Enhancements to a Simple Pavement Frost Model

2016 ◽  
Vol 2579 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Brendan Duffy ◽  
David Orr ◽  
Heather J. Miller
Keyword(s):  
Frost Model

Threshold limit theorems for some epidemic processes

1980 ◽  
Vol 12 (02) ◽  
pp. 319-349 ◽  
Author(s):  
Bengt Von Bahr ◽  
Anders Martin-Löf
Keyword(s):  
Limit Distribution ◽  
Limit Theorems ◽  
Polymerization Process ◽  
Connected Components ◽  
Critical Threshold ◽  
Infected Person ◽  
Initial Number ◽  
Total Size ◽  
Frost Model ◽  
Healthy Persons

The Reed–Frost model for the spread of an infection is considered and limit theorems for the total size, T, of the epidemic are proved in the limit when n, the initial number of healthy persons, is large and the probability of an encounter between a healthy and an infected person per time unit, p, is λ/n. It is shown that there is a critical threshold λ = 1 in the following sense, when the initial number of infected persons, m, is finite: If λ ≦ 1, T remains finite and has a limit distribution which can be described. If λ > 1 this is still true with a probability σ m < 1, and with probability 1 – σ m T is close to n(1 – σ) and has an approximately Gaussian distribution around this value. When m → ∞ also, only the Gaussian part of the limit distribution is obtained. A randomized version of the Reed–Frost model is also considered, and this allows the same result to be proved for the Kermack–McKendrick model. It is also shown that the limit theorem can be used to study the number of connected components in a random graph, which can be considered as a crude description of a polymerization process. In this case polymerization takes place when λ > 1 and not when λ ≦ 1.

VARIABILITY FOR CARRIER-BORNE EPIDEMICS AND REED–FROST MODELS INCORPORATING UNCERTAINTIES AND DEPENDENCIES FROM SUSCEPTIBLES AND INFECTIVES

2010 ◽  
Vol 24 (2) ◽  
pp. 303-328 ◽  
Author(s):  
Eva María Ortega ◽  
Laureano F. Escudero
Keyword(s):  
Risk Assessment ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Random Environments ◽  
Random Parameters ◽  
Infection Rates ◽  
Disease Propagation ◽  
Increasing Concave Order ◽  
Special Cases ◽  
Frost Model

This article provides analytical results on which are the implications of the statistical dependencies among certain random parameters on the variability of the number of susceptibles of the carrier-borne epidemic model with heterogeneous populations and of the number of infectives under the Reed–Frost model with random infection rates. We consider dependencies among the random infection rates, among the random infectious times, and among random initial susceptibles of several carrier-borne epidemic models. We obtain conditions for the variability ordering between the number of susceptibles for carrier-borne epidemics under two different random environments, at any time-scale value. These results are extended to multivariate comparisons of the random vectors of populations in the strata. We also obtain conditions for the increasing concave order between the number of infectives in the Reed–Frost model under two different random environments, for any generation. Variability bounds are obtained for different epidemic models from modeling dependencies for a range of special cases that are useful for risk assessment of disease propagation.

The Frost Model of Concrete in the View of Damage Mechanics

2011 ◽  
Vol 194-196 ◽  
pp. 919-923 ◽  
Author(s):  
Dong Fang Pan ◽  
Yun Feng Qiao ◽  
Cheng Shuai Sun ◽  
Xue Bing Liu
Keyword(s):  
Plastic Deformation ◽  
Damage Mechanics ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Dissipation Function ◽  
Continuum Damage ◽  
Thawing Cycle ◽  
Frost Model ◽  
Elastic Modules ◽  
The Continuum

To propose the damage model of concrete in the freezing-thawing cycles, the reasonable dissipation function and micro plastic deformation expression have been determined based on the continuum damage mechanics. The damage variable is expressed as a function of the number of freezing-thawing cycle. The damage is defined in terms of the loss of the dynamic elastic modules and the damage model of the concrete in the freezing-thawing cycles has been presented.

A Simple Frost Model for Calculation of the Frost Thickness over Ground Aircraft Surfaces

2011 ◽  
Vol 121-126 ◽  
pp. 667-671
Author(s):  
Li Wen Wang ◽  
Dan Dan Xu
Keyword(s):  
Simple Model ◽  
Surface Temperature ◽  
Air Temperature ◽  
Temperature Decrease ◽  
Atmospheric Conditions ◽  
Air Velocity ◽  
Frost Formation ◽  
Frost Model

In this study, a simple model that describes frost formation over ground aircraft surfaces is presented. The model uses the data of the aircraft surface temperature, air temperature and air velocity to predict the frost thickness. The frost surface temperature and the frost thickness under different atmospheric conditions are investigated. The results indicate the frost thickness increases with the air velocity and the air temperature, decrease with the surface temperature. This model enables forecast of the frost formation over ground aircraft surface.

An unusual stochastic order relation with some applications in sampling and epidemic theory

1993 ◽  
Vol 25 (1) ◽  
pp. 63-81 ◽  
Author(s):  
Claude Lefevre ◽  
Philippe Picard
Keyword(s):  
Stochastic Order ◽  
Infection Intensity ◽  
Order Relation ◽  
Final Size ◽  
Factorial Moments ◽  
Comparison Results ◽  
Global Cost ◽  
Frost Model ◽  
Sampling Procedures ◽  
Total Damage

One expects, intuitively, that the total damage caused by an epidemic increases, in a certain sense, with the infection intensity exerted by the infectives during their lifelength. The original object of the present work is to make precise in which probabilistic terms such a statement does indeed hold true, when the spread of the disease is described by a collective Reed–Frost model and the global cost is represented by the final size and severity. Surprisingly, this problem leads us to introduce an order relation for -valued random variables, unusual in the literature, based on the descending factorial moments. Further applications of the ordering occur when comparing certain sampling procedures through the number of un-sampled individuals. In particular, it is used to reinforce slightly comparison results obtained earlier for two such samplings.

A point-charge representation of frost-model wave functions

1975 ◽  
Vol 40 (3) ◽  
pp. 221-230 ◽  
Author(s):  
A. Terry Amos ◽  
Jonathan A. Yoffe
Keyword(s):  
Point Charge ◽  
Wave Functions ◽  
Model Wave ◽  
Frost Model
Sign in / Sign up

Export Citation Format

Share Document