Steady flux in a continuous-space Sinai chain

We examine the steady-state flux of particles diffusing in a one-dimensional finite chain with Sinai-type disorder, i.e., the system in which in addition to the thermal noise, particles are subject to a stationary random-correlated in space Gaussian force. For this model we calculate the disorder average (over configurations of the random force) flux exactly for arbitrary values of system's parameters, such as chain lengthN, strength of the force, and temperature. We prove that within the limitN1 the average flux decreases withN as J(N)=C/N and thus confirm our recent predictions that the flux in the discrete-space Sinai model is anomalous.     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Conformational statistics of polymer chain terminally attached to wall (Ⅲ)——NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the "loop" conformation.Investigation has been made on the conformational statistics of a model loop chain by the normal landom walk (NRW) on a lattice confined in the half-infinite space.Based on the conformational distribution function of the NRW model tail chain,it is easy to deduce an analytical formula expressing the conforma-tional number of the model loop chain.It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power function N-2/3 when the chain length N→∞ The same result was obtained by means of the recursion equation.The ratio of the mean square end-to-end distance h2 for the model loop chain to its mean square bond length I2 is 2N/3 Compared with the free chain with the same length N,the mean square end-to-end distance of the model loop chain contracts to a certain extent.The basic relationships deduced were support     

Analysis of grid file algorithms

Grid file algorithms were suggested in [12] to provide multi-key access to records in a dynamically growing file. We specify here two algorithms and derive the average sizes of the corresponding directories. We provide an asymptotic analysis. The growth of the indexes appears to be non-linear for uniform distributions:O(v ^c ) orO(v ), wherec=1+b^–1, =1+(s-1)/(sb+1),s is the number of attributes being used,v the file size, andb the page capacity of the system. Finally we give corresponding results for biased distributions and compare transient phases.     

SHAPE MEMORY EFFECT OF PU IONOMERS WITH IONIC GROUPS ON HARD-SEGMENTS

SMPU （shape memory polyurethane） non-ionomers and ionomers, synthesized with poly（c-caprolactone） （PCL）, 4, 4＇-diphenylmethane diisocyanate （MDI）, 1,4-butanediol （BDO）, dimethylolpropionic acid （DMPA） were measured with cyclic tensile test and strain recovery test. The relations between the structure and shape memory effect of these two series were studied with respect to the ionic group content and the effect of neutralization. The resulting data indicate that, with the introduction of asymmetrical extender, the stress at 100% elongation is decreased for PU non-ionomer and ionomer series, especially lowered sharply for non-ionomer series; the fixation ratio of ionomer series is not affected obviously by the ionic group content; the total recovery ratio of ionomer series is decreased greatly. After sufficient relaxation time for samples stretched beforehand, the switching temperature is raised slightly, whereas the recovery ratio measured with strain recovery test method is lowered with increased DMPA content. The characterization with FT-IR, DSC, DMA elucidated that, the ordered hard domain of the two series is disrupted with the introduction of DMPA which causes more hard segments to dissolve in soft phase; ionic groups on hard segment enhance the cohesion between hard segments especially at high ionic group content and significantly facilitate the phase separation compared with the corresponding non-ionomer at moderate ionic group content.     

Fractal behavior in trapping and reaction: A random walk study

We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimensiond. We interpolate between these two limits by introducing a scaling law. An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimensiond.     

The mean spherical model in a random external field and the replica method

We provide a quick elementary solution of the mean spherical model in a random external field. This also allows an immediate proof of the self-averaging property of the free energy. We calculate the free energy by means of the replica method, i.e., for any (not necessarily integer) replica numbern, and show that when a phase transition occurs the limits andn 0 are not interchangeable.     

Open-access liquid chromatography/mass spectrometry in a drug discovery environment

The use of open-access mass spectrometry to monitor synthetic chemistry reactions, and also the integrity and purity of new chemical entities, has been a part of the medicinal chemist's tool-box for more than 5 years. Originally in our group at Wyeth Research there were two open-access methods available to the chemists, flow injection analysis (FIA) and liquid chromatography/mass spectrometry (LC/MS). The FIA method was approximately 3 min long, while the LC/MS method was approximately 20 min long (including an 8 min gradient). Within the first 2 years, the total number of open-access analyses increased by approximately 125%. It is interesting, however, that the number of LC/MS analyses increased by more than 285%. This is attributed to the fact that the chemists began using the LC/MS data to monitor reactions and also to check final product integrity and purity. In addition, the number of chemists performing parallel synthesis reactions has increased; thus, individual chemists can produce sample sets of up to 100 vials. This paper describes the implementation of new methodology, which accommodates the need for much faster run times and also the ability to acquire alternating positive and negative ion spectra within the same run. In addition, the instrument has been configured to e-mail the resulting processed data report to the submitting chemist. Several methods have been developed, including structure elucidation using in-source collision-induced dissociation (CID) and night-time analysis. The LC/MS methods for this system are described herein and are applicable to both industrial and academic synthetic chemistry optimization efforts.     

Quasi‐random integration in quantum chemistry: Efficiency,stability, and application to the study of small atoms and molecules constrained in spherical boxes

This project consists of two parts. In the first part, a series of test calculations is performed to verify that the integrals involved in the determination of atomic and molecular properties by standard self‐consistent field (SCF) methods can be obtained through Halton, Korobov, or Hammersley quasi‐random integration procedures. Through these calculations, we confirm that all three methods lead to results that meet the levels of precision required for their use in the calculation of properties of small atoms or molecules at least at a Hartree–Fock level. Moreover, we have ensured that the efficiency of quasi‐random integration methods that we have tested is Halton=Korobov>Hammersley?pseudo‐random. We also find that these results are comparable to those yielded by ordinary Monte Carlo (pseudo‐random) integration, with a calculation effort of two orders of smaller magnitude. The second part, which would not have been possible without the integration method previously analyzed, contains a first study of atoms constrained in spherical boxes through SCF calculations with basis functions adapted to the features of the problem: Slater‐type orbitals (STOs) trimmed by multiplying them by a function that yields 1 for 0 < r < (R‐δ), polynomial values for (R‐δ) < r < R and null for r > R, R being the radius of the box and δ a variationally determined interval. As a result, we obtain a equation of state for electrons of small systems, valid just in the limit of low temperatures, but fairly simple. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007