scholarly journals Simple analytic solution of fireball hydrodynamics

Open Physics ◽  
2004 ◽  
Vol 2 (4) ◽  
Author(s):  
Tamás Csörgő
Keyword(s):  
Equation Of State ◽  
Temperature Profile ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Ideal Gas ◽  
New Family ◽  
Special Cases ◽  
Rotationally Symmetric

AbstractA new family of simple analytic solutions of hydrodynamics is found for slowly expanding, rotationally symmetric fireballs assuming an ideal gas equation of state. The temperature profile is position-independent only in the collisionless gas limit. The Zimányi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamic particle sources are recovered as special cases. The results are applied to predict new features of proton correlations and spectra for 1.93 AGeV Ni+Ni collisions.

GRAVITATIONAL COLLAPSE OF NEWTONIAN STARS

2000 ◽  
Vol 09 (01) ◽  
pp. 35-42 ◽  
Author(s):  
JUNG-HWAN JUN ◽  
YOUNG KWAK HO
Keyword(s):  
Equation Of State ◽  
Gravitational Collapse ◽  
Analytic Solutions ◽  
Ideal Gas ◽  
Oscillatory Behavior ◽  
Small Oscillation ◽  
Spherically Symmetric ◽  
Thermodynamic Equation ◽  
Spherically Symmetric Solutions ◽  
Collapse Behavior

We investigate spherically symmetric solutions for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars of ideal gas. Using simple ansätze it is shown that the assumption of a polytrope, [Formula: see text], at the center of the star only suffices to obtain analytic solutions. We find collapse behavior for γ≤4/3 and oscillatory behavior for γ>4/3 along with the discussion on their mechanisms. For the oscillatory behavior we obtained the frequency of small oscillation ω which is [Formula: see text] times that obtained by Zel'dovich and Novikov.

Oscillation of a Piston in a Cylinder and Its Approximate Solutions

2021 ◽  
Vol 03 (03) ◽  
pp. 2150011
Author(s):  
Yuji Kajiyama
Keyword(s):  
Nonlinear Equation ◽  
Harmonic Oscillator ◽  
Small Amplitude ◽  
Analytic Solution ◽  
Approximate Solutions ◽  
Equation Of Motion ◽  
Analytic Solutions ◽  
Ideal Gas ◽  
Elementary Functions ◽  
Adiabatic Processes

We discuss the oscillation of a piston in a cylinder with various amplitudes in adiabatic processes. When a piston in a cylinder moves due to the pressure of a contained ideal gas, it will oscillate like a harmonic oscillator in the case of small amplitude. However, it is difficult to obtain an analytic solution of the equation of motion because of its nonlinearity in general. In this paper, we find that analytic solutions are expressed by elementary functions under approximations of various amplitudes, which can well describe the motion of the piston. It will help students to understand a nonlinear equation of motion appearing in thermodynamics.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

scholarly journals Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

scholarly journals A New Family of High-Order Ehrlich-Type Iterative Methods

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1855 ◽  
Author(s):  
Petko D. Proinov ◽  
Maria T. Vasileva
Keyword(s):  
Iterative Methods ◽  
Local Convergence ◽  
Semilocal Convergence ◽  
High Order ◽  
Convergence Theorems ◽  
New Family ◽  
Special Cases ◽  
Iteration Functions ◽  
Iteration Function ◽  
Local Convergence Analysis

One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.

scholarly journals On the determination of molecular fields. —II. From the equation of state of a gas

1924 ◽  
Vol 106 (738) ◽  
pp. 463-477 ◽  
Keyword(s):  
Equation Of State ◽  
Molecular Model ◽  
Virial Coefficients ◽  
Preceding Paper ◽  
Molecular Field ◽  
Inverse Power ◽  
Theoretical Expression ◽  
Inverse Power Law ◽  
Special Cases ◽  
Molecular Fields

The investigation of a preceding paper has shown that the temperature variation of viscosity, as determined experimentally, can be satisfactorily explained in many gases on the assumption that the repulsive and attractive parts of the molecular field are each according to an inverse power of the distance. In some cases, in argon, for example, it was further shown that the experimental facts can be explained by more than one molecular model, from which we inferred that viscosity results alone are insufficient to determine precisely the nature of molecular fields. The object of the present paper is to ascertain whether a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field. Such an investigation is made possible by the elaborate analysis by Kamerlingh Onnes of the observational material. He has expressed the results in the form of an empirical equation of state of the type pv = A + B/ v + C/ v 2 + D/ v 4 + E/ v 6 + F/ v 8 , where the coefficients A ... F, called by him virial coefficients , are determined as functions of the temperature to fit the observations. Now it is possible by various methods to obtain a theoretical expression for B as a function of the temperature and a strict comparison can then be made between theory and experiment. Unfortunately the solution for B, although applicable to any molecular model of spherical symmetry, is purely formal and contains an integral which can be evaluated only in special cases. This has been done up to now for only two simple models, viz., a van der Waals molecule, and a molecule repelling according to an inverse power law (without attraction), but it is shown in this paper that it can also be evaluated in the case of the model, which was successful in explaining viscosity results. As the two other models just mentioned are particular cases of this, the appropriate formulæ for B are easily deduced from the general one given here.

scholarly journals The modified beta transmuted family of distributions with applications using the exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0258512
Author(s):  
Phillip Oluwatobi Awodutire ◽  
Oluwafemi Samson Balogun ◽  
Akintayo Kehinde Olapade ◽  
Ethelbert Chinaka Nduka
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Life Time ◽  
Time Data ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
Family Of Distributions

In this work, a new family of distributions, which extends the Beta transmuted family, was obtained, called the Modified Beta Transmuted Family of distribution. This derived family has the Beta Family of Distribution and the Transmuted family of distribution as subfamilies. The Modified beta transmuted frechet, modified beta transmuted exponential, modified beta transmuted gompertz and modified beta transmuted lindley were obtained as special cases. The analytical expressions were studied for some statistical properties of the derived family of distribution which includes the moments, moments generating function and order statistics. The estimates of the parameters of the family were obtained using the maximum likelihood estimation method. Using the exponential distribution as a baseline for the family distribution, the resulting distribution (modified beta transmuted exponential distribution) was studied and its properties. The modified beta transmuted exponential distribution was applied to a real life time data to assess its flexibility in which the results shows a better fit when compared to some competitive models.

Thermoelasticity

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Equation Of State ◽  
Elastic Deformation ◽  
Additional Assumption ◽  
Polymer Network ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Constant Volume ◽  
Conformational Energy ◽  
Network Chain ◽  
Constant Deformation

The important postulate that intermolecular interactions are independent of extent of deformation leads directly to the conclusion that such interactions cannot contribute to an energy of elastic deformation ΔEel at constant volume. In the earliest theories of rubberlike elasticity, it was additionally assumed that, intramolecular contributions to ΔEel were likewise nil. In this idealization that the total ΔEel is zero, the elastic retractive force exhibited by a deformed polymer network would be entirely entropic in origin. At the molecular level, this would correspond, of course, to assuming all configurations of a network chain to be of exactly the same conformational energy and thus the average configuration to be independent of temperature. Under these circumstances, the dependence of stress on temperature is strikingly simple, as shown, for example, by the equation . . . f* = υkT/V (〈r2〉i/〈r2〉0)(α – α-2) . . . . . . (9.1) . . . that characterizes a polymer network in elongation where, it should be recalled, 〈r2〉i3/2 is proportional to the volume of the network. This additional assumption that 〈r2〉0 is independent of temperature would lead to the prediction that the elastic stress determined at constant volume and elongation α is directly proportional to the absolute temperature. Such network chains would be akin to the particles of an ideal gas, which would obey the equation of state p = nRT(1/V) and thus exhibit a pressure at constant deformation (1/V) likewise directly proportional to the temperature.

scholarly journals A New Family of Extended Lindley Models: Properties, Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2146
Author(s):  
Abdulrahman Abouammoh ◽  
Mohamed Kayid
Keyword(s):  
Power Distribution ◽  
Data Sets ◽  
Simulation Studies ◽  
Biological Engineering ◽  
Unified Approach ◽  
Right Censored Data ◽  
New Family ◽  
Special Cases ◽  
Life Distributions ◽  
And Behavior

There are many proposed life models in the literature, based on Lindley distribution. In this paper, a unified approach is used to derive a general form for these life models. The present generalization greatly simplifies the derivation of new life distributions and significantly increases the number of lifetime models available for testing and fitting life data sets for biological, engineering, and other fields of life. Several distributions based on the disparity of the underlying weights of Lindley are shown to be special cases of these forms. Some basic statistical properties and reliability functions are derived for the general forms. In addition, comparisons among various forms are investigated. Moreover, the power distribution of this generalization has also been considered. Maximum likelihood estimator for complete and right-censored data has been discussed and in simulation studies, the efficiency and behavior of it have been investigated. Finally, the proposed models have been fit to some data sets.

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