Concentration of Hydrogen in the Upper Atmosphere of the Earth in the 300-600 Km Altitude Range According to Ionospheric Data

Concentration of hydrogen in upper atmosphere according to ionospheric dat

Manifestation of reptation motions of macromolecules on diffusional attenuation of the stimulated spin echo signal

The effect of fluctuations in the characteristic time of motion of defects and the length of the force pipe on the diffusional attenuation profile of the spin echo signal in the long wave region is discussed. When the correlation times of these fluctuations are more than the average time of pipe regeneration the diffusional attenuation has an essentially non-exponential character and can be described in terms of a random fluctuating coefficient of self-diffusion. The true coefficient of self-diffusion can be determined from the initial inclination of the diffusional attenuation profile. © 1988

Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur

Viscoelastic properties of linear polymer melts as effect of broken axial symmetry and mutual uncrossability of macromolecules

On the basis of the exact Green-Kubo formula for viscosity it is rigorously shown that the zero-shear viscosity of polymer melts is totally determined by the Fixman stress-tensor which represents interchain interactions. The Curtiss-Bird approximation for the Fixman tensor permits one to consider it as a sum of effectively single chain tensors. Considering an arbitrary conformation of a macromolecule as a state with broken axial symmetry, the mean-field part of the Curtiss-Bird stress tensor can be expressed as a sum of two terms. The first term reflects the local geometry of the chain conformation and is proportional to the local curvature of the polymer chain. It is proportional to the effective intramolecular entropic stress-tensor. The second term, which has been never considered before, reflects global properties of the spatial distribution of the probe chain segments and mutual uncrossability of polymer chains. It is proportional to the concentration gradient of the probe chain segments. This term leads to a molecular-mass independent plateau of the relaxation modulus and gives the same molecular mass dependence for the viscosity and the terminal relaxation time in polymer melts with molecular masses large enough. The plateau modulus is derived as GN 0 ∝ kBT / (ρmŜ2(0)b6), where kBT is the temperature factor, ρm is the Kuhn segment number density, Ŝ(0) is the collective structure factor of polymer melts in the long wavelength limit, and b is the Kuhn segment length. For the Gaussian thread chain model introduced by Schweizer and Curro, the plateau modulus becomes GN 0 ∝ kBT / (ρmb2)3. This expression is in qualitative agreement with well-known experimental data. © 2002 Elsevier Science B.V. All rights reserved

Anomalous relaxation and self-organization in non-equilibrium processes

We study thermal relaxation in ordered arrays of coupled nonlinear elements with external driving. We find, that our model exhibits dynamic self-organization manifested in a universal stretched-exponential form of relaxation. We identify two types of self-organization, cooperative and anti-cooperative, which lead to fast and slow relaxation, respectively. We give a qualitative explanation for the behavior of the stretched exponent in different parameter ranges. We emphasize that this is a system exhibiting stretched-exponential relaxation without explicit disorder or frustration.Comment: submitted to PR

Nuclear spin-lattice relaxation dispersion and segment diffusion in entangled polymers. Renormalized Rouse formalism

A formalism for polymer melts was derived linking the spin-lattice relaxation time T1, the correlation function of chain tangent vectors and the mean-square segment displacement with memory functions. Potential normal-mode number dependences are included. In the limit of infinitely fast decaying memory functions the theory reproduces known expressions characteristic for Rouse dynamics. Interchain excluded-volume forces were taken into account in the frame of the renormalized Rouse approach [K. S. Schweizer, J. Chem. Phys. 91, 5802 (1989)]. The power law limits predicted on this basis are T 1, ∝ω1/2, T1∝ω1/4, and T1∝ω1/5 for the T1 dispersion in a sequence of regimes from high to low frequencies. The mean-square segment displacement obeys 〈r2〉∝t1/4, 〈r2〉∝ t3/8, and 〈r2〉∝2/5 in a sequence of limits for increasing times. The spin-lattice relaxation dispersion of different polymers was studied mainly by the aid of the field-cycling NMR technique. The covered proton frequency range is less than 103 Hz to more than 108 Hz. The frequency dependence can be described by a series of power laws arising from chain dynamics. Two of these, namely T 1∝ω0.5 and T1∝ω0.25 tending to appear at high and low frequencies, respectively, can be perfectly explained on the basis of the derived renormalized Rouse limits. The third power law, T1∝ω0.44, which was observed only at rather low frequencies, has no theoretical counterpart in the frame of the renormalized Rouse theory. Some hints that farther reaching polymer theories such as the mode-mode coupling approach [K. S. Schweizer, J. Chem. Phys. 91, 5822 (1989)] can help to understand this finding are discussed. © 1994 American Institute of Physics

The intra- and intermolecular basis of the zero-shear viscosity in unentangled polymers

A general expression for the zero-shear viscosity in unentangled polymers is derived on the basis of chain pair correlations of normal modes and mutual interaction forces. © 1999 American Institute of Physics

Short-time diffusion behavior of Brownian particles in porous solids

© Kazan Federal University (KFU). The process of self-diffusion of particles confined to porous solids is studied for time intervals corresponding to particle displacements shorter than the characteristic pore size. The solid matrix is modeled as a (random) potential field with an infinitely large potential within the solid which decays to zero at distances of the order of a few particle sizes from the pore walls. Diffusion of particles in the thus created potential field is described by the Smoluchowski diffusion equation. It is shown that, for short diffusion times, the resulting equation for the time-depended diffusivity reproduces that earlier obtained in the literature [Mitra et al., Phys. Rev. Lett. 68, 3555 (1992)], but with the numerical constant differing by factor 2. The conditions under which this discrepancy arises are highlighted and discussed