Asymptotic behaviour of particle motion under repulsive forces

The asymptotic nature of motions, as time tends to infinity, is investigated for classical point particles interacting by repulsive two-body potentialsU _ij . It is found that the conditions are necessary and sufficient for asymptotically straight line uniform motion. In the case of equal asymptotic velocities the proof depends only on a certain property of the motion (partial center of mass convexity) implied by the repulsivity of the potentials.The original version of this paper was edited and re-written by A. Lenard from Indiana University. The author expresses his gratitude to Professor Lenard for his work which has significantly improved both the mathematical presentation and the style of the paper     

Asymptotic behavior of the Rayleigh-Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin and Williams for which we give a simplified demonstration. In particular, we observe that the spike's curvature evolves as t(3), while the overshoot in acceleration shows good agreement with the suggested 1/t(5) law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.     

Asymptotic behavior of the Kohn-Sham exchange potential

The Kohn-Sham exchange potential of finite systems is shown to approach different asymptotic limits on nodal surfaces of the energetically highest-occupied orbital than in other regions. This leads to barrier-well structures in the near asymptotic region, which have a strong influence on virtual orbitals and thus on excitation energies. Common approximations for the exchange potential do not exhibit these features. These asymptotic structures, however, can be correctly described by effective exact-exchange methods. Conditions for the presence of an asymptotic barrier well in the full exchange-correlation potential are discussed.     

Asymptotic magnetic behavior of gas transport properties

The nonvanishing elements of the viscosity and thermal conductivity tensors of polyatomic gases fall into two classes: those that change sign with a rotation about the magnetic field line and those that do not. It is shown that the boundedness of the linearized Waldmann-Snider collision operator and its properties under symmetry transformations imply that for linear Zeeman splitting the first class vanishes at zero and infinite field as ¦B ¦ and ¦B ¦^–1 and that the second class approaches its asymptotes as ¦B ¦² and ¦B ¦^–2.Supported by the Department of Naval Ordnance Systems Command N-00017-62-C-0604.     

Asymptotic behavior and the Cabibbo-Radicati sum rule

The Cabibbo-Radicati sum rule has previously been explicitly evaluated (in terms of resonance saturation) to an energy ≈1.7 GeV. An investigation of higher contributions indicates that the sum rule is reasonably well satisfied.     

Asymptotic behavior of the composite nucleon form factors

A new method is proposed for evaluating the nucleon electromagnetic form factors in terms of the p₁₁ pion-nucleon phase shift. The asymptotic behavior of the form factors is discussed.     

Asymptotic behavior of neutron small-angle multiple scattering spectra

The asymptotic behavior of the spectra for large values of the scattering vector for the case of elastic multiple small-angle neutron scattering (SANS) is investigated theoretically and experimentally. An expansion of the spectrum in terms of the reciprocal of the magnitude of the momentum transfer is obtained taking account of the influence of the instrumental line. It is shown that, to within some factor, the leading term of the expansion is identical to the differential single-scattering cross section averaged over a statistical ensemble of particles; several subsequent terms in the expansion are calculated and the range of applicability of the resulting expressions is determined. The asymptotic behavior of the multiple SANS spectrum is measured, using a two-crystal neutron spectrometer, for samples of an HTSC ceramic, the alloy Fe-Ni, and Al powder. The agreement between the experimental results and the theoretical predictions is analyzed. Zh. éksp. Teor. Fiz. 114, 2194–2203 (December 1998)     

Plasma-enhanced chemical vapor deposition of organic particle thin films

Five organic precursors, 2,5-dimethyl-2,4-hexadiene, 2,5-norbornadiene, α-terpinine, limonene, and styrene have been studied as precursors for plasma deposition of low-k films. The films have been produced under particle-forming conditions in the plasma. Accordingly, films have a granular structure with grain sizes in the range 40–400 nm, as determined by AFM. Annealing at 400 °C preserves the granular structure of the films while the grain size decreases. Of the five precursors examined, 2,5-dimethyl-2,4-hexadiene and 2,5-norbornadiene produce films with the lowest dielectric constant, with a value of 3.3. While the dielectric constant varies with deposition conditions (pressure, flow rate, concentration of precursor), we find that the grain size of the films correlates most closely with the dielectric constant and conclude that the lowest value of the dielectric constant are obtained under conditions that promote the formation of particles larger than about 200 nm.     

Reentrant adhesion behavior in nanocluster deposition

We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of incident kinetic energy, we find a transition from adhesion to reflection at low kinetic energies. We also identify a second adhesive regime at intermediate kinetic energies, where strong deformation of the cluster leads to an increase in contact area and adhesive energy.     

Asymptotic behavior of the density for two-particle annihilating exclusion

We consider a stochastic process which presents an evolution of particles of two types,A andB, onZ ^d with annihilations between particles of opposite types. Initially, at each site ofZ ^d, independently of the other sites, we put a particle with probability 2<1 and assign to it one of two types with equal chances. Each particle evolves onZ ^d in the following manner: independently from the others, it waits an exponential time with mean 1, chooses one of its neighboring sites on the latticeZ ^d with equal probabilities, and jumps to the site chosen. If the site to which a particle attempts to move is occupied by another particle of the same type, the jump is suppressed; if it is occupied by a particle of the opposite type, then both are annihilated and disappear from the system. The considered process may serve as a model for the chemical reactionA+Binert. Let (t) denote the density of particles in this process at timet. We prove that there exist absolute finite constantsc(d) andC(d) such that for all sufficiently larget,c(d)t ^–d/4 (t)C(d)t ^–d/4 in the dimensionsd4 andc(d)t ^–1 (t)C(d)t ^–1 in all higher dimensions. This completes and makes more precise the results obtained by us earlier and shows that asymptotically the density behaves like that in a similar process called two-particle annihilating random walks which was studied by Bramson and Lebowitz. Our proofs are based on the approach developed in their and our works. We use the basic properties of random walk and various tools which have been designed to study simple symmetric exclusion processes.     

Asymptotic behavior of densities for two-particle annihilating random walks

Consider the system of particles on ^d where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle meets aB-particle, both disappear, i.e., are annihilated. This system serves as a model for the chemical reactionA+B inert. We analyze the limiting behavior of the densities _A (t) and _B (t) when the initial state is given by homogeneous Poisson random fields. We prove that for equal initial densities _A (0)= _B (0) there is a change in behavior fromd4, where _A (t)= _B (t)C/t ^d /4, tod4, where _A (t)= _B (t)C/tast. For unequal initial densities _A (0)< _B (0), _A (t)e ^–cl ind=1, _A (t)e ^–Ct/logt ind=2, and _A (t)e ^–Ct ind3. The termC depends on the initial densities and changes withd. Techniques are from interacting particle systems. The behavior for this two-particle annihilation process has similarities to those for coalescing random walks (A+AA) and annihilating random walks (A+Ainert). The analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system.     

Asymptotic behavior of pion clusters in different nuclear reactions

This paper is aimed to analyze nuclear processes by means of invariant variables b _ik based on four-velocity vectors. Pion clusters generated in different nuclear reactions are investigated in order to point out their properties able to indicate universal laws for nuclear matter behavior. Some interesting results concerning pion clusters invariant parameters are presented.     

Asymptotic behavior of the Gell-Mann-Low function in quantum field theory

The reconstruction of the Gell-Mann-Low function in quantum field theory from its asymptotic series, whose first terms are calculated using perturbation theory, is discussed. This mathematical problem cannot be solved uniquely. Nevertheless, the desired function can be reconstructed in a certain finite range of coupling constant g under reasonable assumptions about this function. However, attemps to determine the behavior of the function for g→∞ are, in our opinion, groundless. Conditions under which the sum of the divergent perturbation series can rapidly decrease at infinity are determined.