Size distribution of different types of sites in Abelian sandpile avalanches

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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Relations Among Moments of Waiting Time and Queue Size Distribution in Bulk Queueing Systems

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319870107 ◽

1987 ◽

Vol 36 (1-2) ◽

pp. 63-68

Author(s):

A. Ghosal ◽

S. Madan ◽

M.L. Chaudhry

Keyword(s):

Size Distribution ◽

Waiting Time ◽

Queueing Systems ◽

Queueing Models ◽

Queue Size ◽

Different Types

This paper brings out relations among the moments of various orders of the waiting time and the queue size in different types of bulk queueing models.

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Sensitivity Analysis of Major Parameters on Piping Failure Probabilities

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.261-263.821 ◽

2004 ◽

Vol 261-263 ◽

pp. 821-826

Author(s):

Sung Gyu Jung ◽

Chang Soon Lee ◽

In Gyu Park ◽

Se Hwan Lee ◽

Tae Eun Jin

Keyword(s):

Sensitivity Analysis ◽

Size Distribution ◽

Nuclear Power ◽

Power Plants ◽

Nuclear Power Plants ◽

Crack Size ◽

Deterministic Approach ◽

Inspection Interval ◽

Different Types ◽

Failure Probabilities

In-service inspections (ISI) of pipes in the nuclear power plants are currently performed based on mandated requirements in the ASME Section XI, which is based on deterministic approach of the critical welds. The 20 years of ISI experience in U.S.A. has revealed less correlation between the critical welds and actual failures, and much conservatism in current ISI requirements. To reduce those problems, risk-informed ISI technology has been developed and proved to be useful. This paper presented a method for predicting piping failure probabilities in an application of risk-informed ISI, and analyzed the effect of input parameters on piping failure probabilities. Results generated using this approach revealed that the calculated failure probabilities can be sensitive to the different types of stressors, crack size distribution, inspection interval, etc..

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Fluctuation of Firm Size in the Long-Run and Bimodal Distribution

Advances in Operations Research ◽

10.1155/2011/269239 ◽

2011 ◽

Vol 2011 ◽

pp. 1-21 ◽

Cited By ~ 3

Author(s):

Hideaki Aoyama ◽

Lars Grüne ◽

Willi Semmler ◽

Yoshi Fujiwara ◽

Wataru Souma

Keyword(s):

Size Distribution ◽

Firm Size ◽

Time Distribution ◽

Decision Problem ◽

Bimodal Distribution ◽

Economic Literature ◽

Data Set ◽

Firm Size Distribution ◽

Long Run ◽

Different Types

We study empirically and analytically growth and fluctuation of firm size distribution. An empirical analysis is carried out on a US data set on firm size, with emphasis on one-time distribution as well as growth-rate probability distribution. Both Pareto's law and Gibrat's law are often used to study firm size distribution. Their theoretical relationship is discussed, and it is shown how they are complementable with a bimodal distribution of firm size. We introduce economic mechanisms that suggest a bimodal distribution of firm size in the long run. The mechanisms we study have been known in the economic literature since long. Yet, they have not been studied in the context of a dynamic decision problem of the firm. Allowing for these mechanism thus will give rise to heterogeneity of firms with respect to certain characteristics. We then present different types of tests on US data on firm size which indicate a bimodal distribution of firm size.

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Effects of Processing Factors on Microstructure and Diffusivity of Diethylbenzene Dehydrogenation Catalyst

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.297-301.233 ◽

2010 ◽

Vol 297-301 ◽

pp. 233-238

Author(s):

Mohammad Ebrahim Zeynali ◽

I. Soltani

Keyword(s):

Grain Size ◽

Pore Size Distribution ◽

Pore Size ◽

Size Distribution ◽

Bulk Diffusion ◽

Effective Diffusivity ◽

Catalyst Pellet ◽

Different Types ◽

Effective Diffusivities ◽

Processing Factors

In this study, different mechanisms of diffusion such as Knudsen and bulk were investigated for diethylbenzene diffusion into a catalyst and it was concluded that the pore sizes should be in the range that permit transitional diffusion (both Knudsen and bulk diffusion). The catalyst grain size can be controlled and varied by different parameters such as speed and time of mixing, type of alkali, temperature and pH. Particle size distribution experiments were conducted for different types of alkali and speed of mixing to characterize the catalyst. The effects of grain size formed during coprecipitation on pore size distribution of the catalyst pellet which affect the effective diffusivity were discussed. Pore size distribution of the model catalyst was obtained and the effective diffusivities were calculated by numerical integration of Johanson-Stewart equation.

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SEPARATION OF PARTICLES IN POLYDISPERSE NANOSUSPENSION IN THE LASER RADIATION FIELD

Physical and Chemical Aspects of the Study of Clusters Nanostructures and Nanomaterials ◽

10.26456/pcascnn/2021.13.146 ◽

2021 ◽

pp. 146-155

Author(s):

Валерий Иванович Иванов ◽

Сергей Анатольевич Пячин

Keyword(s):

Laser Radiation ◽

Size Distribution ◽

Radiation Field ◽

Aqueous Suspension ◽

Single Mode ◽

Initial Distribution ◽

Entire Volume ◽

Light Pressure ◽

Different Types ◽

Laser Radiation Field

На основе стационарного решения уравнения диффузии изучена сепарация наночастиц в прозрачной полидисперсной водной суспензии с различными типами распределений по размерам под действием силы светового давления, возникающей в поле лазерного излучения интенсивностью 0,5 - 500 кВт/см. Установлено, что на дно кюветы преимущественно будут осаждаться частицы радиусом более 100 нм, а концентрация более мелких наночастиц во всем объеме суспензии останется без изменений. В случае симметричного начальное распределения наночастиц по размерам воздействие интенсивного светового пучка на суспензию приводит к нарушению симметрии кривой функции распределения, а также смещению максимума в область меньших размеров частиц на облучаемой поверхности. Если начальное распределение по размерам имеет несимметричный характер, исходное одномодовое распределение частиц по размерам трансформируется в двумодовое. Данная методика может быть использована для выделения наночастиц определенных размеров в зависимости от плотности мощности излучения. On the basis of a stationary solution of a diffusion equation separation of nanoparticles in a transparent polydisperse aqueous suspension with different types of size distributions was studied under the action of the light pressure arising in the laser radiation field with the intensity of 0,5 - 500 kW/cm. It was found that particles with a radius of more than 100 nm will mainly be precipitated at the bottom of the cell, and the concentration of smaller nanoparticles in the entire volume of the suspension will remain unchanged. In the case of a symmetrical initial distribution of nanoparticles size, the effect of a light beam with high intensity on the suspension leads to a violation of the symmetry of the distribution function curve, as well as a shift of the maximum to the region of smaller particle sizes on the irradiated surface. If the initial size distribution is asymmetric, the initial single-mode particle size distribution is transformed into a two-mode one. This technique can be used to isolate nanoparticles of certain sizes depending on the power density of the radiation.

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Virtual 3D Microstructures with Specified Characteristics of State Variable Distributions

Materials Science Forum ◽

10.4028/www.scientific.net/msf.702-703.540 ◽

2011 ◽

Vol 702-703 ◽

pp. 540-543

Author(s):

Edgar Gomes ◽

Kim Verbeken ◽

Leo Kestens

Keyword(s):

Experimental Data ◽

Grain Size ◽

Boundary Conditions ◽

Size Distribution ◽

Experimental Measurements ◽

Material Microstructure ◽

Model Calculations ◽

State Variable ◽

3D Microstructure ◽

Different Types

For a wide variety of model calculations a hypothetical 3D microstructure is required as input. Although experimental data are frequently used to this purpose, 3D microstructures are difficult to measure experimentally. In order to circumvent these difficulties, a virtual microstructure generator to simulate a specific 3D material microstructure is proposed. Such a virtual microstructure could serve as input for different types of models, would allow a faster model prototyping, would help to explore the boundary conditions of models and reduces the number of unnecessary experimental measurements. In the current paper, the method to generate and to control the grain size distribution as well as texture are discussed.

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The size distribution of protein families within different types of folds

Biochemical and Biophysical Research Communications ◽

10.1016/j.bbrc.2011.02.020 ◽

2011 ◽

Vol 406 (2) ◽

pp. 218-222 ◽

Cited By ~ 4

Author(s):

Xinsheng Liu ◽

Bo Lv ◽

Wanlin Guo

Keyword(s):

Size Distribution ◽

Protein Families ◽

Different Types

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Aerosol microphysics modules in the framework of the ECHAM5 climate model – intercomparison under stratospheric conditions

Geoscientific Model Development Discussions ◽

10.5194/gmdd-2-209-2009 ◽

2009 ◽

Vol 2 (1) ◽

pp. 209-246 ◽

Cited By ~ 2

Author(s):

H. Kokkola ◽

R. Hommel ◽

J. Kazil ◽

U. Niemeier ◽

A.-I. Partanen ◽

...

Keyword(s):

Size Distribution ◽

Climate Model ◽

Extreme Values ◽

Reference Model ◽

Time Integration ◽

Volcanic Eruptions ◽

Aerosol Size Distribution ◽

Different Types ◽

Large Volcanic Eruptions ◽

Good Agreement

Abstract. In this manuscript, we present an intercomparison of three different aerosol microphysics modules that are implemented in the climate model ECHAM5. The comparison was done between the modal aerosol microphysics module M7, which is currently the default aerosol microphysical core in ECHAM5, and two sectional aerosol microphysics modules SALSA, and SAM2. A detailed aerosol microphycical model MAIA was used as a reference model to evaluate the results of the aerosol microphysics modules with respect to sulphate aerosol. The ability of the modules to describe the development of the aerosol size distribution was tested in a zero dimensional framework. We evaluated the strengths and weaknesses of different approaches under different types of stratospheric conditions. Also, we present an improved method for the time integration in M7 and study how the setup of the modal approach affects the evolution of the aerosol size distribution. Intercomparison simulations were carried out with varying SO2 concentrations from background conditions to extreme values arising from stratospheric injections of large volcanic eruptions. Under background conditions, all microphysics modules were in good agreement describing the shape of the size distribution but the scatter between the model results increased with increasing SO2 concentrations. In particular for the volcanic case the module setups have to be redefined to be applied in global model simulations capturing respective sulphate particle formation events. Summarized, this intercomparison serves as a review on the different aerosol microphysics modules which are currently available for the climate model ECHAM5.

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A new easy-to-use tool for grain size distribution analysis

10.5194/egusphere-egu2020-2498 ◽

2020 ◽

Author(s):

Yuming Liu ◽

Xingxing Liu ◽

Youbin Sun

Keyword(s):

Grain Size ◽

Size Distribution ◽

Grain Size Distribution ◽

Quaternary Geology ◽

Distribution Analysis ◽

Lacustrine Deposits ◽

Mean Grain Size ◽

Different Types ◽

Geological Information ◽

End Members

Grain size distribution (GSD) data have been widely used in Earth sciences, especially Quaternary Geology, due to its convenience and reliability. However, the usages of GSD are still oversimplified. The geological information contained in GSD is very abundant, but only some simplified proxies (e.g. mean grain size) are widely used. The most important reason is that GSD data are hard to interpret and visualize directly.To overcome this, some researchers have developed the methods to unmix the mixed multi-modal GSD to some components to make the interpretation and visualization easier. These methods can be divided into two routes. One is end-member analysis (EMA) which takes a batch of samples for the calculation of the end-members. Another is called single-specimen unmixing (SSU) (Sun et al., 2002) which treats each sample as an individual. The key difference between the two routes is that whether the end-members of a batch of samples are consistent. EMA believes that the end-members between different samples are consistent, the variations of GSD are only caused by the changing of fractions of the end-members. On the contrary, SSU has no assumption on the end-members, i.e. it admits that the end-members may vary between different samples. Some mature tools (Paterson and Heslop, 2015; Dietze and Dietze, 2019) taking the EMA route have appeared, but there is no available public and easy-to-use tool for SSU.Here we introduce a free and open-source GUI tool which is called QGrain, it can help researchers to analyze the GSD data easily and bring new insights for the interpretation of GSD. QGrain is based on SSU but applied some algorithms (e.g. data preprocessing and global optimization) to improve its precision and robustness. It supports Lognormal or Weibull as the base distribution and it is easy to add more base distributions. QGrain can handle different types of sediments (e.g. aeolian, fluvial and lacustrine deposits). QGrain can export all detailed data and generate the charts automatically.

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