The origin of stretched exponential function in dynamic response of photodarkening in amorphous chalcogenides

2009 ◽  
Vol 95 (5) ◽  
pp. 051908 ◽  
Author(s):  
K. Shimakawa ◽  
N. Nakagawa ◽  
T. Itoh
Keyword(s):  
Dynamic Response ◽  
Exponential Function ◽  
Stretched Exponential ◽  
Amorphous Chalcogenides

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.

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.

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.

WINDING ANGLE DISTRIBUTION OF SELF-AVOIDING WALKS IN TWO DIMENSIONS

2000 ◽  
Vol 11 (04) ◽  
pp. 721-729 ◽  
Author(s):  
IKSOO CHANG
Keyword(s):  
Exponential Function ◽  
Low Temperatures ◽  
Gaussian Function ◽  
Two Dimensions ◽  
Analytical Prediction ◽  
Angle Distribution ◽  
Linear Polymers ◽  
Stretched Exponential ◽  
Self Avoiding Walks ◽  
Winding Angle

Winding angle problem of two-dimensional self-avoiding walks (SAWs) on a square lattice is studied intensively by the scanning Monte Carlo simulation at high, theta (Θ), and low-temperatures. The winding angle distribution PN(θ) and the even moments of winding angle [Formula: see text] are calculated for lengths of SAWs up to N = 300 and compared with the analytical prediction. At the infinite temperature (good solvent regime of linear polymers), PN(θ) is well described by either a Gaussian function or a stretched exponential function which is close to Gaussian, so, it is not incompatible with an analytical prediction that it is a Gaussian function exp [-θ2/ ln N] in terms of a variable [Formula: see text] and that [Formula: see text]. However, the results for SAWs at Θ and low-temperatures (Θ and bad solvent regime of linear polymers) significantly deviate from this analytical prediction. PN(θ) is then described much better by a stretched exponential function exp [-|θ|α/ln N] and [Formula: see text] with α = 1.54 and 1.51 which is far from being a Gaussian. We provide a consistent numerical evidence that the winding angle distribution for SAWs at the finite temperatures may not be a Gaussian function but a nontrivial distribution, possibly a stretched exponential function.

WINDING ANGLE DISTRIBUTION OF LATTICE TRAILS IN TWO DIMENSIONS

2000 ◽  
Vol 11 (04) ◽  
pp. 731-738 ◽  
Author(s):  
IKSOO CHANG
Keyword(s):  
Exponential Function ◽  
Low Temperatures ◽  
Gaussian Function ◽  
Two Dimensions ◽  
Square Lattice ◽  
Angle Distribution ◽  
Stretched Exponential ◽  
Self Avoiding Walks ◽  
Winding Angle ◽  
Infinite Temperature

The winding angle problem of two-dimensional lattice trails on a square lattice is studied intensively by the scanning Monte Carlo simulation at infinite, tricritical, and low-temperatures. The winding angle distribution PN(θ) and the even moments of winding angle [Formula: see text] are calculated for the lengths of trails up to N = 300. At infinite temperature, trails share the same universal winding angle distribution with self-avoiding walks (SAWs), which is a stretched exponential function close to a Gaussian function exp [-θ2/ln N] and [Formula: see text]. However, trails at tricritical and low-temperatures do not share the same winding angle distribution with SAWs. For trails, PN(θ) is described well by a stretched exponential function exp [-|θ|α/ln N] and [Formula: see text] with α ~ 1.69 which is far from being a Gaussian and also different from those of SAWs at Θ and low-temperatures with α ~ 1.54. We provide a consistent numerical evidence that the winding angle distribution for trails at finite temperatures may not be a Gaussian function, but, a nontrivial distribution, possibly a stretched exponential function. Our result also demonstrates that the universality argument between trails and SAWs at infinite and tricritical temperatures indeed persists to the distribution function of winding angle and its associated scaling behavior.

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