Unbiased computation of transition times by pathway recombination

In many systems, the time scales of the microscopic dynamics and macroscopic dynamics of interest are separated by many orders of magnitude. Examples abound, for instance, nucleation, protein folding, and chemical reactions. For these systems, direct simulation of phase space trajectories does not efficiently determine most physical quantities of interest. The past decade has seen the advent of methods circumventing brute force simulation. For most dynamical quantities, these methods all share the drawback of systematical errors. We present a novel method for generating ensembles of phase space trajectories. By sampling small pieces of these trajectories in different phase space domains and piecing them together in a smart way using equilibrium properties, we obtain physical quantities such as transition times. This method does not have any systematical error and is very efficient; the computational effort to calculate the first passage time across a free energy barrier does not increase with the height of the barrier. The strength of the method is shown in the Ising model. Accurate measurements of nucleation times span almost ten orders of magnitude and reveal corrections to classical nucleation theory.     

On the core of routing games

A repairman makes a round-trip along a set of customers. He starts in his home location, visits each customer exactly once, and returns home. The cost of his trip has to be shared by the customers. A cooperative cost game, calledrouting game, is associated with this allocation problem, and anO(n ²) algorithm is given which computes a core element of a routing game if the core is non-empty. The non-emptiness of the core depends on the tour which is traversed by the repairman. Several procedures are given to construct tours which guarantee the non-emptiness of the core.     

Fluorescence lifetime fluctuations of single molecules probe local density fluctuations in disordered media: a bulk approach

We investigated the nanometer scale mobility of polymers in the glassy state by monitoring the dynamics of embedded single fluorophores. Recently we reported on fluorescence lifetime fluctuations which reflect the segmental rearrangement dynamics of the polymer in the surroundings of the single molecule probe. Here we focus on the nature of these fluorescence lifetime fluctuations. First the potential role of quenching and molecular conformational changes is discussed. Next we concentrate on the influence of the radiative density of states on the spontaneous emission of individual dye molecules embedded in a polymer. To this end we present a theory connecting the effective-medium theory to a cell-hole model, originating from the Simha-Somcynsky free-volume theory. The relation between the derived distributions of free volume and fluorescence lifetime allows one to determine the number of segments involved in the local rearrangement directly from experimental data. Results for two different polymers as a function of temperature are presented.     

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides

We identify a route towards achieving a negative index of refraction at optical frequencies based on coupling between plasmonic waveguides that support backwards waves. We show how modal symmetry can be exploited in metal-dielectric waveguide pairs to achieve negative refraction of both phase and energy. Control of waveguide coupling yields a metamaterial consisting of a one-dimensional multilayer stack that exhibits an isotropic index of -1 at a free-space wavelength of 400?nm. The concepts developed here may inspire new low-loss metamaterial designs operating close to the metal plasma frequency.     

Near-field probing of photonic crystals

Photonic crystals form an exciting new class of optical materials that can greatly affect optical propagation and light emission. As the relevant length scale is smaller than the wavelength of light, sub-wavelength detection forms an important ingredient to obtain full insight in the physical properties of photonic crystal structures. Spatially resolved near-field measurements allow the observation of phenomena that remain hidden to diffraction-limited far-field investigations. Here, we present near-field investigations in both collection and illumination modes that highlight the power of local studies. We show how propagation losses are unambiguously determined and that light detected in far-field transmission can actually contain contributions from different, sometimes unexpected, local scattering phenomena. Simulations are used to support our findings. Furthermore, it is shown that local coupling of light to a thick three-dimensional photonic crystal is position-dependent and that the spatial distribution of the coupling efficiency itself is frequency-dependent.     

Computing an Element in the Lexicographic Kernel of a Game

The lexicographic kernel of a game lexicographically maximizes the surplusses s _ij (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can efficiently compute the surplusses s _ij (x) corresponding to a given allocation x. This approach improves the results in Faigle et al. (in Int J Game Theory 30:79–98, 2001) and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm.We thank the referees for clarifying the presentation of the proof of Proposition 2.1.     

On the motion of a row of colliding particles

Summary This report is concerned with the dynamic behaviour of a row of loose particles performing collisions which are not perfectly elastic. It deals with the following problem usually met in the theory of mechanical transport: a layer of particles impinges upon a moving plate and the incipient motion of the particles is to be investigated. The problem has been solved using a simplified mathematical model; some properties of this model have been examined in detail.

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Übersicht In der vorliegenden Arbeit wird das Verhalten einer Reihe locker gelagerter Teilchen untersucht, die elastisch-plastischen Stößen unterworfen sind. Es wird dabei ein in der Theorie des mechanischen Transports auftretendes Problem untersucht: eine Schicht von Teilchen möge auf eine bewegte Platte stoßen, gesucht ist die Bewegung der Teilchen nach den Stoß. Diese Aufgabe wird unter Verwendung eines vereinfachten mathematischen Modells gelöst, wobei einige Besonderheiten des Modells genauer untersucht werden.