Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods

We report on new results in Witten's cubic string field theory for the off-shell factor in the 4-tachyon amplitude that was not fully obtained explicitly before. This is achieved by completing the derivation of the Veneziano formula in the Moyal star formulation of Witten's string field theory (MSFT). We also demonstrate detailed agreement of MSFT with a number of on-shell and off-shell computations in other approaches to Witten's string field theory. We extend the techniques of computation in MSFT, and show that the j=0 representation of SL(2,R) generated by the Virasoro operators $L_{0},L_{\pm1}$ is a key structure in practical computations for generating numbers. We provide more insight into the Moyal structure that simplifies string field theory, and develop techniques that could be applied more generally, including nonperturbative processes.Comment: 40 pages, 2 figures, LaTe

Dominance-solvable lattice games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs

Clustering of matter in waves and currents

The growth rate of small-scale density inhomogeneities (the entropy production rate) is given by the sum of the Lyapunov exponents in a random flow. We derive an analytic formula for the rate in a flow of weakly interacting waves and show that in most cases it is zero up to the fourth order in the wave amplitude. We then derive an analytic formula for the rate in a flow of potential waves and solenoidal currents. Estimates of the rate and the fractal dimension of the density distribution show that the interplay between waves and currents is a realistic mechanism for providing patchiness of pollutant distribution on the ocean surface.Comment: 4 pages, 1 figur

Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power-law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.Comment: 13 pages, version accepted to Journal of Statistical Mechanic

Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics

It has been recently shown (Fouxon et al. 2007) that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. This work reports molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the "attempted" density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.Comment: 11 pages, 9 figures, accepted for publication on Physical Review

Comparison of Different Anthropometric Measurements and Inflammatory Biomarkers

Introduction. Different anthropometric variables have been shown to be related to cardiovascular morbidity and mortality. Our aim was to compare the association between different anthropometric measurements and inflammatory status. Methods and results. A cross-sectional study design in which we analyzed the data collected during a five-year period in the Tel Aviv Medical Center Inflammation Survey (TAMCIS). Included in the study were 13,033 apparently healthy individuals at a mean (SD) age of 43. Of these, 8,292 were male and 4,741 female. A significant age-adjusted and multiple-adjusted partial correlation was noted between all anthropometric measurements and all inflammatory biomarkers. There was no significant difference in the correlation coefficients between different biomarkers and anthropometric variables. Conclusion. Most of the common used anthropometric variables are similarly correlated with inflammatory variables. The clinician can choose the variable that he/she finds easiest to use

A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases

We use hydrodynamics to investigate non-stationary channel flows of freely cooling dilute granular gases. We focus on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation is exactly soluble, and the solution develops a finite-time density blowup. The heat diffusion, however, becomes important near the attempted singularity. It arrests the density blowup and brings about novel inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. Both the density profile of an ICS, and the characteristic relaxation time towards it are determined by a single dimensionless parameter that describes the relative role of the inelastic energy loss and heat diffusion. At large values of this parameter, the intermediate cooling dynamics proceeds as a competition between low-density regions of the gas. This competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio

Correlation Differences in Heartbeat Fluctuations During Rest and Exercise

We study the heartbeat activity of healthy individuals at rest and during exercise. We focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise. For exercise the interval series is anticorrelated at short time scales and correlated at intermediate time scales, while for rest we observe the opposite crossover pattern -- from strong correlations in the short-time regime to weaker correlations at larger scales. We suggest a physiologically motivated stochastic scenario to explain the scaling differences between rest and exercise and the observed crossover patterns.Comment: 4 pages, 4 figure

Computing in String Field Theory Using the Moyal Star Product

Using the Moyal star product, we define open bosonic string field theory carefully, with a cutoff, for any number of string oscillators and any oscillator frequencies. Through detailed computations, such as Neumann coefficients for all string vertices, we show that the Moyal star product is all that is needed to give a precise definition of string field theory. The formulation of the theory as well as the computation techniques are considerably simpler in the Moyal formulation. After identifying a monoid algebra as a fundamental mathematical structure in string field theory, we use it as a tool to compute with ease the field configurations for wedge, sliver, and generalized projectors, as well as all the string interaction vertices for perturbative as well as monoid-type nonperturbative states. Finally, in the context of VSFT we analyze the small fluctuations around any D-brane vacuum. We show quite generally that to obtain nontrivial mass and coupling, as well as a closed strings, there must be an associativity anomaly. We identify the detailed source of the anomaly, but leave its study for future work.Comment: 77 pages, LaTeX. v3: corrections of signs or factors (for a list of corrections see beginning of source file