional theory showed that…
We propose the superintegrable generalization of Smorodinsky-Winternitz system on the $N$-dimensional complex Euclidian space which is specified by the presence of constant magnetic field. We find out that in addition to $2N$ Liouville…
The higher-order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals) a third integral of higher-order in the momenta that can be obtained as the…
Recently a hypothesis explaining the non-resonant mechanism of subwavelength imaging granted by a dielectric microsphere has been suggested. In accordance to the hypothesis, the far-field image of a subwavelength scatterer strongly coupled…
We present computer simulations of a system of purely repulsive soft colloidal particles interacting via the Hertz potential and constrained to a two-dimensional plane. This potential describes the elastic interaction of weakly deformable…
Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can be constructed by Staeckel transform. In this paper a…