Spatiotemporal Regimes in the Kuramoto–Battogtokh System of Nonidentical Oscillators

Journal of Experimental and Theoretical Physics - We consider the spatiotemporal states of an ensemble of nonlocally coupled nonidentical phase oscillators, which correspond to different regimes of...     

Phase Turbulence in the Complex Ginzburg-Landau Equation via Kuramoto–Sivashinsky Phase Dynamics

We study the Complex Ginzburg-Landau initial value problem for a complex field uC, with ,R. We consider the Benjamin–Feir linear instability region We show that for all and for all initial data u₀ sufficiently close to 1 (up to a global phase factor eⁱ₀,₀R) in the appropriate space, there exists a unique (spatially) periodic solution of space period L₀. These solutions are small even perturbations of the traveling wave solution, and s, have bounded norms in various L^p and Sobolev spaces. We prove that apart from corrections whenever the initial data satisfy this condition, and that in the linear instability range the dynamics is essentially determined by the motion of the phase alone, and so exhibits phase turbulence. Indeed, we prove that the phase satisfies the Kuramoto–Sivashinsky equation for times while the amplitude 1+² s is essentially constant.Supported in part by the Fonds National Suisse.     

On the Acid–Base State of the Surface of Semiconductor Components of the ZnSe–CdS System Exposed to Different Media

Using the methods of hydrolytic adsorption, mechanochemistry, and nonaqueous conductometric titration, the acid–base properties of the surfaces of binary semiconductors and solid solutions of the ZnSe?CdS system are studied. The nature of acid sites, and the extent, character, and mechanism of the surface (absorption) interaction are established. The interrelationships in the changes of the acid–base and bulk physical properties upon changing the chemical composition are determined, which make it possible to draw conclusions that are fundamentally important in scientific and practical aspects.     

The Most Effective Model for Describing the Universal Behavior of a Noisy Kuramoto–Sivashinsky Equation as a Paradigmatic Model

We study a noisy Kuramoto–Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar–Parisi–Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation.     

Stability of Circular Orbits in General Relativity: a Phase Space Analysis

Phase space method provides a novel way for deducing qualitative features of nonlinear differential equations without actually solving them. The method is applied here for analyzing stability of circular orbits of test particles in various physically interesting environments. The approach is shown to work in a revealing way in Schwarzschild spacetime. All relevant conclusions about circular orbits in the Schwarzschild-de Sitter spacetime are shown to be remarkably encoded in a single parameter. The analysis in the rotating Kerr black hole readily exposes information as to how stability depends on the ratio of source rotation to particle angular momentum. As a wider application, it is exemplified how the analysis reveals useful information when applied to motion in a refractive medium, for instance, that of optical black holes.     

Bifurcation Cascades and Self-Similarity of Periodic Orbits with Analytical Scaling Constants in Hénon–Heiles Type Potentials

We investigate the isochronous bifurcations of the straight-line librating orbit in the Hénon–Heiles and related potentials. With increasing scaled energy e, they form a cascade of pitchfork bifurcations that cumulate at the critical saddle-point energy e=1. The stable and unstable orbits created at these bifurcations appear in two sequences whose self-similar properties possess an analytical scaling behavior. Different from the standard Feigenbaum scenario in area preserving two-dimensional maps, here the scaling constants and corresponding to the two spatial directions are identical and equal to the root of the scaling constant that describes the geometric progression of bifurcation energies e_n in the limit n. The value of is given analytically in terms of the potential parameters.     

Present Status of the Bethe–Salpeter Approach in Minkowski Space

Recently developed methods allowing to find the solutions of the Bethe–Salpeter equations in Minkowski space, both for the bound and scattering states, are reviewed. For the bound states, one obtains the bound state mass and the corresponding BS amplitude. For the scattering states, the phase shifts (complex above the meson creation threshold) and the half-off-shell BS amplitude are found. Using these solutions, the elastic and transition electromagnetic form factors are calculated.     

Friction Force and Radiative Heat Exchange in a System of Two Parallel Plates in Relative Motion: Corollaries of the Levine–Polevoi–Rytov Theory

Physics of the Solid State - It has been shown that the fundamental results obtained in the works by Levine–Polevoi–Rytov (1980) and Rytov (1990) adequately describe the rate of...     

Global Wellposedness in the Energy Space for the Maxwell-Schrödinger System

We prove that the Maxwell-Schrödinger system in \({\mathbb{R}^{3+1}}\) is globally well-posed in the energy space. The key element of the proof is to obtain a short time wave packet parametrix for the magnetic Schrödinger equation, which leads to linear, bilinear and trilinear estimates. These, in turn, are extended to larger time scales via a bootstrap argument.     

Formation of Composites in the System of Organic Europium Complexes–Silica

Lanthanide doped sol–gel glasses are an attractive type of luminescent material which can be processed at ambient temperatures. However, it is very difficult to obtain a uniform distribution of the complexes in glass materials because of their strong tendency to cluster formation. This problem can be solved by covalently linking of lanthanide complexes to silica matrix. In our work such materials were obtained by the sol–gel method of hydrolysis and polycondensation of tetramethoxysilane with europium complexes containing trimethoxysilyl groups. For this purpose we synthesized a novel ligand — (N-3-trimethoxysilylpropyl)-N′-1,10-phenanthroline-5-yl-thiocarbamide — and corresponding complexes [Eu(tta)₃phen′]Cl₃ and [Eu(pta)₃phen′]Cl₃. Our approach enabled us to simplify the synthetic procedure. A number of uniform samples showing intense luminescence have been obtained and the concentration dependence of their luminescence has been studied.     

Investigation of the Three-Nucleon System Dynamics in the Deuteron–Proton Breakup Reaction

Precise and large sets of cross section, vector A _x , A _y and tensor A _xx , A _xy , A _yy analyzing power data for the ¹ H(d, pp)n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the SALAD and BINA detectors at KVI and the Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon system dynamics. The cross section data reveal a sizable three-nucleon force (3NF) and Coulomb force influence. In case of the analyzing powers very low sensitivity to these effects was found and the data are well describe by 2N models only. For A _xy at 130 MeV, serious disagreements were observed when 3NF models are included in the calculations.     

Acoustics of the Great Hall of the Moscow State Conservatory after reconstruction in 2010–2011

The Great Hall of the Moscow State Conservatory was built in the early 20th century. For more than 100 years of service, it had a high acoustic reputation both among musicians and audience. By the beginning of the 21st century, the hall was in nearly critical condition. Thus, major renovation was needed. In terms of architectural acoustics, the main task was to keep the good acoustics of the hall. This paper presents the results of acoustic parameter measurements of the hall after Reconstruction in 2010–2011. The parameters of the hall measured before and after reconstruction are also compared. The comparative acoustic characteristics between the Great Hall and world leading concert halls are given.     

Solving the Bethe–Salpeter Equation in Euclidean Space

Different approaches to solve the spinor–spinor Bethe–Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.