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

Stationary mass distribution and nonlocality 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 non-local (collision between particles of widely different masses give the main contribution to the mass flux). We show that the non-local regime is further divided into two sub-regimes corresponding to weak and strong non-locality. We also observe that at the boundaries between the local and non-local 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 non-rigorous 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 non-local 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 non-locality of the kernel.Comment: Published versio

BATSE Observations of Gamma-Ray Burst Tails

I discuss in this paper the phenomenon of post-burst emission in BATSE gamma-ray bursts at energies traditionally associated with prompt emission. By summing the background-subtracted signals from hundreds of bursts, I find that tails out to hundreds of seconds after the trigger may be a common feature of long events (duration greater than 2s), and perhaps of the shorter bursts at a lower and shorter-lived level. The tail component appears independent of both the duration (within the long GRB sample) and brightness of the prompt burst emission, and may be softer. Some individual bursts have visible tails at gamma-ray energies and the spectrum in at least a few cases is different from that of the prompt emission.Comment: 33 Pages from LaTex including 7 figures, with aastex. To appear in Astrophysical Journa

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

The effect of loading on disturbance sounds of the Atlantic croaker Micropogonius undulatus: Air versus water

Physiological work on fish sound production may require exposure of the swimbladder to air, which will change its loading (radiation mass and resistance) and could affect parameters of emitted sounds. This issue was examined in Atlantic croaker Micropogonius chromis by recording sounds from the same individuals in air and water. Although sonograms appear relatively similar in both cases, pulse duration is longer because of decreased damping, and sharpness of tuning (Q factor) is higher in water. However, pulse repetition rate and dominant frequency are unaffected. With appropriate caution it is suggested that sounds recorded in air can provide a useful tool in understanding the function of various swimbladder adaptations and provide reasonable approximation of natural sounds. Further, they provide an avenue for experimentally manipulating the sonic system, which can reveal details of its function not available from intact fish underwater

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