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.

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.

The Stokes constants for a cluster of transition points

1988 ◽  
Vol 104 (1) ◽  
pp. 153-179 ◽  
Author(s):  
Nanny Fröman ◽  
Per Olof Fröman ◽  
Bengt Lundborg
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Travelling Waves ◽  
Stokes Line ◽  
Constant Flow ◽  
One Dimensional ◽  
Stokes Constant ◽  
Transition Points ◽  
The One ◽  
Anti Stokes

AbstractThe connection problems associated with the one-dimensional Schrödinger equation in the presence of a general isolated cluster containing an unspecified number of complex transition points in unspecified positions can be studied by means of the phase-integral method developed by Fröman and Fröman. Any anti-Stokes line, i.e. any line in the complex z-plane on which the solutions behave as travelling waves with constant flow, must asymptotically (i.e. in the limit of large values of |z|) point in one of m +2 possible directions, which divide the region around the cluster into m +2 sectors, where m is the degree of the cluster. The tracing of these waves from an anti-Stokes line, bounding a sector, to an anti-Stokes line constituting the other boundary of the same sector is expressed by means of the Stokes constant for the sector in question. This paper examines the relation between these m + 2 Stokes constants in the general case when the transition points in the cluster may also be close-lying in the sense that it is impossible to treat them individually, when the solutions are traced. Under the assumption that the effective potential in the Schrodinger equation is a regular analytic function in a sufficiently large region containing the cluster, it is shown that the m + 2 Stokes constants are in general constrained by three algebraic relations, which are obtained for arbitrary m. The cases m = 1, 2, 3 and 4 are worked out in detail.

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 Experimental validation of a quasi-two-dimensional radial turbine model

2018 ◽  
Vol 21 (6) ◽  
pp. 915-926 ◽  
Author(s):  
José Galindo ◽  
Francisco José Arnau ◽  
Luis Miguel García-Cuevas ◽  
Pablo Soler
Keyword(s):  
Experimental Validation ◽  
Combustion Engine ◽  
Travelling Waves ◽  
Experimental Results ◽  
Two Dimensional ◽  
One Dimensional ◽  
Radial Turbine ◽  
Variable Geometry Turbine ◽  
The One ◽  
Turbine Model

This article presents the experimental validation of a quasi-two-dimensional radial turbine model able to be used in turbocharged reciprocating internal combustion engine simulations. A passenger car variable-geometry turbine has been tested under steady and pulsating flow conditions, instrumented with multiple pressure probes, temperature sensors and mass flow sensors. Using the data obtained, a pressure decomposition has been performed. The pressure at the turbine inlet and outlet has been split into forward and backward travelling waves, employing the reflected and transmitted waves to verify the goodness of the model. The experimental results have been used to compare the quasi-two-dimensional radial turbine model as well as a classic one-dimensional model. The quasi-two-dimensional code presents a good degree of correlation with the experimental results, providing better results than the one-dimensional approach, especially when studying the high-frequency spectrum.

scholarly journals The Role of Scales in the Dynamics of Parameterization Uncertainties

2006 ◽  
Vol 63 (6) ◽  
pp. 1659-1671 ◽  
Author(s):  
S. Vannitsem
Keyword(s):  
Spectral Characteristics ◽  
Atmospheric Model ◽  
Model Error ◽  
Error Growth ◽  
Model Uncertainties ◽  
One Dimensional ◽  
Spatially Distributed ◽  
The One ◽  
Sivashinsky Equation

Abstract The dynamics of model error due to parameterization uncertainties are investigated in the context of two spatially distributed systems: the one-dimensional convection system known as the extended Kuramoto–Sivashinsky equation and a quasigeostrophic atmospheric model. In addition to the different phases of error growth already reported for low-order systems, unexpected behaviors associated with the spectral characteristics of the model perturbation sources have been brought out. Notably, the predictability of the system is less affected by model uncertainties acting at small scales than at larger ones. An interpretation in terms of the spectral properties of the Lyapunov vectors is advanced.

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.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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