Density dependence of the ratio of second to first order terms in a perturbation expansion of characteristic thermodynamic properties of dense noble gases

1976 ◽  
Vol 65 (8) ◽  
pp. 2982-2986 ◽  
Author(s):  
Paulette Clippe
Keyword(s):  
Thermodynamic Properties ◽  
Density Dependence ◽  
Noble Gases ◽  
Perturbation Expansion ◽  
First Order

Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons

2009 ◽  
Vol 75 (5) ◽  
pp. 593-607 ◽  
Author(s):  
SK. ANARUL ISLAM ◽  
A. BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Perturbation Expansion ◽  
Magnetized Plasma ◽  
Wave Number ◽  
First Order ◽  
Zk Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

AbstractA theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.

Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water

1993 ◽  
Vol 37 (04) ◽  
pp. 354-383
Author(s):  
Willard J. Pierson
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Perturbation Expansion ◽  
The United States ◽  
Order Perturbation ◽  
Naval Academy ◽  
Third Order ◽  
First Order ◽  
Stokes Waves ◽  
Perturbation Solutions

Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

Pseudo-first order reaction kinetics and thermodynamic properties study of neem oil esterification using MgO grafted natural hydroxyapatite

RSC Advances ◽  
2016 ◽  
Vol 6 (11) ◽  
pp. 8892-8901 ◽  
Author(s):  
Himadri Sahu ◽  
Kaustubha Mohanty
Keyword(s):  
Thermodynamic Properties ◽  
Reaction Kinetics ◽  
Fish Bone ◽  
Order Reaction ◽  
Neem Oil ◽  
Pseudo First Order Reaction ◽  
First Order ◽  
Pseudo First Order ◽  
Natural Hydroxyapatite ◽  
Kinetics And Thermodynamic

In this work, waste fish bone was used as a source of natural hydroxyapatite which was later used for the preparation of a metal grafted catalyst.

Wave-number dependence of the static screening function of an interacting electron gas. II. Higher-order exchange and correlation effects

1970 ◽  
Vol 48 (2) ◽  
pp. 167-181 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Density Dependence ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Interpolation Formula ◽  
Higher Order ◽  
Wave Number ◽  
Correlation Effects ◽  
Many Body ◽  
Static Screening

An interpolation formula is suggested for the wave-number and density dependence of the static screening function for an interacting electron gas in its ground state. The approximate screening function simulates a number of properties of the exact screening function which have been established by analysis of its many-body perturbation expansion. The accuracy of the interpolation formula is discussed and is considered to be adequate for practical calculations in the range of intermediate metallic densities.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

scholarly journals The effect of core size on the speed of compressible hollow vortex streets

2017 ◽  
Vol 836 ◽  
pp. 797-827 ◽  
Author(s):  
Darren G. Crowdy ◽  
Vikas S. Krishnamurthy
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Vortex Core ◽  
Perturbation Expansion ◽  
Core Size ◽  
Flow Equations ◽  
Stable Case ◽  
First Order ◽  
Aspect Ratios ◽  
Vortex Streets

The effect of weak compressibility on the speed of steadily translating staggered vortex streets of hollow vortices in isentropic subsonic flow is studied. A small-Mach-number perturbation expansion about the incompressible solutions for staggered streets of hollow vortices found recently by Crowdy & Green (Phys. Fluids, 2011, vol. 23, 126602) is carried out; the latter solutions provide a desingularization of the classical point vortex streets of von Kármán. The first-order compressible flow correction is calculated. We employ a novel scheme based on a complex variable formulation of the compressible flow equations (the Imai–Lamla method) combined with conformal mapping theory to track the vortex shape in this free boundary problem. The analysis to find the perturbed streamfunction and compressible vortex shapes is greatly facilitated by exploiting a calculus based on use of the Schottky–Klein prime function of a conformally equivalent parametric annulus. It is found that, for a vortex street of specified aspect ratio comprising vortices of specified circulation, the vortex core size is a key determinant of whether compressibility increases or decreases the steady propagation speed (relative to the incompressible street with the same parameters) and that both eventualities are possible. We focus attention on streets with aspect ratios around 0.28, which is close to the neutrally stable case for incompressible flow, and find that a critical vortex core size exists at which compressibility does not affect the speed of the street at first order in the (squared) Mach number. Streets comprising vortices with core size below the critical value speed up due to compressibility; larger vortices slow down.

scholarly journals Electronic structure, low-temperature transport and thermodynamic properties of polymorphic β-As2Te3

RSC Advances ◽  
2016 ◽  
Vol 6 (57) ◽  
pp. 52048-52057 ◽  
Author(s):  
J.-B. Vaney ◽  
J.-C. Crivello ◽  
C. Morin ◽  
G. Delaizir ◽  
J. Carreaud ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Low Temperature ◽  
Thermodynamic Properties ◽  
Transport Properties ◽  
Lattice Distortion ◽  
First Order

The first-order lattice distortion undergone by β-As2Te3 around 200 K results in a cycling effect on its transport properties.

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