Electric birefringence study of an amyloid fibril system: The short end of the length distribution

In this article, a system of amyloid fibrils, based on the protein β-lactoglobulin, is studied by transient electric birefringence. Single pulses of an electric field were applied to the solution, and the initial rise and subsequent decay of birefringence analysed. The decay takes place on a range of relaxation times, and therefore contains information about the length distribution of fibrils in the system. The information can be extracted using theories of the electric polarisability of polyelectrolyte rods, since the fibrils are an example of these. Despite the long-standing complications of such theories, useful quantitative information about the system can still be obtained. Using the Fixman model of polyelectrolyte polarisability, we obtain a measurement of the short end of the length distribution which shows the fibril concentration as a function of length rising linearly from 0.02-2 μm. The short end of the length distribution was unobtainable in our previous study using rheo-optics (S.S. Rogers et al., Macromolecules 38, 2948 (2005)), but reasonable agreement between the two techniques shows they are complementary.     

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n > 2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses. PACS Number: 05.20.-y, 02.30.Mv, 66.10.-x, 78.70.Nx, 05.60.Cd     

Two New Classes of Isochronous Hamiltonian Systems

Abstract

An isochronous dynamical system is characterized by the existence of an open domain of initial data such that all motions evolving from it are completely periodic with a fixed period (independent of the initial data). Taking advantage of a recently introduced trick, two new Hamiltonian classes of such systems are identified.     

Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg-de Vries equation

The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence. The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found. Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation) is completely solved. Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999)     

Computational study of cold ions trapped in a double-well potential

We report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence.     

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter – the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A 322, 267 (2003)] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.     

Experimental study of the focusing of submicrosecond pressure pulses in liquids

Experimental data are presented from a study of the focusing of single, submicrosecond pressure pulses in water. The effects of the initial amplitude distribution, the initial pressure level, and the geometric parameters of the opto-acoustic concentrator are studied. It is found that the focusing efficiency can be substantially enhanced by going from a bell-shaped distribution of the initial amplitude to an annular distribution. Zh. Tekh. Fiz. 68, 111–117 (June 1998)     

Analysis of the focusing efficiency of pulsed pressure waves as a function of the initial amplitude distribution and temporal profile

Solutions of the parabolic diffraction equation for the focusing of pressure pulses with a monopolar or bipolar initial profile and a bell-shaped or annular amplitude distribution are presented. These results are analyzed and conditions determined under which more efficient focusing occurs during the transition from a bell-shaped to an annular distribution of the initial amplitude, as well as when a monopolar pulse is replaced by a bipolar pulse. Zh. Tekh. Fiz. 68, 120–123 (July 1998)     

Advanced Optical Network

The following article describes an advanced dense wavelength division multiplexing (DWDM) Optical Network developed by L-3 Photonics. The network, configured as an amplified optical bus, carries traffic simultaneously in both directions, using multiple wavelengths. As a result, data distribution is of the form peer-to-multi-peer, it is protocol independent, and it is scalable. The network leverages the rapid growth in commercial optical technologies, including wavelength division multiplexing (WDM), and when applied to military and commercial platforms such as aircraft, ships, unmanned and other vehicles, provides a cost-effective, low-weight, high-speed, and high noise-immune data distribution system.     

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, , with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as ‘past terminal accumulation points’ of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's ‘Chronology Protection Conjecture’, according to which the laws of physics prevent one from manufacturing a ’time machine‘. Specifically, we prove: Theorem 1. There is no extension to of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M × M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of φ² or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the ‘Propagation of Singularities’ theorems of Duistermaat and H?rmander. Received: 14 March 1996/Accepted: 11 June 1996     

Dynamics studies of O+ + D2 reaction using the time-dependent wave packet method

Based on the potential energy surface (PES) reported by Li et al. (Phys. Chem. Chem. Phys. 20, 1039 (2018)), the initial state dynamics calculation of O⁺?+?D₂ (v?=?0, j?=?0) reaction was conducted using the time-dependent wave packet method with a second order split operator. Dynamics properties such as reaction probability, integral cross section, differential cross section, and distribution of products were calculated and compared with available experimental and theoretical results. The present integral cross section values were in good agreement with experimental results. In addition, the differential cross section indicates that the mechanism of the complex-formation reaction plays a dominant role during the reaction.     

Plasma density gratings induced by intersecting laser pulses in underdense plasmas

Electron and ion density gratings induced by two intersecting ultrashort laser pulses at intensities of 10¹⁶ W/cm² or lower are investigated. The ponderomotive force generated by the inhomogeneous intensity distribution in the intersecting region of the interfering pulses produces deep electron and ion density modulations at a wavelength less than a laser wavelength in vacuum. Dependence of the density modulation on the plasma densities, temperatures, and the ion mass, as well as the laser pulse parameters are studied analytically and by particle-in-cell simulations. It is found that the density peaks of such gratings can be a few times that of the initial plasma density and last as long as a few picoseconds. It is also demonstrated that the scattering of signal pulses by such a bulk density grating results in high-harmonic generation. The density gratings may be incorporated into ion-ripple lasers [K.R. Chen and J.M. Dawson, Phys. Rev. Lett. 68, 29 (1992)] to generate ultrashort X-ray pulses of a few angstroms by using electron beams at only a few tens of MeV only. PACS 52.35.Mw; 42.65.Ky; 52.25.Os     

Multiply connected Fermi sphere and fermion condensation

We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T ₀, above which the behavior of the system is the same as in the theory of fermion condensation, and for T<T ₀ the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed. Zh. éksp. Teor. Fiz. 114, 2078–2088 (December 1998)     

Self-referential order

Abstract

We introduce the concept of self-referential order which provides a way to quantify structural organization in non-crystalline materials. The key idea consists in the observation that, in a disordered system, where there is no ideal, reference, template structure, each sub-portion of the whole structure can be taken as reference for the rest and the system can be described in terms of its parts in a self-referential way. Some parts carry larger information about the rest of the structure and they are identified as motifs. We discuss how this method can efficiently reduce the amount of information required to describe a complex disordered structure by encoding it in a set of motifs and matching rules. We propose an information-theoretic approach to define a self-referential-order-parameter and we show that, by means of entropic measures, such a parameter can be quantified explicitly. A proof of concept application to equal disk packing is presented and discussed.     

Basic features of coherent radiation generated by relativistic charge bunches

Abstract

Radiation generated by relativistic charges can be analyzed and described in exquisite detail. One reason that such detailed analysis is possible is because the phases of radiated photons often are determined completely by the initial conditions of the relativistic charges and the radiating system. The phase relationships between the initial charges and the radiated photons represent coherence in the emitted radiation. A previous paper decribed how this coherence could affect the spatial and spectral distributions of radiation generated by a single charge in a periodic radiator. The present paper discusses a complementary issue; namely, how the temporal shape of a relativistic charge bunch can emphasize specific features of the radiation generated at a single interaction site.     

Mechanisms and kinetics of the initial stages of growth of films grown by chemical vapor deposition

The initial stages of growth of films and coatings by chemical vapor deposition are investigated. A system of equations is derived which describes the evolution of an island film at the stage of Ostwald ripening under conditions characteristic of vapor deposition. Solving this system of equations yields the dependence of all of the main characteristics of island films (the size distribution function of the islands, the dependence of the mean radius and density of the islands) as functions of time and the spatial coordinate. Suggestions are given for the preparation of films with prescribed properties. Zh. Tekh. Fiz. 68, 111–117 (July 1998)     

Exact Solutions of a Quark Plasma Equilibrium in the Abelian Dominance Approximation

Abstract

Stationary kinetic equations for a quark plasma (QP) in the Abelian dominance approximation are reduced to the nonlinear system of A ₂-periodic Toda chains (with elliptic operator). Using solutions of this system, which are found with the help of the first integrals and Hirota’s method, such characteristics of QPas the distribution function and the potential of the self-consistent field are constructed.     

Formation and Development of Phase Morphology and Structure on Polystyrene Blends. I. Study of Phase Behavior and Structure Character of Polystyrene/Poly (cis‐butadiene) Rubber Immiscible System During Melt Blending by Scanning Electron Microscopy

Abstract

Polystyrene/poly(cis‐butadiene) rubber blends were prepared by melt blending. The morphology development of the blend system was examined by intermittent extraction of material and scanning electron microscopy. The mixing process of the immiscible system was described through the characteristic length L and the average characteristic length L _m. The distribution of L was shown to be consonant with a log‐normal distribution. The mixing system was demonstrated to possess self‐similarity in a certain range of time and space, as shown through a scale function. Furthermore, the fractal dimension D at different times was calculated and shown to be a parameter that can be used to describe the dynamic process of the melt blending.     

Latent track structure in polymers as observed by a highly sensitive electrolytical conductivity measurement

Abstract

First results of a new electrolytical conductivity cell are reported concerning the initial stage of the pore opening process during track etching in vitreous solids. On the basis of the soft mode (low-energy excitation) model for track etching, a distribution function for the number of perforated micropores as function of time is calculated by accounting for the radial etch rate as function of the effective pore radius.