Spatial Structures and Giant Number Fluctuations in Models of Active Matter

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.Comment: 5 pages, 3 figure

Violation of Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.Comment: 4 pages, 5 figure

Pattern Formation in the Inhomogeneous Cooling State of Granular Fluids

We present results from comprehensive event-driven (ED) simulations of nonlinear pattern formation in freely-evolving granular gases. In particular, we focus on the the morphologies of density and velocity fields in the inhomogeneous cooling state (ICS). We emphasize the strong analogy between the ICS morphologies and pattern formation in phase ordering systems with a globally conserved order parameter.Comment: 11 pages, 4 figures. to appear in Europhys. Let

Coarse grained dynamics of the freely cooling granular gas in one dimension

We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1 depending on whether the relative speed is greater or smaller than a velocity scale $\delta$. The effective fragmentation rate of a cluster is shown to rise sharply beyond a $\delta$ dependent time scale. This crossover is coincident with the velocity fluctuations within a cluster becoming order $\delta$. Beyond this crossover time, the cluster size distribution develops a nontrivial power law distribution, whose scaling properties are related to those of the velocity fluctuations. We argue that these underlying features are responsible behind the recently observed nontrivial coarsening behaviour in the one dimensional freely cooling granular gas.Comment: 7 Pages, 9 Figure

Universality in Fluid Domain Coarsening: The case of vapor-liquid transition

Domain growth during the kinetics of phase separation is studied following vapor-liquid transition in a single component Lennard-Jones fluid. Results are analyzed after appropriately mapping the continuum snapshots obtained from extensive molecular dynamics simulations to a simple cubic lattice. For near critical quench interconnected domain morphology is observed. A brief period of slow diffusive growth is followed by a linear viscous hydrodynamic growth that lasts for an extended period of time. This result is in contradiction with earlier inclusive reports of late time growth exponent 1/2 that questions the uniqueness of the non-equilibrium universality for liquid-liquid and vapor-liquid transitions.Comment: 6 pages, 5 figure

Leptogenesis and muon (g−2)\boldsymbol{(g-2)} in a scotogenic model

We present a detailed study of a scotogenic model accommodating dark matter, neutrino masses and the anomalous magnetic moment of the muon while being consistent with the existing constraints on flavour violating decays of the leptons. Moreover, this model offers the possibility to explain the baryon asymmetry of the Universe via leptogenesis. We determine the viable regions of the model's parameter space in view of dark matter and flavour constraints using a Markov Chain Monte Carlo setup combined with a particular procedure to accommodate neutrino masses and the anomalous magnetic moment of the muon at the same time. We also discuss briefly the resulting collider phenomenology.Comment: 38 pages, 14 figure

Determining R-parity violating parameters from neutrino and LHC data

In supersymmetric models neutrino data can be explained by R-parity violating operators which violate lepton number by one unit. The so called bilinear model can account for the observed neutrino data and predicts at the same time several decay properties of the lightest supersymmetric particle. In this paper we discuss the expected precision to determine these parameters by combining neutrino and LHC data and discuss the most important observables. We show that one can expect a rather accurate determination of the underlying R-parity parameters assuming mSUGRA relations between the R-parity conserving ones and discuss briefly also the general MSSM as well as the expected accuracies in case of a prospective e+ e- linear collider. An important observation is that several parameters can only be determined up to relative signs or more generally relative phases.Comment: 13 pages, 13 figure

Right-handed Sneutrinos as Nonthermal Dark Matter

When the minimal supersymmetric standard model is augmented by three right-handed neutrino superfields, one generically predicts that the neutrinos acquire Majorana masses. We postulate that all supersymmetry (SUSY) breaking masses as well as the Majorana masses of the right-handed neutrinos are around the electroweak scale and, motivated by the smallness of neutrino masses, assume that the lightest supersymmetric particle (LSP) is an almost-pure right-handed sneutrino. We discuss the conditions under which this LSP is a successful dark matter candidate. In general, such an LSP has to be nonthermal in order not to overclose the universe, and we find the conditions under which this is indeed the case by comparing the Hubble expansion rate with the rates of the relevant thermalizing processes, including self-annihilation and co-annihilation with other SUSY and standard model particles.Comment: 17 pages v.2: References adde

Perturbation Expansion in Phase-Ordering Kinetics: II. N-vector Model

The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in the scalar case, one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). The second-order corrections for the nonequilibrium exponents are worked out explicitly in $d$ dimensions and as a function of the number of components $n$ of the order parameter. In the formulation developed here the corrections to the OJK results are found to go to zero in the large $n$ and $d$ limits. Indeed, the large-$d$ convergence is exponential.Comment: 20 pages, no figure