This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be re...
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This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.
A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for t...
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A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed.
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective...
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective Action of this spatial field theory and investigate its general properties and some numerical solutions. The equation is completely universal, and allows for the scale invariant solutions in the inertial range. The critical indices are not fixed at the kinematical level, but rather should be found from certain eigenvalue conditions, as in the field theory of critical phenomena. Unlike the Wyld field theory, there are no divergences in our Feynman integrals, due to some magic cancellations. The simplest possible Gaussian approximation yields crude but still reasonable results (there are deviations from Kolmogorov scaling in 3 dimensions, but at 2.7544 dimensions it would be exact). Our approach allows us to study some new problems, such as spontaneous parity breaking in 3d turbulence. It turns out that with the appropriate helicity term added to the velocity correlation function, logarithmic infrared divergences arise in our field theory which effectively eliminates these terms. In order to build a quantitative theory of turbulence, one should consider more sophisticated Ansatz for the effective Action, which would require serious numerical work.
The important features of the rescattering trajectories in strong field ionization process such as the cutoff of the return energy at 3.17Up and that of the final energy at 10Up are obtained, based on the adiabatic ap...
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The important features of the rescattering trajectories in strong field ionization process such as the cutoff of the return energy at 3.17Up and that of the final energy at 10Up are obtained, based on the adiabatic approximation in which the initial momentum of the electron is assumed to be zero. We theoretically study the nonadiabatic effect by assuming a nonzero initial momentum on the rescattering trajectories based on the semiclassical simpleman model. We show that the nonzero initial momentum will modify both the maximal return energy at collision and the final energy after backward scattering, but in different ways for odd and even number of return trajectories. The energies are increased for even number of returns but are decreased for odd number of returns when the nonzero （positive or negative） initial momentum is applied.
We consider a reaction-diffusion equation to model a multi-allelic, single locus problem. The population can migrate in a homogeneous region and the diffusion rates depend upon the genotype. It is shown that if there ...
We consider a reaction-diffusion equation to model a multi-allelic, single locus problem. The population can migrate in a homogeneous region and the diffusion rates depend upon the genotype. It is shown that if there is an equilibrium point with all alleles present and if this polymorphism is stable for the classical reaction system then it is also stable for the reaction-diffusion equation. Also a simplified model is used to investigate which allele will spread in the two-allele case. Alleles which are associated with large fitness and small dispersion do best.
Waves propagating in a medium with highly variable refractive index tend to focus forming caustics. The energy content of the wave field in the vicinity of a caustic is higher than that of the ambient field away from ...
Waves propagating in a medium with highly variable refractive index tend to focus forming caustics. The energy content of the wave field in the vicinity of a caustic is higher than that of the ambient field away from the caustic. Consequently, waves scattering from heterogeneities located near caustics have more energy than a field scattering a little further away from the caustic. For a suitable choice of Sobolev norms for the domain and range spaces of the scattering operator, the restriction to scatterers supported away from caustics is a bounded operator, whereas the restriction to scatterers supported in a neighborhood of caustics is unbounded.
We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in...
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We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.
The classical idea of an evolutionarily stable strategy (ESS) does not involve any spatial dependence. An evolution equation for analyzing games in a region is suggested and the possibility of spatial patterns is inve...
The classical idea of an evolutionarily stable strategy (ESS) does not involve any spatial dependence. An evolution equation for analyzing games in a region is suggested and the possibility of spatial patterns is investigated. It is shown that an ESS is so stable that it forbids any spatial dependence but that other equilibria may have patterns associated with them if the dispersion rates are suitably chosen.
The effects of a toroidal magnetic field on the flow features of a rotating magnetosphere containing a conducting fluid are investigated by means of a similarity solution. It is shown that the effects of the toroidal ...
The effects of a toroidal magnetic field on the flow features of a rotating magnetosphere containing a conducting fluid are investigated by means of a similarity solution. It is shown that the effects of the toroidal field are, in general, small in comparison with those of rotation. The solution is applied to the equatorial plasma sheet observed in the middle magnetosphere of Jupiter and is found to be in reasonable agreement with some recorded data.
The effect of the mesons σ＊ and Φ and the variety of UΣ（N ）on the transition density of hyperon stars is examined within the framework of relativistic mean field theory for the baryon octet {n,p,Λ,Σ-,Σ0,Σ＋,...
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The effect of the mesons σ＊ and Φ and the variety of UΣ（N ）on the transition density of hyperon stars is examined within the framework of relativistic mean field theory for the baryon octet {n,p,Λ,Σ-,Σ0,Σ＋,Ξand Ξ0} *** is found that,compared with that without considering the mesons σ＊ and Φ,the transition density of hyperon stars decreases,the critical baryon density that hyperons Σ-,Σ0,Σ＋,Ξand Ξ0 appears to decrease too,but for Λ the effect is not *** U Σ（N ）goes up,the critical baryon density of Σ＋,Σ0 and Σincreases,that of Ξ0 decreases and that of Λ and Ξis *** addition,it is found that the variety of UΣ（N ）almost does not influence the transition density.
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