Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

On the derivation of the incompressible Mavier-Stokes equation for Hamiltonian particle systems

We consider a Hamiltonian paticle system interacting by means of a pair potetial. We look at the behavior of the system on a space scale of order ^-1, times of order ^-2 and mean velocities of order , with a scale parameter. Assuming that the phase space density of the particles is give by a series in (the analog of the Chapman-Enskog expansion), the behavior of the system under this rescaling is described, to the lowest order in , by the incompressible Navier-Stokes equations. The viscosity is given in terms of microscopic correlations, and its expression agrees with the Green-Kubo formula.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

Operator Semigroup Compactifications

A weakly continuous, equicontinuous representation of a semitopological semigroup on a locally convex topological vector space gives rise to a family of operator semigroup compactifications of , one for each invariant subspace of . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.

     

A strong limit theorem for generalized Cantor-like random sequences

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The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

Analysis and simulation on the performance of a gyro-penitron amplifier

A cylindrical waveguide gyro-peniotron amplifier is analysed theoretically in this paper. By a ballistic method and directly using the energy conservation in the beam-wave system, a set of interaction equations for the cylindrical waveguide gyro-peniotron amplifier is derived. Computer simulation shows that under defined conditions an interaction efficiency of 47%, an output power of 240kW at a gain of 22. 5 dB and a 3 dB-instantaneous bandwidth of 1. 9% for a central frequency of 35GHz, TE₀₃ mode gyro-peniotron amplifier could be achieved. The influence of the operation parameters on the amplifier performance is also presented.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Peculiarities of changes of some physicomechanical characteristics of monoisotopes B, B and natural β-boron

Real structure and some physicomechanical characteristics of the samples of natural beta-rhombohedral boron B as well as of its ¹⁰B and ¹¹B monoisotopes have been studied. It was shown that the influence of ¹⁰B and ¹¹B isotopes on physicomechanical properties of boron had a different character. In particular, the samples enriched with ¹¹B had high values of microhardness, shear modulus (SM) and elastic limit if compared to those of boron, while the samples enriched with ¹⁰B monoisotopes were characterized with high values of thermal expansion coefficient (TEC) and thermal conductivity; lattice parameters a and c increased by the sequence: ¹¹B, B, ¹⁰B. It was established that TEC, thermal conductivity, microhardness, SM and shear elastic limit increased in all samples at annealing for 5 h at 1500 °C regardless of isotope content.