scholarly journals Simulation of Spatial Spread of the COVID-19 Pandemic on the Basis of the Kinetic-Advection Model

Physics ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 85-102
Author(s):  
Vladimir V. Aristov ◽  
Andrey V. Stroganov ◽  
Andrey D. Yastrebov
Keyword(s):  
Geographical Location ◽  
Spreading Rate ◽  
Equation Model ◽  
Dynamic Density ◽  
Spatial Spread ◽  
One Dimensional ◽  
Average Spreading ◽  
The One ◽  
Two Parameters ◽  
Two Parameter

A new two-parameter kinetic equation model is proposed to describe the spatial spread of the virus in the current pandemic COVID-19. The migration of infection carriers from certain foci inherent in some countries is considered. The one-dimensional model is applied to three countries: Russia, Italy, and Chile. Both their geographical location and their particular shape stretching in the direction from the centers of infection (Moscow, Lombardy, and Santiago, respectively) make it possible to use such an approximation. The dynamic density of the infected is studied. Two parameters of the model are derived from known data. The first is the value of the average spreading rate associated with the transfer of infected persons in transport vehicles. The second is the frequency of the decrease in numbers of the infected as they move around the country, associated with the arrival of passengers at their destination. An analytical solution is obtained. Simple numerical methods are also used to perform a series of calculations. Calculations us to make some predictions, for example, about the time of recovery in Russia, if the beginning of recovery in Moscow is known.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (03) ◽  
pp. 714-716
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (3) ◽  
pp. 714-716 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

scholarly journals Closed-Form Exact Solutions for the Unforced Quintic Nonlinear Oscillator

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Augusto Beléndez ◽  
Enrique Arribas ◽  
Tarsicio Beléndez ◽  
Carolina Pascual ◽  
Encarnación Gimeno ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Elliptic Integral ◽  
First Integral ◽  
Jacobi Elliptic Function ◽  
Complete Elliptic Integral ◽  
One Dimensional ◽  
The Common ◽  
The One ◽  
Two Parameters

Closed-form exact solutions for the periodic motion of the one-dimensional, undamped, quintic oscillator are derived from the first integral of the nonlinear differential equation which governs the behaviour of this oscillator. Two parameters characterize this oscillator: one is the coefficient of the linear term and the other is the coefficient of the quintic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative values of these coefficients which provide periodic motions are considered. The set of possible combinations of signs of these coefficients provides four different cases but only three different pairs of period-solution. The periods are given in terms of the complete elliptic integral of the first kind and the solutions involve Jacobi elliptic function. Some particular cases obtained varying the parameters that characterize this oscillator are presented and discussed. The behaviour of the periods as a function of the initial amplitude is analysed and the exact solutions for several values of the parameters involved are plotted. An interesting feature is that oscillatory motions around the equilibrium point that is not at x=0 are also considered.

Travelling waves in exothermic systems

1988 ◽  
Vol 416 (1850) ◽  
pp. 103-113 ◽  
Keyword(s):  
Travelling Waves ◽  
Physical Situation ◽  
Theoretical Problem ◽  
Thermal Ignition ◽  
Adiabatic Temperature Rise ◽  
One Dimensional ◽  
Infinite Extent ◽  
Spatially Distributed ◽  
The One ◽  
Two Parameters

The classical theoretical problem of thermal ignition and extinction in a reactive slab of infinite extent under conditions near transition to continuous behaviour is revisited. It is assumed that the system is governed by two parameters. The first corresponds to the Frank-Kamenetskii parameter, δ; the second is in some circumstances related to the dimensionless ambient temperature of inverse activation energy ( β = RT a / E ) and in other circumstances to the dimensionless adiabatic temperature rise ( θ ad or B ). The value of the second parameter ( β or B ) is assumed to be close to its transition value, where a ‘cuspoidal’ behaviour of the reacting system appears. A perturbation analysis of the problem shows that additional, spatially distributed states exist in the system in the form of travelling waves of reaction. One of the newly discovered solutions is stable and corresponds to the one-dimensional combustion wave. The second solution is unstable and cannot be related to a real physical situation.

Perfect and ε-perfect simulation methods for the one-dimensional Kac equation

2016 ◽  
Vol 22 (4) ◽  
Author(s):  
Jem N. Corcoran ◽  
Dale Jennings ◽  
Paul VaughanMiller
Keyword(s):  
Poisson Process ◽  
Single Particle ◽  
Marginal Distribution ◽  
Direct Simulation Monte Carlo ◽  
Equation Model ◽  
Perfect Sampling ◽  
One Dimensional ◽  
Kac Equation ◽  
Simulation Monte Carlo ◽  
The One

AbstractWe review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single particle at any given time. We describe and implement a new algorithm that efficiently and more fully leverages properties of the Poisson process, show that it performs at least as well as existing methods, and give empirical evidence that it may perform better at capturing the tails of the single particle velocity distribution. Finally, we derive and implement a novel “ε-perfect sampling” algorithm for the limiting marginal distribution as time goes to infinity. In this case the importance is a proof of concept that has the potential to be expanded to more interesting (DSMC) direct simulation Monte Carlo applications.

scholarly journals A two parameter design storm for Mediterranean convective rainfall

2016 ◽  
Author(s):  
Rafael García-Bartual ◽  
Ignacio Andrés-Doménech
Keyword(s):  
Return Period ◽  
Geographic Location ◽  
Temporal Patterns ◽  
Auxiliary Variable ◽  
Rainfall Regime ◽  
Design Storm ◽  
Starting Point ◽  
The One ◽  
Two Parameters ◽  
Two Parameter

Abstract. The following research explores the feasibility of building effective design storms for extreme hydrological regimes, such as the one which characterizes the rainfall regime of the East and Southeast of the Iberian Peninsula, without employing IDF curves as a starting point. Nowadays and after decades of functioning of hydrological automatic networks, there exist abundant high resolution rainfall data with a reasonable statistic representation, which enables the direct research of temporal patterns and inner structures of rainfall events at a given geographic location with the aim of establishing a statistical synthesis directly based on those observed patterns. On the former work basis, the authors propose a temporal design storm defined in analytical terms, through a two parameter gamma-type function. The two parameters are directly estimated from 73 independent storms identified from rainfall records of highly temporal resolution in Valencia (Spain). All the relevant analytical properties deriving from that function are developed in order to use this storm in real applications. In particular, in order to assign a probability to the design storm (return period), an auxiliary variable combining maximum intensity and total cumulated rainfall is introduced. As a result, for every return period, three storms with different temporal patterns but a similar magnitude are defined. The consistency of the results is verified by means of comparison with the classic method of alternating blocks based on an IDF curve, for the above mentioned study case.

Statistical Reconstruction of the One-Dimensional Mechanical and Fatigue Strengths

2007 ◽  
Vol 353-358 ◽  
pp. 2493-2496 ◽  
Author(s):  
Yong Xiang Zhao ◽  
Bing Yang ◽  
Wei Hua Zhang
Keyword(s):  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Statistical Distributions ◽  
One Dimensional ◽  
Statistical Reconstruction ◽  
Confidence Levels ◽  
Maximum Value ◽  
Production Practice ◽  
The One ◽  
Two Parameter

A Monte-Carlo simulation method for the reconstruction of one-dimensional probabilistic mechanical and fatigue strengths is developed to realize reliability analysis at arbitrary probability and confidence levels. This method is valid to the cases of the probabilistic parameters given at special probabilities (Ps) or probability-confidences (P-Cs). To overcome the shortage of common simulations with numerous samples which is out of true production practice, a simulation policy is newly suggested with 7 to 20 samples for material small specimens and, at most 10 for structural specimens and 5 percentages for the error of simulated parameters fitting the original ones. Details of the method in practice are studied for the six possible statistical distributions i.e. normal, lognormal, three-parameter Weibull, two-parameter Weibull, maximum value, and minimum value ones. The reconstructions of the fatigue limits of 10 Chinese engineering materials have indicated the availability and feasibility of the present method.

Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

2001 ◽  
Vol 32 (3) ◽  
pp. 133-141 ◽  
Author(s):  
Gerrit Antonides ◽  
Sophia R. Wunderink
Keyword(s):  
Willingness To Pay ◽  
Energy Saving ◽  
Subjective Time ◽  
Durable Good ◽  
Discount Function ◽  
Hyperbolic Discount ◽  
The One ◽  
Two Parameter ◽  
Difference Effect ◽  
Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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