On the energy momentum dispersion in the lattice regularization

For a free scalar boson field and for U(1) gauge theory finite volume (infrared) and other corrections to the energy-momentum dispersion in the lattice regularization are investigated calculating energy eigenstates from the fall off behavior of two-point correlation functions. For small lattices the squared dispersion energy defined by $E_{\rm dis}^2=E_{\vec{k}}^2-E_0^2-4\sum_{i=1}^{d-1}\sin(k_i/2)^2$ is in both cases negative ($d$ is the Euclidean space-time dimension and $E_{\vec{k}}$ the energy of momentum $\vec{k}$ eigenstates). Observation of $E_{\rm dis}^2=0$ has been an accepted method to demonstrate the existence of a massless photon ($E_0=0$) in 4D lattice gauge theory, which we supplement here by a study of its finite size corrections. A surprise from the lattice regularization of the free field is that infrared corrections do {\it not} eliminate a difference between the groundstate energy $E_0$ and the mass parameter $M$ of the free scalar lattice action. Instead, the relation $E_0=\cosh^{-1} (1+M^2/2)$ is derived independently of the spatial lattice size.Comment: 9 pages, 2 figures. Parts of the paper have been rewritten and expanded to clarify the result

Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at the origin by a source which is turned on at time t=0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection and the probability density of such a particle. We show that asymptotically the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.Comment: 7 pages; version 2: section IV is re-written, references added, 8 pages (final version

Monte Carlo simulation and global optimization without parameters

We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett

Bubbly Turbulent Drag Reduction Is a Boundary Layer Effect

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4×105), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effec

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

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

Trajectory Deflection of Spinning Magnetic Microparticles, the Magnus Effect at the Microscale

The deflection due to the Magnus force of magnetic particles with a diameter of 80 micrometer dropping through fluids and rotating in a magnetic field was measured. With Reynolds number for this experiment around 1, we found trajectory deflections of the order of 1 degree, in agreement within measurement error with theory. This method holds promise for the sorting and analysis of the distribution in magnetic moment and particle diameter of suspensions of microparticles, such as applied in catalysis, or objects loaded with magnetic particles.Comment: 12 pages, 3 figures. Appendix with 6 figure

A morphological study of membranes obtained from the systems polylactide-dioxane-methanol, polylactide-dioxane-water and polylactide-N-methyl pyrrolidone-water

The influence of liquid-liquid demixing, solid-liquid demixing, and vitrification on the membrane morphologies obtained from several polylactide-solvent-nonsolvent systems has been investigated. The polymers investigated were the semicrystalline poly-L-lactide (PLLA) and the amorphous poly-DL-lactide (PDLLA). The solvent-nonsolvent systems used were dioxane-water, N-methyl pyrrolidone-water and dioxane-methanol. For each of these systems it was attempted to relate the membrane morphology to the ternary phase diagram at 25°C. It was demonstrated that for the amorphous poly-DL-lactide the intersection of a glass transition and a liquid-liquid miscibility gap in the phase diagram was a prerequisite for the formation of stable membrane structures. For the semicrystalline PLLA a wide variety of morphologies could be obtained ranging from cellular to spherulitical structures. For membrane-forming combinations that show delayed demixing, trends expected on the basis of phase diagrams were in reasonable agreement with the observed membrane morphologies. Only for the rapidly precipitating system PLLA-N-methyl pyrrolidone-water were structures due to liquid-liquid demixing obtained when structures due to solid-liquid demixing were expected. Probably, rapid precipitation conditions promote solid-liquid demixing over liquid-liquid demixing, because the activation energy necessary for liquid-liquid demixing is lower than that for crystallization