Efficient approach to nucleation and growth dynamics. Stationary diffusion flux model. (artikelnr. 164508)

A new model describing the evolution of clusters in the processes of nucleation and growth is proposed. The diffusion flux in the nonstationary Fokker–Planck equation with an unknown distribution function is approximated by the closed form expression containing the steady-state solution of the Zeldovich–Frenkel equation. This is justified due to the smallness of induction time of cluster formation compared to the time scale observed in experiments. The resulting stationary diffusion flux model is valid for all cluster sizes, computationally efficient and applicable to various types of cluster formation processes. Its application to a nucleation pulse experiment shows an excellent agreement with the solution of the set of formally exact Becker–Döring equation

Uniqueness in MHD in divergence form: right nullvectors and well-posedness

Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of well-posedness, and identify a preferred linear combination in this divergence formulation. The limit of weak magnetic fields shows the slow magnetosonic and Alfven waves to bifurcate from the contact discontinuity (entropy waves), while the fast magnetosonic wave is a regular perturbation of the hydrodynamical sound speed. These results are further reported as a starting point for characteristic based shock capturing schemes for simulations with ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy

The experimental modification of a computer software package for graphing algebraic functions

No Abstract Available South African Journal of Education Vol.25(2) 2005: 61-6

Modeling pathological brain rhythms: constructing a neural mass model from single cell dynamics

Neural mass models (NMM) describe neural activity on a macroscopic scale, which can be compared to the electroencephalogram (EEG). This allows a better understanding of the processes responsible for various EEG patterns, including pathological rhythms as diffuse slowing or burst-suppression [1]. Using available models which contain explicit expressions for the synaptic response and number of synapses [2], pathological conditions that modulate synaptic function, such as anesthetics [3] and hypoxia, can be included easily. However, it is less obvious how to incorporate conditions which alter the excitability of neurons, such as hyperkalemia or channel blockers. Here, we present a method for constructing a neural mass model by using the relation between synaptic input of a single cell model and its firing rate. This allows an easy implementation for pathological conditions. We describe the average firing rate of a single population of neurons receiving one type of synaptic input, but this can readily be extended to multiple populations. A set of differential equations describes, traditionally, the average synaptic conductance [2]. Assuming Poisson statistics for the input, we can derive another equation, which describes the time evolution of the standard deviation of the synaptic conductance across the population. The average and standard deviation of the conductance then determine the distribution and the corresponding average of the firing rates in the population. As initial verification, the constructed mean field model is numerically compared to a network of single cells. From the single cell model we determine the dependence of the firing rate on (constant) synaptic conductance numerically. Furthermore, we show that, for fluctuating inputs, the firing rate is well approximated by the instantaneous synaptic conductance. 120 Hodgkin-Huxley type cells were connected all-to-all with inhibitory synapses: a simple configuration which results in intrinsic oscillations. Each cell receives inhibitory external input as well, consisting of Poisson trains. We find a close agreement between the constructed neural mass model and the network simulation (Figure 1). Figure 1. Comparison of step response of the derived NMM and a detailed network model The proposed method can easily be extended to model heterogeneous populations, multiple types of synapses, spatial structures, propagation delays, and bursting dynamics [4]. Any pathophysiology can readily be incorporated by adapting the single cell model. This allows for testing hypotheses on processes underlying abnormal EEGs

Inventory of assessment practices in people with profound intellectual and multiple disabilities in three European countries

BACKGROUND: Knowledge about the quality of assessment methods used in the support of people with profound intellectual and multiple disabilities (PIMD) is scarce. This study aimed to provide an overview of the assessment methods used in practice and to examine whether these instruments were studied for their psychometric properties for people with PIMD. METHOD: Professionals (N = 148) from three European countries completed a survey on assessment practices. We performed a literature search to find information about the psychometric properties of the instruments that were identified in the survey. RESULTS: Of the participants, 78.1% used assessments that were not developed for people with PIMD. Documentation on psychometric properties was found for 8 out of 116 instruments. CONCLUSIONS: Most of the instruments in use were not designed for people with PIMD, and information about their quality is lacking. Guidelines are needed regarding the use and development of assessment methods for people with PIMD

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.