Instability of the finite‐difference split‐step method applied to the nonlinear Schrödinger equation. I. standing soliton

We consider numerical instability that can be observed in simulations of solitons of the nonlinear Schrödinger equation (NLS) by a split‐step method (SSM) where the linear part of the evolution is solved by a finite‐difference discretization. The von Neumann analysis predicts that this method is unconditionally stable on the background of a constant‐amplitude plane wave. However, simulations show that the method can become unstable on the background of a soliton. We present an analysis explaining this instability. Both this analysis and the features and threshold of the instability are substantially different from those of the Fourier SSM, which computes the linear part of the NLS by a spectral discretization. For example, the modes responsible for the numerical instability are not similar to plane waves, as for the Fourier SSM or, more generally, in the von Neumann analysis. Instead, they are localized at the sides of the soliton. This also makes them different from “physical” (as opposed to numerical) unstable modes of nonlinear waves, which (the modes) are localized around the “core” of a solitary wave. Moreover, the instability threshold for thefinite‐difference split‐step method is considerably relaxed compared with that for the Fourier split‐step. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1002–1023, 2016     

Comparison of strange baryon production at LEP with various models

The strange baryon production rates measured at LEP are compared to several models: isospin, LPHD, QCM, Jetset, Herwig and MOPS. In particular, the parameters of the new MOPS model are adjusted in an attempt to reproduce the spin and strangeness dependence of the observed rates. Received: 8 April 1998 / Revised version: 27 August 1998 / Published online: 19 November 1998     

Separation of variables in anisotropic models and non-skew-symmetric elliptic <Emphasis Type="Italic">r</Emphasis>-matrix

We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic \(so(3)\otimes so(3)\)-valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the “separating functions” B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler’s top, Steklov–Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and “spin” generalization of Steklov–Lyapunov model.     

Classifying homeomorphism groups of infinite graphs

In this paper, we classify topologically the homeomorphism groups H(Γ) of infinite graphs Γ with respect to the compact-open and the Whitney topologies.     

On functors preserving skeletal maps and skeletally generated compacta

A map $f:X\to Y$ between topological spaces is skeletal if the preimage $f^{?1}(A)$ of each nowhere dense subset $A?Y$ is nowhere dense in X. We prove that a normal functor $F:\mathbf{Comp}\to \mathbf{Comp}$ is skeletal (which means that F preserves skeletal epimorphisms) if and only if for any open surjective map $f:X\to Y$ between metrizable zero-dimensional compacta with two-element non-degeneracy set $N^f=\{x\in X:|f^{?1}(f(x))|>1\}$ the map $Ff:FX\to FY$ is skeletal. This characterization implies that each open normal functor is skeletal. The converse is not true even for normal functors of finite degree. The other main result of the paper says that each normal functor $F:\mathbf{Comp}\to \mathbf{Comp}$ preserves the class of skeletally generated compacta. This contrasts with the known ??epin?s result saying that a normal functor is open if and only if it preserves the class of openly generated compacta.     

Low-power,phase-preserving 2R amplitude regenerator

We propose a modification of a NALM-based 2R regenerator of phase-encoded signals which operates at considerably lower input powers than was studied earlier. Our modification consists of replacing the core-matched and lossless fiber coupler in the NALM by a coupler with a propagation constant mismatch and loss asymmetrically distributed between the two cores. The performance of the modified regenerator and the one studied earlier is approximately the same.     

Heterogeneous oligomerization catalysts: properties and efficiency

A number of heterogeneous acid type catalysts of silica-alumina nature, which are proposed to be used for petrochemistry by-product oligomerization, have been investigated. Particularly, such key indicators as active site concentration and strength have been determined. These parameters have been determined by the method based on potentiometric titration that is relatively seldom used in heterogeneous catalysis. The number of active site types present in investigated catalysts, as well as concentrations of each type of site, has been determined by mathematical processing of potentiometric titration data. The sequence of mathematical processing of titration data is described. The relationship between the properties of the investigated catalysts and their effectiveness in heterogeneous catalytic cooligomerization of the C₉ fraction of liquid products of diesel fuel pyrolysis has been analyzed. The relationships between yields achieved in the presence of various catalysts and the properties of these catalysts have been defined. Namely, it was determined that the product yield is almost proportional to the active site??s concentration of the catalysts (activated clay materials). The relationship between the strength of active sites and average molecular weight of the cooligomers has been found. The causes of obtained regularities have been analyzed and explained.      

Nanostructured diamine-fullerene derivatives: computational density functional theory study and experimental evidence for their formation via gas-phase functionalization

Nanostructure derivatives of fullerene C(60) are used in emerging applications of composite matrices, including protective and decorative coating, superadsorbent material, thin films, and lightweight high-strength fiber-reinforced materials, etc. In this study, quantum chemical calculations and experimental studies were performed to analyze the derivatives of diamine-fullerene prepared by the gas-phase solvent-free functionalization technique. In particular, the aliphatic 1,8-diamino-octane and the aromatic 1,5-diaminonaphthalene, which are diamines volatile in vacuum, were studied. We addressed two alternative mechanisms of the amination reaction via polyaddition and cross-linking of C(60) with diamines, using the pure GGA BLYP, PW91, and PBE functionals; further validation calculations were performed using the semiempirical dispersion GGA B97-D functional which contains parameters that have been specially adjusted by a more realistic view on dispersion contributions. In addition, we looked for experimental evidence for the covalent functionalization by using laser desorption/ionization time-of-flight mass spectrometry, thermogravimetric analysis, and atomic force microscopy.