A flow conservation law for surface processes

1996 ◽  
Vol 28 (1) ◽  
pp. 13-28 ◽  
Author(s):  
G. Last ◽  
R. Schassberger
Keyword(s):  
Vector Field ◽  
Random Vector ◽  
Conservation Law ◽  
Point Processes ◽  
Surface Processes ◽  
Random Surface ◽  
Gauss Divergence Theorem ◽  
Contact Distribution ◽  
Flow Conservation ◽  
Random Vector Field

The object studied in this paper is a pair (Φ, Y), where Φ is a random surface in and Y a random vector field on . The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field Y is smooth outside Φ but may have discontinuities on Φ. Gauss' divergence theorem is applied to derive a flow conservation law for Y. For this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of Φ are derived.

A flow conservation law for surface processes

1996 ◽  
Vol 28 (01) ◽  
pp. 13-28 ◽  
Author(s):  
G. Last ◽  
R. Schassberger
Keyword(s):  
Vector Field ◽  
Random Vector ◽  
Conservation Law ◽  
Point Processes ◽  
Surface Processes ◽  
Random Surface ◽  
Gauss Divergence Theorem ◽  
Contact Distribution ◽  
Flow Conservation ◽  
Random Vector Field

The object studied in this paper is a pair (Φ, Y), where Φ is a random surface in and Y a random vector field on . The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field Y is smooth outside Φ but may have discontinuities on Φ. Gauss' divergence theorem is applied to derive a flow conservation law for Y. For this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of Φ are derived.

Generation of a random vector field with a specified coherence matrix in vibrational tests

2016 ◽  
Vol 36 (1) ◽  
pp. 25-29
Author(s):  
Yu. Ya. Betkovskii ◽  
V. N. Yakovlev
Keyword(s):  
Vector Field ◽  
Random Vector ◽  
Random Vector Field

scholarly journals Generalized contact distributions of inhomogeneous Boolean models

2002 ◽  
Vol 34 (01) ◽  
pp. 21-47 ◽  
Author(s):  
Daniel Hug ◽  
Günter Last ◽  
Wolfgang Weil
Keyword(s):  
Convex Body ◽  
Large Class ◽  
Random Vector ◽  
Boundary Point ◽  
Conditional Distribution ◽  
Boolean Model ◽  
Spatial Density ◽  
Boolean Models ◽  
Grain Distribution ◽  
Contact Distribution

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ ℝ d and a gauge body B ⊂ ℝ d , such a generalized contact distribution is the conditional distribution of the random vector (d B (L,Z),u B (L,Z),p B (L,Z),l B (L,Z)) given that Z∩L = ∅, where Z is a Boolean model, d B (L,Z) is the distance of L from Z with respect to B, p B (L,Z) is the boundary point in L realizing this distance (if it exists uniquely), u B (L,Z) is the corresponding boundary point of B (if it exists uniquely) and l B (L,·) may be taken from a large class of locally defined functionals. In particular, we pursue the question of the extent to which the spatial density and the grain distribution underlying an inhomogeneous Boolean model Z are determined by the generalized contact distributions of Z.

A limit theorem for point processes by applications

1978 ◽  
Vol 15 (04) ◽  
pp. 726-747
Author(s):  
Prem S. Puri
Keyword(s):  
Limit Theorem ◽  
Point Process ◽  
Random Vector ◽  
Arbitrary Function ◽  
Point Processes ◽  
Probability Generating Function ◽  
Mild Conditions ◽  
Dimensional Distribution ◽  
Image Position

Let 0 ≦ T 1 ≦ T 2 ≦ ·· · represent the epochs in time of occurrences of events of a point process N(t) with N(t) = sup{k : Tk ≦ t}, t ≧ 0. Besides certain mild conditions on the process N(t) (see Conditions (A1)– (A3) in the text) we assume that for every k ≧ 1, as t →∞, the vector (t – TN (t), t – TN (t)–1, · ··, t – TN (t)–k+1) converges in law to a k-dimensional distribution which coincides with that of a random vector ξ k = (ξ 1, · ··, ξ k ) necessarily satisfying P(0 ≦ ξ 1 ≦ ξ 2 ≦ ·· ·≦ ξ k) = 1. Let R(t) be an arbitrary function defined for t ≧ 0, satisfying 0 ≦ R(t) ≦ 1, ∀0 ≦ t <∞, and certain mild conditions (see Conditions (B1)– (B4) in the text). Then among other results, it is shown that The paper also deals with conditions under which the limit (∗) will be positive. The results are applied to several point processes and to the situations where the role of R(t) is taken over by an appropriate transform such as a probability generating function, where conditions are given under which the limit (∗) itself will be a transform of an honest distribution. Finally the results are applied to the study of certain characteristics of the GI/G/∞ queue apparently not studied before.

scholarly journals The SIS Great Circle Epidemic Model

2008 ◽  
Vol 45 (02) ◽  
pp. 513-530 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Point Processes ◽  
Contact Process ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Asymptotic Results ◽  
Sis Model ◽  
Major Outbreak ◽  
Limiting Behaviour ◽  
Contact Distribution ◽  
Process Approximation

We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.

Sign in / Sign up

Export Citation Format

Share Document