Integration through transients for Brownian particles under steady shear

Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are obtained, which take the form of generalized Green-Kubo relations. They require integration of transient dynamics. Equations of motion with memory effects for transient density fluctuation functions are derived from the same microscopic starting point. We argue that the derived formal expressions provide useful starting points for approximations in order to describe the stationary non-equilibrium state of steadily sheared dense colloidal dispersions.Comment: 17 pages, Submitted to J. Phys.: Condens. Matter; revised version with minor correction

Prospective memory impairment in chronic heart failure

Although cognitive deficits are common in patients with chronic heart failure (CHF), no study to date has investigated whether these deficits extend to the capacity to execute delayed intentions (prospective memory, PM). This is a surprising omission given the critical role PM plays in correctly implementing many important CHF self-care behaviors. The present study aimed to provide the first empirical assessment of PM function in people with CHF. The key dependent measure was a laboratory measure of PM that closely simulates PM tasks in daily life - Virtual Week. A group comparison design was used, with 30 CHF patients compared to 30 demographically matched controls. Background measures assessing executive functions, working memory, and verbal memory were also administered. The CHF group exhibited significant PM impairment, with difficulties generalizing across different types of PM tasks (event, time, regular, irregular). The CHF group also had moderate deficits on several of the background cognitive measures. Given the level of impairment remained consistent even on tasks that imposed minimal demands on memory for task content, CHF-related difficulties most likely reflects problems with the prospective component. However, exploratory analyses suggest that difficulties with retrospective memory and global cognition (but not executive control), also contribute to the PM difficulties seen in this group. The implications of these data are discussed, and in particular, it is argued that problems with PM may help explain why patient engagement in CHF self-care behaviors is often poor. (JINS, 2015, 21, 1-10)</p

Generalized kinetic and evolution equations in the approach of the nonequilibrium statistical operator

The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrodinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analysed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.Comment: 21 pages, Revte

Extra Dirac Equations

This paper has rather a pedagogical meaning. Surprising symmetries in the $(j,0)\oplus (0,j)$ Lorentz group representation space are analyzed. The aim is to draw reader's attention to the possibility of describing the particle world on the ground of the Dirac "doubles". Several tune points of the variational principle for this kind of equations are briefly discussed.Comment: REVTeX 3.0, 14p

Thermal Segregation Beyond Navier-Stokes

A dilute suspension of impurities in a low density gas is described by the Boltzmann and Boltzman-Lorentz kinetic theory. Scaling forms for the species distribution functions allow an exact determination of the hydrodynamic fields, without restriction to small thermal gradients or Navier-Stokes hydrodynamics. The thermal diffusion factor characterizing sedimentation is identified in terms of collision integrals as functions of the mechanical properties of the particles and the temperature gradient. An evaluation of the collision integrals using Sonine polynomial approximations is discussed. Conditions for segregation both along and opposite the temperature gradient are found, in contrast to the Navier-Stokes description for which no segregation occurs.Comment: 9 figure

Lagrangian for the Majorana-Ahluwalia Construct

The equations describing self/anti-self charge conjugate states, recently proposed by Ahluwalia, are re-written to covariant form. The corresponding Lagrangian for the neutral particle theory is proposed. From a group-theoretical viewpoint the construct is an example of the Nigam-Foldy-Bargmann-Wightman-Wigner-type quantum field theory based on the doubled representations of the extended Lorentz group. Relations with the Sachs-Schwebel and Ziino-Barut concepts of relativistic quantum theory are discussed.Comment: 10pp., REVTeX 3.0 fil

Kinetic Theory of a Dilute Gas System under Steady Heat Conduction

The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.Comment: 36 pages, 4 figures, 5 table

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference