Some features of relationships between physico-chemical and technological parameters in the orientation of polyethylene terephthalate films

Vlasov, S. V.; Кулезнев, В. Н.

doi:10.1016/0032-3950(83)90352-0

Cited by 11 publications

(14 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equation (59) is qualitatively similar to the equation (31) except the presence of the third and the fourth term of the left hand side of (59). These two terms are qualitatively similar to the second term of the same equation.…”

Section: Vlasov-boltzmann Equation At the Order ǫ 9/6mentioning

confidence: 71%

“…Longitudinal electron plasma oscillations are damped during the propagation through a collisionless plasma. In particular, Vlasov [31] used the linearized Boltzmann equation to investigate the small amplitude steady state longitudinal electron plasma oscillations. Shortly afterwards, Landau [32] pointed out that these oscillations are damped.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

Dalui

Bandyopadhyay

2020

Indian J Phys

View full text Add to dashboard Cite

A Korteweg-de Vries (KdV) equation including the effect of Landau damping is derived to study the propagation of weakly nonlinear and weakly dispersive ion acoustic waves in a collisionless unmagnetized plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. The hotter energetic electron species follows the nonthermal velocity distribution of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] whereas the cooler electron species obeys the Boltzmann distribution. It is found that the coefficient of the nonlinear term of this KdV like evolution equation vanishes along different family of curves in different parameter planes. In this context, a modified KdV (MKdV) equation including the effect of Landau damping effectively describes the nonlinear behaviour of ion acoustic waves. It has also been observed that the coefficients of the nonlinear terms of the KdV and MKdV like evolution equations including the effect of Landau damping, are simultaneously equal to zero along a family of curves in the parameter plane. In this situation, we have derived a further modified KdV (FMKdV) equation including the effect of Landau damping to describe the nonlinear behaviour of ion acoustic waves. In fact, different modified KdV like evolution equations including the effect of Landau damping have been derived to describe the nonlinear behaviour of ion acoustic waves in different region of parameter space. The method of Ott & Sudan [Phys. Fluids 12, 2388Fluids 12, (1969] has been applied to obtain the solitary wave solution of the evolution equation having the nonlinear term (φ (1) ) r ∂φ (1) ∂ξ , where φ (1) is the first order perturbed electrostatic potential and r = 1, 2, 3. We have found that the amplitude of the solitary wave solution decreases with time for all r = 1, 2, 3.

show abstract

Section: Vlasov-boltzmann Equation At the Order ǫ 9/6mentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

Dalui

Bandyopadhyay

2020

Indian J Phys

View full text Add to dashboard Cite

show abstract

“…If we replace f (v, t) by P (v, t) and f (v ′ , t) by the Maxwellian distribution f (v ′ ) given by Eq. (34), we obtain the Fokker-Planck equation (37) describing the relaxation of a test particle in a bath of field particles at statistical equilibrium (thermal bath). In that case, we recover the results of Sec.…”

Section: Discussionmentioning

confidence: 99%

“…A first treatment of collective effects in plasma physics was introduced by Vlasov (1938Vlasov ( ,1945 [36,37]. He treated collective effects in a self-consistent manner but neglected "collisions" between charges.…”

Section: Introductionmentioning

confidence: 99%

Kinetic theory of spatially homogeneous systems with long-range interactions: II. Historic and basic equations

Chavanis

2013

Eur. Phys. J. Plus

View full text Add to dashboard Cite

We provide a short historic of the early development of kinetic theory in plasma physics and synthesize the basic kinetic equations describing the evolution of systems with long-range interactions derived in Paper I. We describe the evolution of the system as a whole and the relaxation of a test particle in a bath of field particles at equilibrium or out-of-equilibrium. We write these equations for an arbitrary long-range potential of interaction in a space of dimension d. We discuss the scaling of the relaxation time with the number of particles for non-singular potentials. For always spatially homogeneous distributions, the relaxation time of the system as a whole scales like N in d > 1 and like N 2 (presumably) or like e N (possibly) in d = 1. For always spatially inhomogeneous distributions, the relaxation time of the system as a whole scales like N in any dimension of space. For 1D systems undergoing a dynamical phase transition from a homogeneous to an inhomogeneous phase, we expect a relaxation time of the form N δ with 1 < δ < 2 intermediate between the two previous cases. The relaxation time of a test particle in a bath always scales like N . We also discuss the kinetic theory of systems with long-range interactions submitted to an external stochastic potential. This paper gathers basic equations that are applied to specific systems in Paper III.

show abstract

“…By definition, in the meanfield collisionless regime the collisional integral can be neglected: in this case, the phenomenon under investigation has a characteristic time much smaller than the relaxation time [9]. We shall work in this collisionless regime and the 3D Boltzmann-Vlasov equation (1) becomes the so-called 3D Landau-Vlasov (or Hartree-Vlasov) equation [23,24]:…”

Section: Landau-vlasov Equation and Its Dimensional Reductionmentioning

confidence: 99%

Nonequilibrium statistical mechanics in one-dimensional bose gases

Baldovin¹,

Cappellaro²,

Orlandini³

et al. 2016

J. Stat. Mech.

View full text Add to dashboard Cite

Abstract. We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann-Vlasov equation with contact interaction, we derive an effective 1D Landau-Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-ofequilibrium states, obtaining stability criteria similar to those of classical plasmas.

show abstract

Some features of relationships between physico-chemical and technological parameters in the orientation of polyethylene terephthalate films

Cited by 11 publications

References 2 publications

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

Kinetic theory of spatially homogeneous systems with long-range interactions: II. Historic and basic equations

Nonequilibrium statistical mechanics in one-dimensional bose gases

Contact Info

Product

Resources

About