Multicanonical Parallel Tempering

We present a novel implementation of the parallel tempering Monte Carlo method in a multicanonical ensemble. Multicanonical weights are derived by a self-consistent iterative process using a Boltzmann inversion of global energy histograms. This procedure gives rise to a much broader overlap of thermodynamic-property histograms; fewer replicas are necessary in parallel tempering simulations, and the acceptance of trial swap moves can be made arbitrarily high. We demonstrate the usefulness of the method in the context of a grand-multicanonical ensemble, where we use multicanonical simulations in energy space with the addition of an unmodified chemical potential term in particle-number space. Several possible implementations are discussed, and the best choice is presented in the context of the liquid-gas phase transition of the Lennard-Jones fluid. A substantial decrease in the necessary number of replicas can be achieved through the proposed method, thereby providing a higher efficiency and the possibility of parallelization.Comment: 8 pages, 3 figure, accepted by J Chem Phy

Phase separation processes in polymer solutions in relation to membrane formation

This review covers new experimental and theoretical physical research related to the formation of polymeric membranes by phase separation of a polymer solution, and to the morphology of these membranes. Two main phase separation processes for polymeric membrane formation are discussed: thermally induced phase separation and immersion precipitation. Special attention is paid to phase transitions like liquid-liquid demixing, crystallization, gelation, and vitrification, and their relation to membrane morphology. In addition, the mass transfer processes involved in immersion precipitation, and their influence on membrane morphology are discussed

Metastable liquid-liquid and solid-liquid phase boundaries in polymer-solvent-nonsolvent systems

In general liquid-liquid demixing processes are responsible for the porous morphology of membranes obtained by immersion precipitation. For rapidly crystallizing polymers, solid-liquid demixing processes also generate porous morphologies. In this study, the interference of both phase transitions has been analyzed theoretically using the Flory-Huggins theory for ternary polymer solutions. It is demonstrated that four main thermodynamic and kinetic parameters are important for the structure formation in solution: the thermodynamic driving force for crystallization, the ratio of the molar volumes of the solvent and the nonsolvent, the polymer-solvent interaction parameter, and the rate of crystallization of the polymer compared to the rate of solvent-nonsolvent exchange. An analysis of the relevance of each of these parameters for the membrane morphology is presented

The ring-opening polymerization of D,L-lactide in the melt initiated with tetraphenyltin

Melt polymerization conditions for D,L-lactide initiated with tetraphenyltin were studied with regard to polymer molecular weight and weight distributions. "Single" polymerization, "multiple"polymerization (four or eight reactions at the same time), and time-dependent studies are described. Single polymerizations using constant initiator concentrations resulted in a broad scattering of nonreproducible molecular weight values. Multiple polymerizations at constant initiator concentrations, however, resulted in nearly identical molecular weight profiles. Multiple polymerizations at different initiator concentrations did not show an inverse dependency of initiator concentration on polymer molecular weight. Both the single and multiple melt polymerizations resulted in rather broad molecular weight distributions. The presence of hydrolysis products of lactide during the melt polymerization most likely has a detrimental effect on molecular weight. After a short induction period the rather slow polymerization of D,L-lactide resulted in a maximal molecular weight followed by a slight decrease in molecular weight to a constant value. It is concluded that the polymerization of D,L-lactide in the melt initiated with tetraphenyltin does not proceed through a "living" mechanism

Statistical mechanics of random two-player games

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate quantities such as the number of equilibrium points, the expected payoff, and the fraction of strategies played with non-zero probability as a function of the correlation between the payoff matrices of both players and compare the results with numerical simulations.Comment: 16 pages, 6 figures, for further information see http://itp.nat.uni-magdeburg.de/~jberg/games.htm

The Traveling Salesman Problem Under Squared Euclidean Distances

Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. We denote the traveling salesman problem under this distance function by TSP($d,\alpha$). We design a 5-approximation algorithm for TSP(2,2) and generalize this result to obtain an approximation factor of $3^{\alpha-1}+\sqrt{6}^{\alpha}/3$ for $d=2$ and all $\alpha\ge2$. We also study the variant Rev-TSP of the problem where the traveling salesman is allowed to revisit points. We present a polynomial-time approximation scheme for Rev-TSP$(2,\alpha)$ with $\alpha\ge2$, and we show that Rev-TSP$(d, \alpha)$ is APX-hard if $d\ge3$ and $\alpha>1$. The APX-hardness proof carries over to TSP$(d, \alpha)$ for the same parameter ranges.Comment: 12 pages, 4 figures. (v2) Minor linguistic change

In situ analysis of solvent/nonsolvent exchange and phase separation processes during the membrane formation of polylactides

Membrane formation of polylactides has been studied using in situ analysis techniques. An experimental method based on the use of dark ground optics and reflected light illumination is used to monitor the mass transfer and phase separation dynamics during for mation. Additionally, the phase separation and structure formation has been studied using optical microscopy. The results of the dark ground optics technique for the polymer/solvent/nonsolvent systems poly-L-lactide/chloroform/methanol and poly-DL-lactide/chloroform/methanol showed that the diffusion kinetics were similar for the semicrystalline poly-L-lactide (PLLA) and the amorphous poly-DL-lactide. The influence of the molecular weight of the polymers on the diffusion kinetics was found to be negligible. Increasing the polymer concentration of the casting solution decreased the rate of diffusion. The phase separation of poly-DL-lactide was studied with optical microscopy and found to proceed via liquid-liquid demixing. For poly-L-lactide solutions of relatively low concentration (5-6% w/w), phase separation proceeded via liquid-liquid demixing followed by crystallization. For more concentrated PLLA solutions, phase separation proceeded directly via solid-liquid demixing processes. Additionally, for 6% w/w solutions of poly-L-lactide in dioxane immersed in methanol, precipitation also occurred solely via solid-liquid demixing

Phase transitions during membrane formation of polylactides. I. A morphological study of membranes obtained from the system polylactide-chloroform-methanol

The influence of solid-liquid demixing, liquid-liquid demixing and vitrification on the morphology of polylactide membranes has been investigated. To study the effects of crystallization of polylactides on the membrane and morphology, polylactides of varying stereoregularity were used. The polymers applied were poly--lactide (PLLA) and copolymers with different molar ratios of -lactide and -lactide [poly-L95/D5-lactide (PLA95), poly-L80/D20-lactide (PLA80) and poly-L50/D50-lactide (PDLLA)]. Solutions of polylactides in chloroform cast on a glass plate were immersed in methanol. From solutions containing the slowly crystallizing PLA80 or uncrystallizable PDLLA porous membranes were obtained if the phase separated system was removed from the nonsolvent bath within a few hours after immersion. After longer equilibration times in methanol the structure collapsed. The swelling in the nonsolvent methanol was too high to allow stabilization of the liquid-liquid demixed structure by vitrification. Stable membranes were easily obtained with more rapidly crystallizing polymers like PLLA. Casting solutions with low PLLA concentrations gave membranes with a cellular morphology due to liquid-liquid demixing by nucleation and growth of a polymer poor phase. Crystallization only played a role in the fixation of the liquid-liquid demixed structure. At increasing PLLA concentrations the demixing sequence gradually reversed to crystallization followed by liquid-liquid demixing. In these cases membranes with porous spherulites or spherulites surrounded with a cellular layer were obtained