scholarly journals An Approach to Regge Behaviour and Duality Based on an Infinite Sum of One-Particle-Exchange Amplitudes

1972 ◽  
Vol 47 (1) ◽  
pp. 208-227 ◽  
Author(s):  
Kisei Kinoshita ◽  
Masanori Kobayashi ◽  
Kunio Shiga
Keyword(s):  
Regge Behaviour ◽  
Particle Exchange ◽  
Infinite Sum

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

scholarly journals First-Principles Atomistic Thermodynamics and Configurational Entropy

2020 ◽  
Vol 8 ◽  
Author(s):  
Christopher Sutton ◽  
Sergey V. Levchenko
Keyword(s):  
First Principles ◽  
Configurational Entropy ◽  
Functional Materials ◽  
Expansion Method ◽  
Bulk Materials ◽  
Cluster Expansion Method ◽  
Particle Exchange ◽  
Properties Of Materials ◽  
Atomistic Thermodynamics ◽  
Statistical Effects

In most applications, functional materials operate at finite temperatures and are in contact with a reservoir of atoms or molecules (gas, liquid, or solid). In order to understand the properties of materials at realistic conditions, statistical effects associated with configurational sampling and particle exchange at finite temperatures must consequently be taken into account. In this contribution, we discuss the main concepts behind equilibrium statistical mechanics. We demonstrate how these concepts can be used to predict the behavior of materials at realistic temperatures and pressures within the framework of atomistic thermodynamics. We also introduce and discuss methods for calculating phase diagrams of bulk materials and surfaces as well as point defect concentrations. In particular, we describe approaches for calculating the configurational density of states, which requires the evaluation of the energies of a large number of configurations. The cluster expansion method is therefore also discussed as a numerically efficient approach for evaluating these energies.

Rearrangement collisions: two-particle exchange

1964 ◽  
Vol 277 (1369) ◽  
pp. 206-213 ◽  
Keyword(s):  
Energy Dependence ◽  
Cross Section ◽  
Born Approximation ◽  
High Energy ◽  
Electron Exchange ◽  
Final States ◽  
Particle Exchange ◽  
Exchange Cross Section

It is shown that the first Bom approximation for the exchange of two uncorrelated electrons should vanish. A formalism for the T matrix is presented which has this property. The high-energy result for the two-electron exchange cross-section previously calculated in first Born approximation behaves like E -7 . This result is in error due to a lack of orthogonality of initial and final states. When this is corrected the result for uncorrelated electrons has an energy dependence E -11 . The introduction of correlation gives terms behaving like E -10 which cannot be calculated unam biguously.

A Closer Look at Particle Exchange in the Gulf Stream

1994 ◽  
Vol 24 (6) ◽  
pp. 1399-1418 ◽  
Author(s):  
Amy S. Bower ◽  
M. Susan Lozier
Keyword(s):  
Gulf Stream ◽  
Particle Exchange

scholarly journals Perturbative evolution and Regge behaviour

1999 ◽  
Vol 448 (3-4) ◽  
pp. 281-289 ◽  
Author(s):  
J.R. Cudell ◽  
A. Donnachie ◽  
P.V. Landshoff
Keyword(s):  
Regge Behaviour

Numerical integration by systematic sampling

1950 ◽  
Vol 46 (1) ◽  
pp. 111-115 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Numerical Integration ◽  
Bounded Variation ◽  
Mathematical Problem ◽  
Random Variable ◽  
Mean Value ◽  
Lattice Points ◽  
Systematic Sampling ◽  
Image Position ◽  
Infinite Sum

Recent investigations by F. Yates (1) in agricultural statistics suggest a mathematical problem which may be formulated as follows. A function f(x) is known to be of bounded variation and Lebesgue integrable on the range −∞ < x < ∞, and its integral over this range is to be determined. In default of any knowledge of the position of the non-negligible values of the function the best that can be done is to calculate the infinite sumfor some suitable δ and an arbitrary origin t, where s ranges over all possible positive and negative integers including zero. S is evidently of period δ in t and ranges over all its values as t varies from 0 to δ. Previous writers (Aitken (2), p. 45, and Kendall (3)) have examined the resulting errors for fixed t. (They considered only symmetrical functions, and supposed one of the lattice points to be located at the centre.) Here we do not restrict ourselves to symmetrical functions and consider the likely departure of S(t) from J (the required integral) when t is a random variable uniformly distributed in (0, δ). It will be shown that S(t) is distributed about J as mean value, with a variance which will be evaluated as a function of δ, the scale of subdivision.

Consequences of new-heavy-particle exchange ine+e−→W+W−

1992 ◽  
Vol 45 (3) ◽  
pp. 771-776 ◽  
Author(s):  
Y. A. Coutinho ◽  
J. A. Martins Simões ◽  
M. C. Pommot Maia
Keyword(s):  
Heavy Particle ◽  
Particle Exchange
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