scholarly journals Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”

Algorithms ◽  
2012 ◽  
Vol 5 (4) ◽  
pp. 604-628 ◽  
Author(s):  
Joachim Wuttke
Keyword(s):  
Fourier Transform ◽  
Open Source ◽  
Exponential Function ◽  
Error Bounds ◽  
Stretched Exponential ◽  
Double Exponential ◽  
Exponential Transform

scholarly journals An Investigation of Stretched Exponential Function in Quantifying Long-Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
HongGuang Sun ◽  
Lin Yuan ◽  
Yong Zhang ◽  
Nicholas Privitera
Keyword(s):  
Exponential Distribution ◽  
Exponential Function ◽  
Extreme Events ◽  
Stable Distribution ◽  
Wide Spectrum ◽  
Long Term Memory ◽  
Term Memory ◽  
Stretched Exponential ◽  
Stretched Exponential Distribution

Extreme events, which are usually characterized by generalized extreme value (GEV) models, can exhibit long-term memory, whose impact needs to be quantified. It was known that extreme recurrence intervals can better characterize the significant influence of long-term memory than using the GEV model. Our statistical analyses based on time series datasets following the Lévy stable distribution confirm that the stretched exponential distribution can describe a wide spectrum of memory behavior transition from exponentially distributed intervals (without memory) to power-law distributed ones (with strong memory or fractal scaling property), extending the previous evaluation of the stretched exponential function using Gaussian/exponential distributed random data. Further deviation and discussion of a historical paradox (i.e., the residual waiting time tends to increase with an increasing elapsed time under long-term memory) are also provided, based on the theoretical analysis of the Bayesian law and the stretched exponential distribution.

TEMPORAL PROPERTIES OF PHOTOREFRACTIVE MATERIALS

1996 ◽  
Vol 05 (01) ◽  
pp. 9-24 ◽  
Author(s):  
D. STATMAN ◽  
G.C. GILBREATH
Keyword(s):  
Exponential Function ◽  
Modulation Depth ◽  
Rate Equations ◽  
Temporal Properties ◽  
High Modulation ◽  
Beam Coupling ◽  
Double Exponential ◽  
Photorefractive Materials ◽  
Double Exponential Function

Photorefractive two-beam coupling is examined experimentally for the case of high modulation depth. It is seen that the dynamics of signal growth and decay are best described by a double exponential function. The properties of this function with respect to interaction angle and modulation depth are studied. It is suggested that the equations governing photorefractive dynamics may be reduced to a pair of coupled bilinear rate equations which adequately describe photorefractive dynamics for high modulation depth.

A QUANTUM-SPONGE MODEL FOR POROUS SILICON

1996 ◽  
Vol 03 (01) ◽  
pp. 1157-1161
Author(s):  
S. SAWADA ◽  
N. OOKUBO
Keyword(s):  
Porous Silicon ◽  
Exponential Function ◽  
Energy Gap ◽  
Wave Functions ◽  
Stretched Exponential ◽  
Nonexponential Decay ◽  
Fractal Character ◽  
Good Agreement

We propose a “quantum-sponge” model for porous silicon. This model exhibits energy-gap widening and nonexponential decay of photoluminescence describable by the stretched exponential function. These properties are in good agreement with those observed for porous silicon. We suggest that the fractal character of its wave functions is the origin of the nonexponential decay of photoluminescence.

The Hardness Changing Regularity of Quenched-Steel in Tempering Process and Its Double-Exponential Model

2010 ◽  
Vol 146-147 ◽  
pp. 1578-1582
Author(s):  
Cong Sheng Guo ◽  
Shu Ming Long ◽  
Hai Wa Bo ◽  
Hong Bin Tan
Keyword(s):  
Phase Transformation ◽  
Exponential Function ◽  
Optimization Design ◽  
Hardness Test ◽  
Exponential Model ◽  
Physical Metallurgy ◽  
Double Exponential ◽  
Quenched Steel ◽  
Double Exponential Function ◽  
Tempering Process

The transformation of tempering for quenched steel corresponded to complicated process of phase transformation, and mechanical properties of quenched-and-tempered steel were related to the phase transformation. In practice, hardness test was adopted to judge whether the properties of tempered-parts qualified because of its facility. Numerous researches indicated that, there existed correlativity expressed by different function forms between tempering hardness of quenched-steel and its tempering parameters. However, considering physical metallurgy of tempering process, the adoption of double-exponential function would help to describe regularity of hardness changing more exactly for quenched-steel during tempering process. Additionally, results of hardness tests for isothermal tempering and molding/simulation researches have shown that, the model of double-exponential function, which can reflect decline law of tempering hardness for quenched-steel, would provide basis for optimization design of tempering parameters, performance prediction of tempered-parts, and energy-saving heat-treatment on tempering process.

scholarly journals Design of fast ion conducting cathode materials for grid-scale sodium-ion batteries

2017 ◽  
Vol 19 (11) ◽  
pp. 7506-7523 ◽  
Author(s):  
Lee Loong Wong ◽  
Haomin Chen ◽  
Stefan Adams
Keyword(s):  
Exponential Function ◽  
Cathode Materials ◽  
Sodium Ion ◽  
Sodium Ion Batteries ◽  
Rate Performance ◽  
Ion Migration ◽  
Stretched Exponential ◽  
Ion Conducting ◽  
Fast Ion ◽  
Migration Pathways

Using a stretched exponential function the rate performance of sodium-insertion materials is semi-quantitatively determined from characteristics of Na-ion migration pathways.

Sign in / Sign up

Export Citation Format

Share Document