Steered Transition Path Sampling

We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying the dynamics based on that probability, and then reweighting to calculate averages. Because the progress constraint can be formulated in terms of occurrences of events within time intervals, the method is particularly well suited for controlling the sampling of currents of dynamic events. We demonstrate the method for calculating transition probabilities in barrier crossing problems and survival probabilities in strongly diffusive systems with absorbing states, which are difficult to treat by shooting. We discuss the relation of the algorithm to other methods.Comment: 11 pages, 8 figure

A Note on the Classical BRST Symmetry of the Pure Spinor String in a Curved Background

The classical pure spinor version of the heterotic superstring in a supergravity and super Yang-Mills background is considered. We obtain the BRST transformations of the world-sheet fields. They are consistent with the constraints obtained from the nilpotence of the BSRT charge and the holomorphicity of the BRST current.Comment: References adde

Emergence of heterogeneity and political organization in information exchange networks

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases, corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics, and may have applications in a variety of systems including social insects and microbial communities.Comment: 10 pages, 6 figure

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.Comment: 19 pages, LaTex fil

Note About Classical Dynamics of Pure Spinor String on AdS_5 x S_5 Background

We will discuss some properties of the pure spinor string on the AdS_5 x S_5 background. Using the classical Hamiltonian analysis we will show that the vertex operator for the massless state that is in the cohomology of the BRST charges describes on-shell fluctuations around AdS_5 x S_5 background.Comment: 26. pages, added references, v2:corrected typo

The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.Comment: 4 pages, 3 figure

Cascade of Complexity in Evolving Predator-Prey Dynamics

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.Comment: 5 pages, 3 figures; added comments on system size scaling and turbulence analogy, added error estimates of data collapse parameters. Slightly enhanced from the version which will appear in PR

An Alternative Topological Field Theory of Generalized Complex Geometry

We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case that the generalized complex structuredepends on only a symplectic structure. Our new model is $B$ model in the case that the generalized complex structure depends on only a complex structure.Comment: 29 pages, typos and references correcte

Flow profiling of a surface acoustic wave nanopump

The flow profile in a capillary gap and the pumping efficiency of an acoustic micropump employing Surface Acoustic Waves is investigated both experimentally and theoretically. Such ultrasonic surface waves on a piezoelectric substrate strongly couple to a thin liquid layer and generate an internal streaming within the fluid. Such acoustic streaming can be used for controlled agitation during, e.g., microarray hybridization. We use fluorescence correlation spectroscopy and fluorescence microscopy as complementary tools to investigate the resulting flow profile. The velocity was found to depend on the applied power somewhat weaker than linearly and to decrease fast with the distance from the ultrasound generator on the chip.Comment: 12 pages 20 figure

Macroscopic effects of the spectral structure in turbulent flows

Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure