SYMBOLIC DYNAMICS OF THE ONE-DIMENSIONAL BIQUADRATIC MAP WITH 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.

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Travelling waves in exothermic systems

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1988.0030 ◽

1988 ◽

Vol 416 (1850) ◽

pp. 103-113 ◽

Cited By ~ 17

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.

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

Physics ◽

10.3390/physics3010008 ◽

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.

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

Swiss Journal of Psychology ◽

10.1024/1421-0185.67.1.51 ◽

2008 ◽

Vol 67 (1) ◽

pp. 51-60 ◽

Cited By ~ 26

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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ZERO TEMPERATURE CRITICAL BEHAVIOUR OF THE ONE DIMENSIONAL X-Y MODEL WITH RANDOM COUPLING CONSTANTS

Le Journal de Physique Colloques ◽

10.1051/jphyscol:19711360 ◽

1971 ◽

Vol 32 (C1) ◽

pp. C1-1010-C1-1011

Author(s):

E. R. SMITH

Keyword(s):

Coupling Constants ◽

Critical Behaviour ◽

Zero Temperature ◽

One Dimensional ◽

Random Coupling ◽

The One

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FURTHER TESTS OF VALIDITY FOR THE ONE-DIMENSIONAL HONG'S PSYCHOLOGICAL REACTANCE SCALE

Psychological Reports ◽

10.2466/pr0.101.7.871-874 ◽

2007 ◽

Vol 101 (7) ◽

pp. 871 ◽

Cited By ~ 1

Author(s):

PETER K. JONASON

Keyword(s):

Psychological Reactance ◽

One Dimensional ◽

The One

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Adiabatic large polarons in anisotropic molecular crystals

Journal of Research in Physics ◽

10.2478/v10242-012-0002-2 ◽

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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A New Algorithm for the One-Dimensional Cutting Stock Problem

i-manager’s Journal on Future Engineering and Technology ◽

10.26634/jfet.1.2.963 ◽

2006 ◽

Vol 1 (2) ◽

pp. 78-84

Author(s):

Sarath. B. Siyambalapitiya ◽

Keyword(s):

Cutting Stock Problem ◽

Cutting Stock ◽

One Dimensional ◽

The One

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Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

Annals of Glaciology ◽

10.3189/s026030550000567x ◽

1983 ◽

Vol 4 ◽

pp. 297-297

Author(s):

G. Brugnot

Keyword(s):

Finite Difference Method ◽

Transverse Velocity ◽

Longitudinal Velocity ◽

Momentum Conservation ◽

Dimensional Model ◽

One Dimensional ◽

Modelling Techniques ◽

Reference Grid ◽

The One ◽

Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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Effect of leakage and blockage on the acoustic behavior of particle filters

Noise Control Engineering Journal ◽

10.3397/1/376744 ◽

2019 ◽

Vol 67 (6) ◽

pp. 483-492

Author(s):

Seonghyeon Baek ◽

Iljae Lee

Keyword(s):

Transfer Matrix ◽

Particle Filters ◽

Acoustic Analysis ◽

Transmission Loss ◽

One Dimensional ◽

Filter System ◽

The Difference ◽

The One ◽

Analytical Approaches ◽

Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

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