New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

An application of factorial design to the development of fused silica capillary columns

Stationary phase crosslinking conditions for fused silica capillary columns were optimized with the use of a factorial design experiment. This experimental strategy was chosen because it provided for the determination of two-factor interactions. A predictive model was developed for the desired chromatographic performance parameters as a function of the variables of the crosslinking reaction. Confirmatory experiments proved the usefulness of the mathematical model which resulted in the production of capillary columns of superior performance with significant improvements in reproducibility.     

Numerical comparison of several variable-metric algorithms

The paper compares the numerical performances of the LDL decomposition of the BFGS variable-metric algorithm, the Dennis-Mei dogleg algorithm on the BFGS update, and Davidon's projections with the BFGS update with the straight BFGS update on a number of standard test problems. Numerical results indicate that the standard BFGS algorithm is superior to all of the more complex strategies.This research was supported by the National Science Foundation under Research Grant No. MCS77-07327.     

The Enhancement of Efficiency of High-order Harmonic in Intense Laser Field Based on Asymptotic Boundary Conditions and Symplectic Algorithm

Asymptotic boundary condition (ABC) of laser-atom interaction presented recently is applied to transform the initial value problem of the time-dependent Schrödinger equation (TDSE) in infinite space into the initial and boundary value problem in the finite space, and then the TDSE is discretized into linear canonical equations by substituting the symmetry difference quotient for the 2-order partial derivative. The canonical equation is solved by symplectic algorithm. The ground state and the equal weight coherent superposition of the ground state and the first excited state have been taken as the initial conditions, respectively, while we calculate the population of bound states, the evolution of average distance and the high-order harmonic generation (HHG). The conversion efficiency of HHG can be enhanced by initial coherent superposition state and moderate laser intensities     

The optimization of silica gel synthesis from chemical bottle waste using response surface methodology

To reduce the amount of hazardous chemical bottle waste in the environment, we report the optimization research of silica extraction in chemical bottle waste into silica gel. Alkali fusion and sol–gel process were utilised to prepare silica gel effectively. The alkali fusion process was carried out by adding sodium hydroxide to produce sodium silicate. Afterwards, silica gel was prepared by the sol–gel method using hydrochloric acid. Box-Behnken Design (BBD) was applied to Optimisation factors the poptimiseactors affecting the silica recovery. The factors that optimised mass ratio, particle size, and temperature. The optimum recovery of silica gel was obtained by SiO₂: NaOH mass ratio of 1:3, the particle size of 63–74 µm, and a temperature of 800 °C. The purity of silica gel optimum is 63.74% characterised using X-ray fluorescence. The structure of silica gel is the appearance of amorphous peaks at 2θ 20-30° characterised using an x-ray diffractogram. The silica gel surface was characterises using scanning electron microscopy-energy dispersive x-ray. It showed an irregular surface and characteristic showed that silica gel had a radius of 15.74 nm and a specific surface area of 297.08 m².     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

Factor Xa: Simulation studies with an eye to inhibitor design

Factor Xa is a serine protease which activates thrombin and plays a key regulatory role in the blood-coagulation cascade. Factor Xa is at the crossroads of the extrinsic and intrinsic pathways of coagulation and, hence, has become an important target for the design of anti-thrombotics (inhibitors). It is not known to be involved in other processes than hemostasis and its binding site is different to that of other serine proteases, thus facilitating selective inhibition. The design of high-affinity selective inhibitors of factor Xa requires knowledge of the structural and dynamical characteristics of its active site. The three-dimensional structure of factor Xa was resolved by X-ray crystallography and refined at 2.2 Å resolution by Padmanabhan and collaborators. In this article we present results from molecular dynamics simulations of the catalytic domain of factor Xa in aqueous solution. The simulations were performed to characterise the mobility and flexibility of the residues delimiting the unoccupied binding site of the enzyme, and to determine hydrogen bonding propensities (with protein and with solvent atoms) of those residues in the active site that could interact with a substrate or a potential inhibitor. The simulation data is aimed at facilitating the design of high-affinity selective inhibitors of factor Xa.     

Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.     

Functionality map analysis of the active site cleft of human thrombin

Summary The Multiple Copy Simultaneous Search methodology has been used to construct functionality maps for an extended region of human thrombin, including the active site. This method allows the determination of energetically favorable positions and orientations for functional groups defined by the user on the three-dimensional surface of a protein. The positions of 10 functional group sites are compared with those of corresponding groups of four thrombin-inhibitor complexes. Many, but not all features, of known thrombin inhibitors are reproduced by the method. The results indicate that certain aspects of the binding modes of these inhibitors are not optimal. In addition, suggestions are made for improving binding by interaction with functional group sites on the thrombin surface that are not used by the thrombin inhibitors. Abbreviations: MCSS, multiple copy simultaneous search; PPACK, d-phenylalanyl-l-propyl-l-arginine chloromethane; NAPAP, N -(2-naphthylsulfonylglycyl)-d-para-amidinophenylalanylpiperidine; argatroban, (2R,4R)-4-methyl-1-[N -(3-methyl-1,2,3,4-tetrahydro-8-quinolinylsulfonyl)-l-arginyl]-2-piperidine carboxylic acid; rms, root mean square. The thrombin residues are numbered according to the chymotrypsin-based numbering by Bode et al. [8]. P1, P2, P3, etc., denote the peptide inhibitor residues on the amino-terminal side of the scissile peptide bond, and S1, S2, S3, etc., the corresponding subsites of thrombin