Transport coefficients for rigid spherically symmetric polymers or aggregates

In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a dilute suspension of these molecules, starting from a continuum description based on the Debye-Brinkman equation. Instead of numerical methods for solving equations we use perturbative methods, especially methods from boundary-layer analysis. The calculations provide simple analytical formulae for the shear viscosity eta , and the translational and rotational diffusion coefficients DT and DR. The results can also be applied to suspensions of other porous objects, such as aggregates of colloidal particles in which D=3- lambda is called the fractal dimension of the aggregate

Distribution of ions around a charged sphere

Using a new method of calculating the effects of excluded volume, the authors evaluate the distribution of counterions around a charged sphere in thermal equilibrium. In regions of high concentration a saturation of the ion density is found, which is absent in the more conventional Gouy-Chapman model. At the same time the saturation effect of the potential (a property of the Gouy-Chapman model) is removed, giving significant corrections to the values of the potential and concentration at the surface of the sphere

Effects of excluded volume on the electrolyte distribution around a charged sphere

A recently developed method is used to calculate the main effects of excluded volume on the distribution of ions around a charged central sphere in thermal equilibrium. The authors find significant corrections to the results of the conventional Gouy-Chapman theory when the electrostatic energy due to the charge of the sphere is large compared with the thermal energy. The concentration shows a distinct saturation effect, while at the surface of the sphere the known saturation of the potential is lifted. Furthermore, the effect of excluded volume is found to be strongly dominated by the excluded volume of ions with a charge opposite to the charge of the sphere

Assessing TMS-induced D and I waves with spinal H-reflexes

Transcranial magnetic stimulation (TMS) of motor cortex produces a series of descending volleys known as D (direct) and I (indirect) waves. In the present study, we questioned whether spinal H-reflexes can be used to dissect D waves and early and late I waves from TMS. We therefore probed H-reflex facilitation at arrival times of D and I waves at the spinal level and thereby changed TMS parameters that have previously been shown to have selective effects on evoked D and different I waves. We changed TMS intensity and current direction and applied a double-pulse paradigm known as short-interval intracortical inhibition (SICI). Experiments were conducted in flexor carpi radialis (FCR) in the arm and soleus (SOL) in the leg. There were two major findings: 1) in FCR, H-reflex facilitation showed characteristic modulations with altered TMS parameters that correspond to the changes of evoked D and I waves; and 2) H-reflexes in SOL did not, possibly because of increased interference from other spinal circuits. Therefore, the most significant outcome of this study is that in FCR, H-reflexes combined with TMS seem to be a useful technique to dissect TMS-induced D and I waves. NEW & NOTEWORTHY Questions that relate to corticospinal function in pathophysiology and movement control demand sophisticated techniques to provide information about corticospinal mechanisms. We introduce a noninvasive electrophysiological technique that may be useful in describing such mechanisms in more detail by dissecting D and I waves from transcranial magnetic stimulation (TMS). Based on the combination of spinal H-reflexes and TMS in the flexor carpi radialis muscle, the technique was shown to measure selective effects on D and I waves from changing TMS parameters

Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor

Evolution of a Network of Vortex Loops in HeII. Exact Solution of the "Rate Equation"

Evolution of a network of vortex loops in HeII due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function $n(l)$ of number of loops of length $l$ proposed by Copeland with coauthors. By using the special ansatz in the ''collision'' integral we have found the exact power-like solution of ''kinetic equation'' in stationary case. That solution is the famous equilibrium distribution $n(l)\varpropto l^{-5/2}$ obtained earlier in numerical calculations. Our result, however, is not equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of the vortex loop sizes. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of order of interline space. We also obtain that the decay of the vortex tangle obeys the Vinen equation, obtained earlier phenomenologically. We evaluate also the full rate of reconnection events. PACS-number 67.40Comment: 4 pages, submitted to PR

Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time

In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time structure is determined by a condition that mimics the Heisenberg uncertainty relations and the motion in this space-time model is chosen as simple as possible. From these two assumptions we define a path-entropy that measures the number of closed paths associated with a given energy of the system preparation. This entropy has a dynamical character and depends on the time interval on which we count the paths. We show that it exists an like-equilibrium condition for which the path-entropy corresponds exactly to the usual thermodynamic entropy and, more generally, the usual statistical thermodynamics is reobtained. This result derived without using the Gibbs ensemble method shows that the standard thermodynamics is consistent with a motion that is time-irreversible at a microscopic level. From this change of paradigm it becomes easy to derive a $H-theorem$. A comparison with the traditional Boltzmann approach is presented. We also show how our approach can be implemented in order to describe reversible processes. By considering a process defined simultaneously by initial and final conditions a well defined stochastic process is introduced and we are able to derive a Schroedinger equation, an example of time reversible equation.Comment: latex versio

Brownian Motion and Polymer Statistics on Certain Curved Manifolds

We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (function of opening angle and R') contraction of the chain for all lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to appear in Phys. Rev