GROMACS: fast, flexible, and free

This article describes the software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for molecular dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addition, it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequilibrium dynamics and free energy determinations are incorporated. Interfaces with popular quantum-chemical packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and analysis programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.     

Comparative analysis of affine scaling algorithms based on simplifying assumptions

We analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions. We show that, under a strong probabilistic assumption regarding the distribution of the data in an iteration, the decrease in the primal potential function will be with high probability, compared to the guaranteed(1). ( 2n is a parameter in the potential function andn is the number of variables.) Under the same assumption, we further show that the objective reduction rate of Dikin's affine scaling algorithm is with high probability, compared to no guaranteed convergence rate.Research supported in part by NSF Grant DDM-8922636.     

Efficient algorithms for solving rank two and rank three bilinear programming problems

Finitely convergent algorithms for solving rank two and three bilinear programming problems are proposed. A rank k bilinear programming problem is a nonconvex quadratic programming problem with the following structure: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaacaWFTbGaa8% xAaiaa-5gacaWFPbGaa8xBaiaa-LgacaWF6bGaa8xzaiaa-bcacaWF% 7bacbiGaa43yamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+Hhaca% GFRaGaa4hzamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+LhacaGF% RaWaaabuaeaacaGFJbWaa0baaSqaaiaa+PgaaeaacaGF0baaaOGaam% iEaiabl+y6NjaadsgadaqhaaWcbaGaamOAaaqaaiaadshaaaGccaWG% 5bGaaiiFaaWcbaGaa8NAaiaa-1dacaWFXaaabeqdcqGHris5aOGaa4% hEaiabgIGiolaa+HfacaGFSaGaa4xEaiabgIGiolaa+LfacaWF9bGa% a8hlaaaa!5D2E!\[minimize \{ c_0^t x + d_0^t y + \sum\limits_{j = 1} {c_j^t xd_j^t y|} x \in X,y \in Y\} ,\]where X Rⁿ¹ and Y R ⁿ² are non-empty and bounded polytopes. We show that a variant of parametric simplex algorithm can solve large scale rank two bilinear programming problems efficiently. Also, we show that a cutting-cake algorithm, a more elaborate variant of parametric simplex algorithm can solve medium scale rank three problems.This research was supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. 63490010.     

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.     

On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

On the validity of the counterpoise correction for the basis set superposition error including the fragment relaxation terms

It is demonstrated that relatively large geometrical changes make Emsley et al.'s assumption (J Am Chem Soc (1978) 100:3303) on the counterpoise correction for the basis set superposition error including the fragment relaxation terms unacceptable. Received: 23 September 1997 / Accepted: 31 October 1997     

HFC网上行信道时隙同步的性能分析

在分析HFC网络上行信道时隙同步过程的基础上,建立在系统故障恢复情况下上行信道时隙同步过程的数学建模,重点研究了HFC网完成上行信道时隙同步所需的平均时间.文中给出了不同网络规模、冲突解析算法参数值、上行信道带宽分配策略条件下的实验结果.最后提出了优化HFC网上行信道时隙同步性能的措施.