Constant flux relation for diffusion-limited cluster-cluster aggregation

In a nonequilibrium system, a constant flux relation (CFR) expresses the fact that a constant flux of a conserved quantity exactly determines the scaling of the particular correlation function linked to the flux of that conserved quantity. This is true regardless of whether mean-field theory is applicable or not. We focus on cluster-cluster aggregation and discuss the consequences of mass conservation for the steady state of aggregation models with a monomer source in the diffusion-limited regime. We derive the CFR for the flux-carrying correlation function for binary aggregation with a general scale-invariant kernel and show that this exponent is unique. It is independent of both the dimension and of the details of the spatial transport mechanism, a property which is very atypical in the diffusion-limited regime. We then discuss in detail the "locality criterion" which must be satisfied in order for the CFR scaling to be realizable. Locality may be checked explicitly for the mean-field Smoluchowski equation. We show that if it is satisfied at the mean-field level, it remains true over some finite range as one perturbatively decreases the dimension of the system below the critical dimension, d(c)=2, entering the fluctuation-dominated regime. We turn to numerical simulations to verify locality for a range of systems in one dimension which are, presumably, beyond the perturbative regime. Finally, we illustrate how the CFR scaling may break down as a result of a violation of locality or as a result of finite size effects and discuss the extent to which the results apply to higher order aggregation processes

A New Analysis Method for Reconstructing the Arrival Direction of TeV Gamma-rays Using a Single Imaging Atmospheric Cherenkov Telescope

We present a method of atmospheric Cherenkov imaging which reconstructs the unique arrival direction of TeV gamma rays using a single telescope. The method is derived empirically and utilizes several features of gamma-ray induced air showers which determine, to a precision of 0.12 degrees, the arrival direction of photons, on an event-by-event basis. Data from the Whipple Observatory's 10 m gamma-ray telescope is utilized to test selection methods based on source location. The results compare these selection methods with traditional techniques and three different camera fields of view. The method will be discussed in the context of a search for a gamma-ray signal from a point source located anywhere within the field of view and from regions of extended emission.Comment: 24 pages, 16 figures, accepted for publication in Astroparticle Physics May 11, 200

Wave turbulence in the two-layer ocean model

This paper looks at the two-layer ocean model from a wave turbulence perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It turns out that energy is transferred via local triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale. From there it is then transferred to the large-scale barotropic modes via a nonlocal inverse transfer. Using scale separation a sys- tem of coupled equations were obtained for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. It is found that this transfer is mostly anisotropic and mostly to the zonal component

Swift and Fermi observations of X-ray flares: the case of Late Internal Shock

Simultaneous Swift and Fermi observations of gamma-ray bursts (GRBs) offer a unique broadband view of their afterglow emission, spanning more than ten decades in energy. We present the sample of X-ray flares observed by both Swift and Fermi during the first three years of Fermi operations. While bright in the X-ray band, X-ray flares are often undetected at lower (optical), and higher (MeV to GeV) energies. We show that this disfavors synchrotron self-Compton processes as origin of the observed X-ray emission. We compare the broadband properties of X-ray flares with the standard late internal shock model, and find that, in this scenario, X-ray flares can be produced by a late-time relativistic (Gamma>50) outflow at radii R~10^13-10^14 cm. This conclusion holds only if the variability timescale is significantly shorter than the observed flare duration, and implies that X-ray flares can directly probe the activity of the GRB central engine.Comment: 13 pages, 4 figures, accepted for publication in Ap

Growing condensate in two-dimensional turbulence

We report a numerical study, supplemented by phenomenological explanations, of ``energy condensation'' in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard $k^{-5/3}$ one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to $k^{-1}$. The fluctuations decay slowly as the coherent part grows.Comment: 4 pages, 4 figures. This version includes some additional phenomenological explanations of the results, additional references and improved figure

Breakdown of Kolmogorov scaling in models of cluster aggregation with deposition

The steady state of the model of cluster aggregation with deposition is characterized by a constant flux of mass directed from small masses towards large masses. It can therefore be studied using phenomenological theories of turbulence, such as Kolmogorov's 1941 theory. On the other hand, the large scale behavior of the aggregation model in dimensions lower than or equal to two is governed by a perturbative fixed point of the renormalization group flow, which enables an analytic study of the scaling properties of correlation functions in the steady state. In this paper, we show that the correlation functions have multifractal scaling, which violates linear Kolmogorov scaling. The analytical results are verified by Monte Carlo simulations.Comment: 5 pages 4 figure

Stationary mass distribution and non-locality in models of coalescence and shattering

We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the large and small mass asymptotic behavior of the mass distribution depend on whether the collision kernel is local (the aggregation mass flux is essentially generated by collisions between particles of similar masses) or nonlocal (collision between particles of widely different masses give the main contribution to the mass flux). We show that the nonlocal regime is further divided into two subregimes corresponding to weak and strong nonlocality. We also observe that at the boundaries between the local and nonlocal regimes, the mass distribution acquires logarithmic corrections to scaling and calculate these corrections. Exact solutions for special kernels and numerical simulations are used to validate some nonrigorous steps used in the analysis. Our results show that for local kernels, the scaling solutions carry a constant flux of mass due to aggregation, whereas for the nonlocal case there is a correction to the constant flux exponent. Our results suggest that for general scale-invariant kernels, the universality classes of mass distributions are labeled by two parameters: the homogeneity degree of the kernel and one further number measuring the degree of the nonlocality of the kernel

Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov type in the sense that they carry a constant flux of mass from small masses to large. We derive a ``locality criterion'', expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissiblesolution. Whether a given kernel leads to a gelation transition or not can be determined by computing the mass capacity of the Kolmogorov spectrum. As an example, we compute the exact stationary state for the family of kernels,$K_\zeta(m_1,m_2)=(m_1m_2)^{\zeta/2}$ which includes both gelling and non-gelling cases, reproducing the known solution in the case $\zeta=0$. Surprisingly, the Kolmogorov constant is the same for all kernels in this family.Comment: This article is an expanded version of a talk given at IHP workshop "Dynamics, Growth and Singularities of Continuous Media", Paris July 2003. Updated 01/04/04. Revised version with additional discussion, references added, several typographical errors corrected. Revised version accepted for publication by Phys. Rev.