Search results for "quantitative"
showing 10 items of 2409 documents
Solubility of Polymers
2011
Detailed knowledge concerning the phase state (homogeneous or coexistence of two or more condensed phases) of polymer containing mixtures is indispensible in virtually any area related to the production or application of macromolecules. In addition to this qualitative information it is for many purposes highly desirable to dispose of quantitative data regarding solvent quality or, more generally, with respect to the thermodynamic interaction between the components of the mixtures. This contribution starts with a brief presentation of the thermodynamic criteria deciding on the phase state and presents the experimental methods used in this area. The next section gives an overview on typical b…
Entropy of glassy polymer melts: Comparison between Gibbs-DiMarzio theory and simulation.
1996
We calculate the free energy of a model for a polymer melt in a computer simulation of the bond-fluctuation model and determine the entropy of the melt over a wide range of temperatures, including the region close to the glass transition. The results are compared with the Gibbs-DiMarzio theory, a theory by Flory for semiflexible polymers, and a modification of their theories due to Milchev. We can describe the data within the framework of the Flory theory with Milchev's correction and discuss the consequences for the understanding of the glass transition. \textcopyright{} 1996 The American Physical Society.
Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions
2010
Monte Carlo and molecular dynamics simulations are, in principle, powerful tools for carrying out the basic task of statistical thermodynamics, namely the prediction of macroscopic properties of matter from suitable models of effective interactions between atoms and molecules. The state of the art of this approach is reviewed, with an emphasis on solutions of rather short polymer chains (such as alkanes) in various solvents. Several methods of constructing coarse-grained models of the simple bead–spring type will be mentioned, using input either from atomistic models (considering polybutadiene as an example) or from experiment. Also, the need to have corresponding coarse-grained models of t…
Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model
2010
The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics densities that are very distinctive fro…
Editorial message
2006
Geometric Computing and Reasoning (GCR) is a new track of SAC and it is dedicated to the recent trends in the domain of geometric constraint solving and automated, or computer aided, deduction in geometry.
Stochastic equation of population dynamics with diffusion on a domain
2003
We consider Lotka-Volterra competition model with diffusion in a territorial domain with a stochastic perturbation which represents the random variations of environment conditions. We prove the existence, the uniqueness and the positivity of the solution. Moreover, the stochastic boundedness of the solution is analized.
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter
2021
The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.
Classification of precipitation events with a convective response timescale and their forecasting characteristics
2011
[1] The convective timescale τc, which is mainly determined by the ratio of CAPE and precipitation rate, provides a physically-based measure to distinguish equilibrium and non-equilibrium convection. A statistical analysis of this timescale, based upon observational data from radiosonde ascents, rain gauges, and radar for seven warm seasons in Germany, reveals that the equilibrium and non-equilibrium regimes can be regarded as extremes of a continuous distribution. The two regimes characterize very different interactions between the large-scale flow and convection. The quality of precipitation forecasts from a non-hydrostatic regional weather prediction model with parameterized convection d…
Generalization of a finite-difference numerical method for the steady-state and transient solutions of the nernst—planck flux equations
1985
Abstract A generalization of the numerical method of Brumleve and Buck for the solution of Nernst—Planck equations when convective flux and electric current are involved has been developed. The simulation procedure was applied to a specific case: transport of strong electrolytes in a wide-pore membrane with simultaneous diffusion, convection and electric current. Good agreement was found between experimental data and computed results.