Synthetic Mechanochemical Molecular Swimmer

A minimal design for a molecular swimmer is proposed that is a based on a mechanochemical propulsion mechanism. Conformational changes are induced by electrostatic actuation when specific parts of the molecule temporarily acquire net charges through catalyzed chemical reactions involving ionic components. The mechanochemical cycle is designed such that the resulting conformational changes would be sufficient for achieving low Reynolds number propulsion. The system is analyzed within the recently developed framework of stochastic swimmers to take account of the noisy environment at the molecular scale. The swimming velocity of the device is found to depend on the concentration of the fuel molecule according to the Michaelis-Menten rule in enzymatic reactions.Comment: 4 pages, 3 figure

Sharpness versus robustness of the percolation transition in 2D contact processes

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one of our models this requires a reasonable assumption). This is shown to contradict a form of 'robust critical behaviour' with power law cluster size distribution for a range of parameter values, as suggested in [17].Comment: 31 pages, to appear in Stochastic Processes and their Application

Non-Extensive Bose-Einstein Condensation Model

The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular it is proved that it has non-extensive Bose-Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground state (k=0) level

Enhanced diffusion by reciprocal swimming

Purcell's scallop theorem states that swimmers deforming their shapes in a time-reversible manner ("reciprocal" motion) cannot swim. Using numerical simulations and theoretical calculations we show here that in a fluctuating environment, reciprocal swimmers undergo, on time scales larger than that of their rotational diffusion, diffusive dynamics with enhanced diffusivities, possibly by orders of magnitude, above normal translational diffusion. Reciprocal actuation does therefore lead to a significant advantage over non-motile behavior for small organisms such as marine bacteria

Analysis of a Model for Ship Maneuvering

We analyze numerically and theoretically steady states and bifurcations in a model for ship maneuvering provided by MARIN, and in a simplified model that combines rudder and propeller into an abstract ‘thruster’. Steady states in the model correspond to circular motion of the ship and we compute the corresponding radii. We non-dimensionalize the models and thereby remove a number of parameters, so that, due to a scaling symmetry, only the rudder (or thruster) angle remains as a free parameter. Using ‘degree theory’, we show that a slight modification of the model pos- sesses at least one steady state for each angle and find certain constraints on the possible steady state configuration. We show that straight motion is unstable for the Hamburg test case and use numerical continuation and bifurcation software to compute a number of curves of states together with their stability, and the corresponding radii of the ship motion. In particular, straight forward motion can be stabilised by increasing the rudder size parameter, and the smallest possible radius is ∼ 119 m. These analyses illustrate methods and tools from dynamical systems theory that can be used to analyse a model without simulation. Compared with simulations, the numerical bifurcation analysis is much less time consuming. We have implemented the model in MATLAB and the bifurcation software AUTO

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 Canonical Perfect Bose Gas in Casimir Boxes

We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose-Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.Comment: 23 page

Are Simple Real Pole Solutions Physical?

We consider exact solutions generated by the inverse scattering technique, also known as the soliton transformation. In particular, we study the class of simple real pole solutions. For quite some time, those solutions have been considered interesting as models of cosmological shock waves. A coordinate singularity on the wave fronts was removed by a transformation which induces a null fluid with negative energy density on the wave front. This null fluid is usually seen as another coordinate artifact, since there seems to be a general belief that that this kind of solution can be seen as the real pole limit of the smooth solution generated with a pair of complex conjugate poles in the transformation. We perform this limit explicitly, and find that the belief is unfounded: two coalescing complex conjugate poles cannot yield a solution with one real pole. Instead, the two complex conjugate poles go to a different limit, what we call a ``pole on a pole''. The limiting procedure is not unique; it is sensitive to how quickly some parameters approach zero. We also show that there exists no improved coordinate transformation which would remove the negative energy density. We conclude that negative energy is an intrinsic part of this class of solutions.Comment: 13 pages, 3 figure

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