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 .     

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.     

Optimization of inoculum to substrate ratio for enhanced methane yield from leather fleshings in a batch study

One of the most significant issues of the last few decades has been tracing for renewable energy sources. Animal fleshing (ANFL) is the most common proteinaceous solid waste accured during the production of leather and it must be disposed of in an environmentally responsible manner. This paper is attempts to assess the biogas production from solid waste originating from the chrome based tannery. Anaerobic digestion of these wastes will be a viable option for waste stabilization and energy production in the form of biogas to be utilized in the industry. The bio-methane potential of the wastes were examined by mixing these wastes with various sources of inoculum and different inoculum to substrate (I/S) ratio considered. The batch experiments were carried out in 2.5 l glass reactors with a various source of inoculumviz., Cow Dung (CD), Elephant Dung (ED) and Bio-Digested Slurry (BDS) with varied inoculum to substrate (LFs) ratios for a retention time of 50 days with replications. The results obtained from the experiments showed that BDS:LF (25:75) had the highest gas production of 14505 ml (651.85 ml CH₄g^?1 VS) followed by CD:LF (50:50) produced 12072.5 ml (789.36 ml CH₄g^?1 VS) and ED:LF (75:25) produced 11252.5 ml (1492.08 ml CH₄g^?1 VS)with a methane content of 63.77, 61.92 and 62.72%, respectively.     

Chiroptical detection. Novel possibilities of its application to enantiomers

Summary Polarimetric and/or circular dichroic detection of enantiomers after liquid chromatography on optically active sorberts has been used for the following purposes: determination of enantiomeric purity in spite of peak overlap, investigation of enantiomerization during chromatography, monitoring of racemizations and recording of circular dichrograms without preparative enrichment of enantiomers. Novel examples for all applications are give. The general prospects for chiroptical detection are discussed.     

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.