Yuri Borisovich Gaididei

Analytical solutions of jam pattern formation on a ring for a class of optimal velocity traffic models

A follow-the-leader model of traffic flow on a closed loop is considered in the framework of the extended optimal velocity (OV) model where the driver reacts to both the following and the preceding car. Periodic wave train solutions that describe the formation of traffic congestion patterns are found analytically. Their velocity and amplitude are determined from a perturbation approach based on collective coordinates with the discrete modified Korteweg–de Vries equation as the zero order equation. This contains the standard OV model as a special case. The analytical results are in excellent agreement with numerical solutions.

Stability analysis of static solutions in a Josephson junction

We present all the possible solutions of a Josephson junction with bias current and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results are in terms of elliptic functions for the case of inline geometry, and are in agreement with the numerical calculations, explaining also the strong hysteretic phenomena typically seen in the calculation of the maximum tunnelling current. This suggests a different experimental approach based on the use, instead of the external magnetic field, of the modulus of the elliptic function or the related quantity the total magnetic flux to avoid hysteretic behaviour and unfold the overlapping Imax (H ) curves.

Non-relativistic and relativistic scattering by short-range potentials

Relativistic and non-relativistic scattering by short-range potentials is investigated for selected problems. Scattering by the δ′ potential in the Schrödinger equation and δ potentials in the Dirac equation must be solved by regularization, efficiently carried out by a perturbation technique involving a stretched variable. Asymmetric regularizations yield non-unique scattering coefficients. Resonant penetration through the potentials is found. Approximative Schrödinger equations in the non-relativistic limit are discussed in detail.

Langevin dynamics of conformational transformations induced by the charge–curvature interaction

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular chains may undergo transformation to polygonal shape.

Structure and energy of L and D defects in hydrogen bonded systems

Abstract We studied the protonic structure and energy of a D (or L) defect in a zig-zag hydrogen-bonded system. It is shown that the extra (or missing) proton lowers its energy by creating a polarisation defect to which it is coupled. We used a quantum description with intrasite and intersite tunneling, while taking properly into account the polarisation state of the neighboring bonds.

Domain wall dynamics at the local wire bend

In conclusion, we have presented a general approach of the domain wall dynamics at a wire bend with localized curvature. We have analytically found dependence of domain wall eigen frequency on the curvature. For a certain case of parabolic wire bend we performed full-scale micromagnetic simulations to check our analytical predictions. The results of simulations are in good agreement and demonstrate that the approximation of magnetostatic interaction by the effective easy-tangential anisotropy is physically sound for a domain wall dynamics in the thin nanowires.

Torsion effects in a helix nanowire with easy-tangential anisotropy

In conclusion, we have presented a detailed study of statics and linear dynamics of magnetization in the helix wire with easy-tangential anisotropy. We have described equilibrium magnetization states and present them in form of the phase diagram, see Fig. 2. Also we have shown that the magnon spectrum of the helix wire experiences an asymmetry caused by the torsion.

Bjerrum defects as quantum non-linear excitations of hydrogen bonded systems

It is well established that conductivity, dielectric and elastic relaxation, optical spectra etc in ice and other hydrogen-bonded (HB) systems (one- two and three dimensional)1 is connected with structural imperfections (ionic and Bjerrum D and L) violating the Bernai-Fowler rules2, 3. Here we will study the protonic structure of a D or L defect and consider the dominant effect which is the intrasite and intersite tunneling of the protons but taking properly into account the polarisation state of the environment in the sense discussed below. We will consider a zig-zag HB molecular chain model (see Fig.1) of a Bernai-Fowler filament2. As a Bjerrum-like defect we will consider a situation when there are two protons (or lack of it) on the line between two adjacent heavy atoms which we will suppose to be immobile, and the protons are quantum particles. The ground state wavefunction and energy of the HB chain with one D (L) defect is calculated and it is shown that the appearence of D (L) defect is accompanied by the creation of ionic defect bounded to the D (L) defect.

Orientational L, D and polarisation defects as coupled quantum non-linear excitations in hydrogen-bonded systems

Abstract We have studied the proton structure and energy of a d (or an l ) defect in a zig-zag hydrogen-bonded system. It is shown that the extra (or missing) proton lowers its energy by creating a polarisation defect to which it is coupled. We used a quantum description with intrasite and intersite tunneling, while taking into account the polarisation state of the neighboring bonds. In the case of a localised defect a comparison is made with classical double-well potential results.