Investigations on a New Failure Model for Electromigration

1991 ◽  
Vol 225 ◽  
Author(s):  
J. Kitchin ◽  
J. R. Lloyd
Keyword(s):  
Activation Energy ◽  
Grain Boundary ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Failure Model ◽  
Line Segments ◽  
Standard Normal ◽  
The Mean ◽  
Image Position ◽  
Line P

A new statistical model for electromigration failure in fine-line thin film conductors is developed in [1] by extending [2] to incorporate the statistics of microstructure and concomitant variations in the activation energy for grain boundary diffusion. The resulting distribution of time t to failure is well-approximated bywhere N is the number of line segments that are potential independent failure elements, 1μ and σ are, respectively, the mean and standard deviation of an assumed normal distribution of activation energy in grain boundaries, γ is a scaling constant, T is in degrees Kelvin, j is the current density in the line, p1 is the fraction of line segments for which exactly one grain boundary occurs between two blocking boundaries, and Φ is the standard normal cumulative distribution function. (Note: .)

Series expansions for the all-time maximum of α-stable random walks

2016 ◽  
Vol 48 (3) ◽  
pp. 744-767
Author(s):  
Clifford Hurvich ◽  
Josh Reed
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Queueing Theory ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Series Expansions ◽  
Stable Random Variables ◽  
The Mean ◽  
The Stability

AbstractWe study random walks whose increments are α-stable distributions with shape parameter 1<α<2. Specifically, assuming a mean increment size which is negative, we provide series expansions in terms of the mean increment size for the probability that the all-time maximum of an α-stable random walk is equal to 0 and, in the totally skewed-to-the-left case of skewness parameter β=-1, for the expected value of the all-time maximum of an α-stable random walk. Our series expansions generalize previous results for Gaussian random walks. Key ingredients in our proofs are Spitzer's identity for random walks, the stability property of α-stable random variables, and Zolotarev's integral representation for the cumulative distribution function of an α-stable random variable. We also discuss an application of our results to a problem arising in queueing theory.

scholarly journals The Creep Activation Energies of Ice

1978 ◽  
Vol 21 (85) ◽  
pp. 429-444 ◽  
Author(s):  
D. R. Homer ◽  
J. W. Glen
Keyword(s):  
Activation Energy ◽  
Grain Boundary ◽  
Creep Deformation ◽  
Tensile Axis ◽  
Strain Rates ◽  
Boundary Slip ◽  
Creep Tests ◽  
Creep Activation Energy ◽  
Single Grain ◽  
Image Position

AbstractMonocrystals and bicrystals of ice have been creep tested at temperatures between 4 and — 30°C. The bicrystals had a single grain boundary running parallel to the tensile axis; this configuration inhibited grain-boundary slip between the two grains. The creep tests, which were carried out at constant stress σ and temperature T, yielded data of strain ϵ for time elapsed since the start of the test. These data showed accelerating creep for both monocrystals and bicrystals at all strain levels. Strain-rates were derived at strains of 0.01, 0.05. and 0.10, and these rates were fitted to the expressionk is Boltzmann’s constant and E is the creep activation energy. Derived values of n were 1.9 for monocrystals and 2.9 for bicrystals. The creep activation energy was found to be 78 kJ/mol for monocrystals and 75 kJ/mol for bicrystals. The processes of creep deformation in mono-, bi- and polycrystals are discussed.

scholarly journals Asymptotics for the time of ruin in the war of attrition

2017 ◽  
Vol 49 (2) ◽  
pp. 388-410 ◽  
Author(s):  
Philip A. Ernst ◽  
Ilie Grigorescu
Keyword(s):  
Distribution Function ◽  
Explicit Formula ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Fluid Limit ◽  
War Of Attrition ◽  
Time Of Ruin ◽  
Standard Normal ◽  
The Difference ◽  
The Time Of Ruin

AbstractWe consider two players, starting withmandnunits, respectively. In each round, the winner is decided with probability proportional to each player's fortune, and the opponent loses one unit. We prove an explicit formula for the probabilityp(m,n) that the first player wins. Whenm~Nx0,n~Ny0, we prove the fluid limit asN→ ∞. Whenx0=y0,z→p(N,N+z√N) converges to the standard normal cumulative distribution function and the difference in fortunes scales diffusively. The exact limit of the time of ruin τNis established as (T- τN) ~N-βW1/β, β = ¼,T=x0+y0. Modulo a constant,W~ χ21(z02/T2).

scholarly journals Statistical Properties of SNR for Compressed Measurements

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yulong Gao ◽  
Yanping Chen ◽  
Linxiao Su
Keyword(s):  
Numerical Simulation ◽  
Signal Processing ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Communication Signal ◽  
The Mean ◽  
Simulation Results

Some basic statistical properties of the compressed measurements are investigated. It is well known that the statistical properties are a foundation for analyzing the performance of signal detection and the applications of compressed sensing in communication signal processing. Firstly, we discuss the statistical properties of the compressed signal, the compressed noise, and their corresponding energy. And then, the statistical characteristics of SNR of the compressed measurements are calculated, including the mean and the variance. Finally, probability density function and cumulative distribution function of SNR are derived for the cases of the Gamma distribution and the Gaussian distribution. Numerical simulation results demonstrate the correctness of the theoretical analysis.

scholarly journals Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (4) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

scholarly journals Detection of Giant pulses from pulsar PSR B0950+08

2012 ◽  
Vol 8 (S291) ◽  
pp. 502-504
Author(s):  
T. V. Smirnova
Keyword(s):  
Distribution Function ◽  
Flux Density ◽  
Power Law ◽  
Pulse Energy ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Maximum Peak ◽  
Giant Pulses ◽  
Peak Flux ◽  
The Mean

AbstractWe investigated pulse intensities of PSR B0950+08 at 112 MHz at various longitudes (phases) and detected very strong pulses exceeding the amplitude of the mean profile by more than one hundred times. The maximum peak flux density of a recorded pulse is 15240 Jy, and the energy of this pulse exceeds the mean pulse energy by a factor of 153. The analysis shows that the cumulative distribution function (CDF) of pulse intensities at the longitudes of the main pulse is described by a piece-wise power law, with a slope changing from n=−1.25 ± 0.04 to n=−1.84 ± 0.07 at I≥600 Jy. The CDF for pulses at the longitudes of the precursor has a power law with n=−1.5 ± 0.1. Detected giant pulses from this pulsar have the same signature as giant pulses of other pulsars.

Damage to Oil Storage Tanks from the 2011 Mw 9.0 Tohoku-Oki Tsunami

2015 ◽  
Vol 31 (2) ◽  
pp. 1103-1124 ◽  
Author(s):  
Ken Hatayama
Keyword(s):  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Storage Tanks ◽  
Inundation Depth ◽  
Damage Rate ◽  
Oil Storage ◽  
Damage Data ◽  
Standard Normal ◽  
Using Data ◽  
Actual Damage

The Mw 9.0 2011 Tohoku-oki tsunami damaged 418 oil storage tanks and moved 157 of them. Using data on the severity of damage and the maximum inundation depth of the tsunami, a fragility curve representing the damage to oil storage tank plumbing is presented in this paper: P( η)= Φ ((ln η − 1.02)/0.574), where P is the damage rate, η is the maximum inundation depth in meters, and Φ is the standard normal cumulative distribution function. The existing method of predicting the movement of tanks exposed to a tsunami is validated by comparing the predicted damage with actual damage data from the 2011 tsunami. The accuracy (hit rate) is 76%.

scholarly journals Generation of pseudo-random numbers with the use of inverse chaotic transformation

2018 ◽  
Vol 16 (1) ◽  
pp. 16-22
Author(s):  
Marcin Lawnik
Keyword(s):  
Cumulative Distribution Function ◽  
Chaotic Maps ◽  
Continuous Distribution ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Standard Normal Distribution ◽  
Random Numbers ◽  
Simulation And Modeling ◽  
Standard Normal ◽  
The Given

AbstractIn (Lawnik M., Generation of numbers with the distribution close to uniform with the use of chaotic maps, In: Obaidat M.S., Kacprzyk J., Ören T. (Ed.), International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) (28-30 August 2014, Vienna, Austria), SCITEPRESS, 2014) Lawnik discussed a method of generating pseudo-random numbers from uniform distribution with the use of adequate chaotic transformation. The method enables the “flattening” of continuous distributions to uniform one. In this paper a inverse process to the above-mentioned method is presented, and, in consequence, a new manner of generating pseudo-random numbers from a given continuous distribution. The method utilizes the frequency of the occurrence of successive branches of chaotic transformation in the process of “flattening”. To generate the values from the given distribution one discrete and one continuous value of a random variable are required. The presented method does not directly involve the knowledge of the density function or the cumulative distribution function, which is, undoubtedly, a great advantage in comparison with other well-known methods. The described method was analysed on the example of the standard normal distribution.

scholarly journals Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves

2021 ◽  
Author(s):  
Hime Oliveira
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Number ◽  
Probability Distributions ◽  
Cumulative Distribution ◽  
Standard Normal Distribution ◽  
Space Filling ◽  
Space Filling Curves ◽  
Deterministic Sampling ◽  
Standard Normal

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression &rdquo;random number&rdquo; will be used along the text to mean &rdquo;pseudo-random number&rdquo;.

Sign in / Sign up

Export Citation Format

Share Document