Remarks concerning the double cascade as a necessary mechanism for the instability of steady equivalent-barotropic flows

Summary In a recent paper, Petroniet al. claim that a necessary condition for the instability of two-dimensional steady flows is a ?double cascade? of energy and enstrophy respectively to larger and to smaller scales of motion. It is shown here that the analytical reasoning employed by Petroniet al. is flawed and that their conclusions are incorrect. What is true is that in any scale interaction (whether an instability or not), neither energy nor enstrophy can be transferred in one spectral direction only, but this result is extremely well known.     

Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations

High resolution finite difference schemes for solving the nonlinear model Boltzmann equations are presented for the computations of rarefied gas flows. The discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model Boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Then a high order essentially nonoscillatory method due to Harten et al. (J. Comput. Phys. 71, 231, 1987) is adapted and extended to solve them. Explicit methods using operator splitting and implicit methods using the lower-upper factorization are described to treat multidimensional problems. The methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use. The computed results using model Boltzmann equations are found to compare well both with those using the direct simulation Monte Carlo results in the transitional regime flows and those with the continuum Navier-Stokes calculations in near continuum regime flows.     

Brief comment on W. S. Warren et al II: Optical NMR and the B(3) field

It is pointed out that the only possible artifact, free opticalNMR (ONMR) shift of up to 0.1Hz reported by Warrenet al. [1] is the same precisely, 0.1Hz, as that predicted byB ³ theory. However, the great majority of the data by Warrenet al. are almost completely artifactual and cannot be used to discriminate between differentONMR mechanisms with any objectivity. Some references toB ³ theory andrecent ONMR data uncited by Warrenet al. are pointed out, data which show that the Warren group–s failure to see very well known [2,3] polarization-dependent effects of irradiation inNMR is a major design failure, not one of theory.     

Transition probabilities in Pr(II) and the solar praseodymium abundance

We have measured branching ratios for all of the known transitions from five levels in Pr⁺. We use the known mean lifetime of four of these levels to compute transition probabilities for 40 transitions. Five of our stronger lines are seen in the sun. We use the equivalent widths of Moore et al. and the solar model parameters of Righini and Rigutti to compute the photospheric Prabundance: log (N_Pr/N_H) + 12 = 0.66 ± 0.15. This value is a factor of ten lower than the most recent photospheric abundance measurement of Grevesse and Blanquet. The difference arises in part from the new transition probabilities, in part from the equivalent widths. We justify our use of widths from Moore et al. by comparing them with widths measured on the Preliminary Kitt Peak Solar Atlas.     

Resolution of a Classical Gravitational Second-Law Paradox

Sheehan and coworkers have claimed [D. P. Sheehan et al., Found. Phys. 30, 1227 (2000); 32, 441 (2002); D. P. Sheehan, in Quantum Limits to the Second Law, AIP Conference Proceedings 643 (American Institute of Physics, Melville, NY, 2002), p. 391] that a dilute gas trapped between an external shell and a gravitator can support a steady state in which energy flux by particles in one direction is balanced by energy flux by radiation in the opposite direction, and in which work can be extracted from an isothermal heat reservoir, thereby violating the second law of thermodynamics. In this paper, we identify a fundamental error in their simulation and analysis of their model system that vitiates their conclusions. We analyze a simpler, exactly soluble, three-dimensional model of a very dilute gas in a gravitational field between two thermal reservoirs, and show that their conclusions are not supported for the simple model. We show that their method of simulation, when applied to either the simple model or their more complex model under simpler conditions where the answers are known, leads to unphysical results. We also show that, when appropriate sampling is done, their model gives results in accord with the second law and detailed balance.     

Comment on “Isotopic mass effects for low-energy channeling in a silicon crystal”

In April, 2010, after reading “An improved critical angle equation for ion channeling” (Zheng theory) proposed by Zheng et al. (1) in Nuclear Instruments and Methods in Physics Research Section B (NIM-B), we felt very strange, because the theory contradicts the well-known Lindhard theory (2) and many of the experimental results published during the last few decades (3). Therefore, we submitted our first comments (4) to NIM-B for publication on 15 April 2010. In September 2010, we had found a new paper published by Zheng et al. (5) in Radiation Effects and Defects in Solids. In the latter paper (5), Zheng et al. studied the isotopic mass effects for low-energy channeling in a silicon crystal by using Monte Carlo (MC) simulations. Immediately, we remembered that a similar work had been published by Zheng et al. two years before for low-energy ion channeling in single-wall carbon nanotubes (SWCNT) (6). The aim of the two papers (5, 6) is finding simulation evidence to support the Zheng theory (1) by studying isotopic ion channeling.     

Some Stability and Instability Criteria for Ideal Plane Flows

We investigate stability and instability of steady ideal plane flows for an arbitrary bounded domain. First, we obtain some general criteria for linear and nonlinear stability. Second, we find a sufficient condition for the existence of a growing mode to the linearized equation. Third, we construct a steady flow which is nonlinearly and linearly stable in the L² norm of vorticity but linearly unstable in the L² norm of velocity.     

Sea Level Muon Spectrum Derived from the All Particle Primary Spectrum of GRIGOROV et al.

The all particle primary spectrum of GRIGOROV et al. surveyed by HILLAS has been fitted by a power law fit of the form I_{all particle}(>E) = 1.3 E^?1.65 (cm² s sr)^?1 where E is the energy in GeV/nucleus. Using our recently determined conversion factor for protonnuclei flux ratio of equal energies the primary proton spectrum has been calculated and the result agrees with the Goddard Space Flight Centre primary proton spectrum data satisfactorily. The primary nucleon spectrum has also been calculated and follows the form N_nucleons(E) dE = 2.664 E^?2.75 dE (cm² s sr GeV/nucleon)^?1. Using this primary nucleon spectrum as the source of hadrons and accelerator data for various inclusive reactions viz. used for the estimation of hadronic energy moments in the frame work of FEYNMAN- Scaling, the differential meson spectra have been estimated. The meson atmospheric diffusion equation after Bugaev et al. has been considered for the derivation of sea level muon spectrum. The magnetic spectrograph data of Allkofer et al., Ayre et al., Green et al., and MUTRON group are in accord with the calculated muon spectrum.     

Electrostatics of DNA-cationic lipid complexes: isoelectric instability

We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al. Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998     

DeuteronA(q 2 ) structure function in the low and mediumq 2 range

The deuteronA(q ² ) structure function is calculated up toq ²=20 fm^–2 with the Paris potential including relativistic nucleonic and mesonic corrections. Different parametrizations (Iachello et al., Galster et al., Höhler et al., Gari and Krümpelmann (GK)) of the nucleon electromagnetic form factors (emff) are used. Unlike the data of Simon et al., those recently taken at Saclay are reasonably well reproduced by our full predictions for the first three emff considered. On the contrary, the predictions for the GK model fail to fit the Saclay data. The dependence ofA(q ² ) on the cut-off masses of the hadronic form factors is also investigated.     

Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid

We analyze the analog of the Kelvin-Helmholtz instability on the free surface of a superfluid liquid. This instability is induced by the relative motion of superfluid and normal components of the same liquid along the surface. The instability threshold is found to be independent of the value of viscosity, but turns out to be lower than in the absence of dissipation. The result is similar to that obtained for the interface between two sliding super-fluids (with different mechanisms of dissipation) and confirmed by the first experimental observation of the Kelvin-Helmholtz instability on the interface between ³He-A and ³He-B by Blaauwgeers et al. (cond-mat/0111343).     

正压流体中具有β效应与地形效应的强迫Rossby孤立波

正压流体中,从有外源的准地转位涡方程出发采用摄动方法和时空伸长变换推导了具有β效应、地形效应和外源的强迫Rossby孤立波方程,得到孤立Rossby波振幅的演变满足带有地形与外源强迫的非齐次 Boussinesq方程的结论. 通过分析孤立Rossby波振幅的演变,指出β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素,说明在地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次Boussinesq方程,给出在切变基本气流下地形和正压流体中R     

Equivalence of certain convex and nonconvex models of spatially modulated structures

The ground states of a certain class of one-dimensional models with a nonconvex interatomic interaction which exhibit spatially modulated structures are proved to be equivalent to those of the Frenkel-Kontorova-type models with a convex interatomic interaction. One of the nonconvex models numerically studied by Marchandet al. belongs to this class, and it turns out to be equivalent to the exactly solvable model with a complete devil's staircase studied by Aubry.     

The self-similarity of wall-bounded temporally accelerating turbulent flows

From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as U^∧_c(t) = U₀(t/t₀)^m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations.     

Beltrami states for compressible barotropic flows

Beltrami states for compressible barotropic flows are deduced by minimizing the total kinetic energy while keeping the total helicity constant. A Hamiltonian basis for these Beltrami states is sketched. An interesting physical application of the compressible barotropic Beltrami state arises with the Kuzmin-Oseledets formulation of compressible Euler equations. Further, Ertel's invariant is shown to become degenerate in the compressible barotropic Beltrami state.     

Accelerating Universe with a Special Form of Decelerating Parameter

In this article, we try to investigate the quintessence model with a minimally coupled scalar field by taking a special form of decelerating parameter q in such a way that which provides an early deceleration and late time acceleration for barotropic fluid and Chaplygin gas dominated models. We have shown that the potential function V(φ) is always decreases with the scalar field φ for barotropic and Chaplygin both models. The {r,s} diagram shows the behaviour of the universe in different stages during the evolution.     

A quasi-classical trajectory study of the Cl + H<Subscript>2</Subscript> (D<Subscript>2</Subscript>) reaction on a new BW3 potential energy surface

Molecular reaction dynamics of Cl + H₂ (D₂) has been studied on the latest analytical potential energy surface called BW3 using the Monte Carlo quasi-classical trajectory method. Excitation functions, differential cross sections and angular distributions of HCl and DCl products have been calculated. The excitation functions of the Cl (²P_3/2) + n-H₂ and Cl(²P_3/2) + n-D₂ reactions are also studied. The results are compared with those of quasi-classical trajectory [M. Alagia et al.: Phys. Chem. Chem. Phys. 2 (2000); F. J. Aoiz et al.: J. Phys. Chem. 100 (1996)], quantum mechanical (QM) calculations [F. J. Aoiz et al.:J. Chem. Phys. 115 (2001)] and experimental data [S. H. Lee et al.: J. Chem. Phys. 110 (1999); F. Dong et al.: J. Chem. Phys. 115 (2001)]. Discussions are given to some new results.     

On the Kelvin-Helmholtz instability in superfluids

The Kelvin-Helmholtz instability in superfluids is discussed on the basis of the first experimental observation of such an instability at the interface between superfluid ³He-A and superfluid ³He-B (R. Blaauwgeers, V. B. Eltsov, G. Eska et al., cond-mat/0111343). We discuss why the Kelvin-Helmholtz criterion, the Landau critical velocity for nucleation of ripplons, and the free-energy consideration all give different values for the instability threshold.     

Some tentative model considerations based on experimental neuromagnetic data

Summary In this paper we present some tentative model considerations, based on the concept of an equivalent current dipole to account for observed auditory evoked responses, with the aim of attempting a comparison of variations in amplitude and latency with calculations based on Rall’s greatly simplified nerve model. A phenomenological analysis of experimental data on the late, auditory evoked magnetic field from the human auditory cortex is presented. The emphasis is here placed on relations between signal properties (e.g. amplitude and latency) and between signal properties and stimulus properties (e.g. amplitude/latency and relative frequency glide Δf/f for a frequency glide stimulus) rather than on questions related to the location of the equivalent current dipole,e.g. the tonotopic organization discussed by Elberlinget al. and by Romaniet al.. Some results of a numerical calculation based on a linear-cable model are presented and compared with experimental results. Paper presented at the ?IV International Workshop on Biomagnetism?, held in Rome, September 14–16, 1982.     

Exact steady states to a nonlinear surface growth model

We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.