Short time behavior and universal relations in polymer cyclization

1991 ◽  
Vol 1 (4) ◽  
pp. 471-486 ◽  
Author(s):  
Barry Friedman ◽  
Ben O'Shaughnessy
Keyword(s):  
Time Behavior ◽  
Short Time

Short Time Behavior of Solutions to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 60 (5) ◽  
pp. 1168-1200 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Broad Class ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Pinsky Phenomenon ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear ◽  
Short Time

AbstractWe examine the fine structure of the short time behavior of solutions to various linear and nonlinear Schrödinger equations ut = iΔu+q(u) on I×ℝn, with initial data u(0, x) = f (x). Particular attention is paid to cases where f is piecewise smooth, with jump across an (n−1)-dimensional surface. We give detailed analyses of Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon. We give results for general n in the linear case. We also have detailed analyses for a broad class of nonlinear equations when n = 1 and 2, with emphasis on the analysis of the first order correction to the solution of the corresponding linear equation. This work complements estimates on the error in this approximation.

Tensile Stress—Strain and Stress Relaxation Behavior of Raw Elastomers Using a High Speed Tester

1974 ◽  
Vol 47 (2) ◽  
pp. 307-317 ◽  
Author(s):  
H. H. Bowerman ◽  
E. A. Collins ◽  
N. Nakajima
Keyword(s):  
Stress Relaxation ◽  
High Speed ◽  
Strain Rates ◽  
Time Behavior ◽  
Stress Strain ◽  
Strain Behavior ◽  
Relaxation Measurements ◽  
Ultimate Properties ◽  
Short Time ◽  
Acrylonitrile Copolymers

Abstract A high-speed, tensile-testing device was used to determine the stress—strain behavior of uncompounded butadiene—acrylonitrile copolymers over a range of temperatures and deformation rates. The strain rates were varied from 267 to 26,700 per cent/sec and the temperature was varied from 25 to 97° C. The high-speed tester was also used for stress—relaxation measurements by applying the strain nearly instantly in conformity with theoretical requirements in order to obtain the short time behavior. The WLF equation was obtained from the stress—relaxation data and then used to reduce the ultimate properties to one temperature over four decades of the strain rates. The ultimate properties could be represented by a failure envelope similar to those obtained for vulcanizates.

scholarly journals SURVIVAL PROBABILITY (HEAT CONTENT) AND THE LOWEST EIGENVALUE OF DIRICHLET LAPLACIAN

2011 ◽  
Vol 25 (15) ◽  
pp. 1993-2007
Author(s):  
PAVOL KALINAY ◽  
LADISLAV ŠAMAJ ◽  
IGOR TRAVĚNEC
Keyword(s):  
Survival Probability ◽  
Heat Content ◽  
Simple Algorithm ◽  
Time Behavior ◽  
Dirichlet Laplacian ◽  
Geometric Characteristics ◽  
Long Time ◽  
Time Expansion ◽  
Short Time ◽  
Lowest Eigenvalue

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Padé interpolation between the short-time and the long-time behavior of the survival probability, i.e., between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.

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