A note on Janossy's mathematical model of a nucleon cascade

1952 ◽  
Vol 48 (3) ◽  
pp. 451-456 ◽  
Author(s):  
Alladi Ramakrishnan
Keyword(s):  
Mathematical Model ◽  
Specific Problem ◽  
Close Relation ◽  
Diffusion Equations ◽  
Density Functions ◽  
Stochastic Variable ◽  
Product Density ◽  
Stochastic Problems ◽  
Product Densities ◽  
Number Of Particles

In a contribution (3) to these Proceedings the author considered stochastic problems in physics where one had to deal with a stochastic variable representing the number of particles distributed in a continuous infinity of states characterized by a parameter E, and where the distribution varied with another parameter t which might be continuous or discrete (if t represents time or thickness, it is of course continuous). The author introduced the concept of product densities and derived some general results relating to the functions representing these densities. Recently, Janossy(2), using a certain mathematical model for a nuclear cascade, introduced certain functions which bear a close relation to the product-density functions. The object of this note is to establish a complete correspondence between these two sets of functions and apply them to the specific problem of the development of a nucleon cascade. The diffusion equations involving product densities can be derived from the diffusion equations involving Janossy's functions.

Stochastic processes relating to particles distributed in a continuous infinity of states

1950 ◽  
Vol 46 (4) ◽  
pp. 595-602 ◽  
Author(s):  
Alladi Ramakrishnan
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Stochastic Processes ◽  
Stochastic Variable ◽  
Stochastic Problems ◽  
Image Position ◽  
Number Of Particles

Many stochastic problems arise in physics where we have to deal with a stochastic variable representing the number of particles distributed in a continuous infinity of states characterized by a parameter E, and this distribution varies with another parameter t (which may be continuous or discrete; if t represents time or thickness it is of course continuous). This variation occurs because of transitions characteristic of the stochastic process under consideration. If the E-space were discrete and the states represented by E1, E2, …, then it would be possible to define a functionrepresenting the probability that there are ν1 particles in E1, ν2 particles in E2, …, at t. The variation of π with t is governed by the transitions defined for the process; ν1, ν2, … are thus stochastic variables, and it is possible to study the moments or the distribution function of the sum of such stochastic variableswith the help of the π function which yields also the correlation between the stochastic variables νi.

Correlation problems in evolutionary stochastic processess

1961 ◽  
Vol 57 (4) ◽  
pp. 843-847 ◽  
Author(s):  
Alladi Ramakrishnan ◽  
T. K. Radha
Keyword(s):  
Stochastic Process ◽  
Single Point ◽  
Statistical Distribution ◽  
Density Functions ◽  
Product Density ◽  
Continuous Space ◽  
Electron Photon ◽  
Number Of Particles

ABSTRACTIn a previous contribution to these Proceedings (Ramakrishnan(1)) the concept of product density was introduced to describe the statistical distribution of a discrete number of particles in a continuous space E, corresponding to a single point t, where t is the parameter with respect to which the stochastic process evolves. This is extended to densities corresponding to n points on the t axis and correlation problems associated with these density functions are studied with particular reference to electron-photon cascades.

Tissue necrosis and passage of fluid due to cold stress from the thermally damaged human body peripherals: A mathematical model

2015 ◽  
Vol 04 (02) ◽  
pp. 1550012
Author(s):  
M. A. Khanday ◽  
Fida Hussain ◽  
Khalid Nazir
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Heat Equation ◽  
Cold Stress ◽  
Human Body ◽  
Human Subjects ◽  
Diffusion Equations ◽  
Tissue Necrosis ◽  
Cold Temperatures ◽  
Element Technique

The development of cold injury takes place in the human subjects by means of crystallization of tissues in the exposed regions at severe cold temperatures. The process together with the evaluation of the passage of fluid discharge from the necrotic regions with respect to various degrees of frostbites has been carried out by using variational finite element technique. The model is based on the Pennes' bio-heat equation and mass diffusion equations together with suitable initial and boundary conditions. The results are analyzed in relation with atmospheric temperatures and other parameters of the tissue medium.

scholarly journals Mathematical modelling of biosensors with substrate and product degeneration

2012 ◽  
Vol 53 ◽  
Author(s):  
Liana Stonkienė ◽  
Feliksas Ivanauskas
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Linear Term ◽  
Diffusion Equations ◽  
Enzymatic Reactions ◽  
Amperometric Biosensors ◽  
One Dimensional ◽  
Non Linear ◽  
Kinetics Of

This paper presents a one-dimensional-in-space mathematical model of the amperometric biosensors with substrate and product degeneration. The model is based on diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. It was analyzed effect of substrate and product degeneration for the biosensors response.

scholarly journals Influence of the Concentration of Fe and Cu Nanoparticles on the Dynamics of the Size Distribution of Nanoparticles

2020 ◽  
Vol 8 ◽  
Author(s):  
Sergey V. Gudkov ◽  
Ilya V. Baimler ◽  
Oleg V. Uvarov ◽  
Veronika V. Smirnova ◽  
Mikhail Yu Volkov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Size Distribution ◽  
Colloidal Solution ◽  
Relative Concentration ◽  
Initial Distribution ◽  
Cu Nanoparticles ◽  
Distribution Shifts ◽  
Agglomeration Of Nanoparticles ◽  
Individual Nanoparticles ◽  
Number Of Particles

The evolution of the size distribution of nanoparticles depending on the concentration of nanoparticles in a colloidal solution is investigated. The formation of new stable distributions shifted relative to the initial distribution is directly related to the processes of agglomeration of nanoparticles. Using successive two-fold dilutions of nanoparticles by 2–32 times, it was shown that the maximum of the nanoparticle size distribution shifts toward smaller sizes with a decrease in the concentration of nanoparticles, both for distributions by the number of nanoparticles and for distributions by mass of nanoparticles. Thus, with dilutions, the relative concentration of individual nanoparticles increases, while the number of particles in one aggregate decreases. A mathematical model has been created that predicts a change in distribution with a change in the concentration of nanoparticles in a colloid.

scholarly journals Arrival Traffic Separations Modelling By Using Continuous Probability Distributions

2019 ◽  
Vol 285 ◽  
pp. 00013
Author(s):  
Adrian Pawełek ◽  
Piotr Lichota
Keyword(s):  
Mathematical Model ◽  
Quantitative Analysis ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Air Traffic ◽  
Density Functions ◽  
Traffic Intensity ◽  
Traffic Data ◽  
Model Application ◽  
Comparing Distributions

This article presents a method that allows to analyze selected aspects of past arrival traffic by modelling distributions of time separations of arriving aircraft in a chosen navigationpoint of Terminal Manoeuvring Area with the use of continuous probability distributions. Modelling arriving aircraft time separations distribution with continuous probability density functions allows to apply various mathematical tools to analyze separations distributions. Moreover, by comparing distributions parameters, quantitative analysis of separations for days with various arrival traffic intensity can be performed. Assumptions, mathematical model, application in the exemplary experimental scenario with an airport and days with low and high traffic intensity, and results are presented in this article. Real air traffic data was used for the experimental scenario. Outcomes show that the method can be used for air traffic post-analysis, e.g assessment of maintaining separation.

Monte Carlo simulation of the influence of pressure and target–substrate distance on the sputtering process for metal and semiconductor layers

2016 ◽  
Vol 30 (20) ◽  
pp. 1650253 ◽  
Author(s):  
Abdelkader Bouazza ◽  
Abderrahmane Settaouti
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Vapor Deposition ◽  
Physical Vapor Deposition ◽  
Close Relation ◽  
Gas Pressure ◽  
Substrate Distance ◽  
Good Agreement ◽  
Number Of Particles

The energy and the number of particles arriving at the substrate during physical vapor deposition (PVD) are in close relation with divers parameters. In this work, we present the influence of the distance between the target and substrate and the gas pressure in the sputtering process of deposited layers of metals (Cu, Al and Ag) and semiconductors (Ge, Te and Si) for substrate diameter of 40 cm and target diameter of 5 cm. The nascent sputter flux, the flux of the atoms and their energy arriving at the substrate have been simulated by Monte Carlo codes. A good agreement between previous works of other groups and our simulations for sputter pressures (0.3–1 Pa) and target–substrate distances (8–20 cm) is obtained.

The Influence of the Diffusion Space Geometry on Behavior of some Processes in Biochemistry and Electrochemistry

2000 ◽  
Vol 5 ◽  
pp. 3-38 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys ◽  
M. Sapagovas ◽  
A. Survila
Keyword(s):  
Mathematical Model ◽  
Reaction Diffusion ◽  
Electrode Reaction ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Carbon Paste ◽  
Diffusion Type ◽  
Function Modelling ◽  
Partially Blocked Electrodes ◽  
The Mathematical Model

The reaction-diffusion and diffusion equations were applied for modelling of some processes in biochemistry and electrochemistry. Modelling of the amperometric biosensors based on carbon paste electrodes encrusted with a single nonhomogeneous microreactor is analyzed. The mathematical model of the biosensor operation is based on nonstationary reaction-diffusion equations containing a non-linear term given by Michaelis-Menten function. Modelling of a simple redox-electrode reaction, involving two soluble species, is also considered. The model of the electrode behavior, taking into account the resist layer of the partially blocked electrodes, was expressed as a system of differential equations of the diffusion type with initial and boundary conditions. The mathematical model generalizing both processes: biochemical and electrochemical is presented in this paper. The generalized problem was solved numerically. The finite-difference technique was used for discretisation of the model. Using the numerical solution of the generalized problem, the influence of the size, shape and position of a microreactor as well as the thickness of the resist layer on the current dynamics was investigated.

A New Method of Evaluating the Sensitivity of Sensitive Load to Voltage Sag

2014 ◽  
Vol 960-961 ◽  
pp. 746-754
Author(s):  
Rui Bin Luo
Keyword(s):  
Mathematical Model ◽  
Probability Density ◽  
Probability Density Functions ◽  
New Method ◽  
Voltage Sag ◽  
Density Functions ◽  
Weighted Sum ◽  
Tolerance Curve ◽  
Function Models ◽  
The Mathematical Model

This paper proposes a new method to evaluate the voltage sag sensitivity (VSS) of the sensitive load by the combination of several probability density function models, which can fully describe the randomness of load sensitivity. Firstly, five common probability density functions were respectively used to build the mathematical model of voltage tolerance curve (VTC) of sensitive load in uncertainty region. Secondly, the VSS of sensitive load was respectively evaluated by five models, and the weighted sum of five models’ results was calculated by unbiased variance method. In the end, the proposed method was verified to be rational according to an application example.

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