Related papers: The Cost of Two-dimensional Rearrangement
Searching for novel two-dimensional (2D) materials is crucial for the development of the next generation technologies such as electronics, optoelectronics, electrochemistry and biomedicine. In this work, we designed a series of 2D materials…
We study a self-interacting scalar $\varphi^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the counterterms required by one-loop renormalization. We discuss higher loops in two…
We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.
A dipole picture of high energy scattering is developed in the 2+1 dimensional QCD, following Mueller. A generalized integral equation for the dipole density with a given separation and center of mass position is derived, and meson-meson…
Dielectronic recombination resonance strengths, energy-differential cross sections, and recombination rate coefficients are calculated fully relativistically for Fe$^{2+}$ ions. The ground-state and resonance energies are determined using…
In this paper we use complex techniques to study the structure of real Henon diffeomorphisms of maximal topological entropy.
A twist is a datum playing a role of a local system for topological $K$-theory. In equivariant setting, twists are classified into four types according to how they are realized geometrically. This paper lists the possible types of twists…
Presented is a primary step towards quantization of infinitesimal rigid body moving in a two-dimensional manifold. The special stress is laid on spaces of constant curvature like the two-dimensional sphere and pseudosphere (Lobatschevski…
We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…
Toroidal templates such as vesicles with hexatic bond orientational order are discussed. The total energy including disclination charges is explicitly computed for hexatic order embedded in a toroidal geometry. Related results apply for…
Parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena. In this paper we consider parabolic bifurcations of families of diffeomorphisms in two complex dimensions. Specifically we…
It is argued that the dynamics of the elastic scattering of high-energy protons at intermediate transferred momenta changes with the energy increase. It evolves from the multiple scattering at the external layer for energies about 10 GeV to…
In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can…
A two-dimensional binary composite system composed of ellipse inclusions and a host medium is considered. Dielectric permittivity of the system is calculated as a function of orientation angle, the volume fraction of the inclusions and…
We provide an arithmetic condition weaker then the Bryuno condition for which it is possible to apply a KAM scheme in dimension greater then one. The KAM scheme will be provided in the setting of linearization of analytic diffeomorphisms of…
Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale…
There exists a smooth foliation with 3 singular points on the two-dimensional torus such that any lifting of a leaf of this foliation on the universal covering of the torus is a dense subset of the covering.
We investigate two-loop higher-order binding corrections to the fine structure, which contribute to the spin-dependent part of the Lamb shift. Our calculation focuses on the so-called ``two-loop self-energy'' involving two virtual closed…
In two-dimensional decaying homogeneous isotropic turbulence, kinetic energy and enstrophy are respectively transferred to larger and smaller scales. In such spatiotemporally complex dynamics, it is challenging to identify the important…
In this paper we give an algebraic description of fundamental groups of orbits of circle-valued smooth functions from some subspace of the space of smooth functions with isolated singularities on $2$-torus $T^2$ with respect to the action…