Ballistic aggregation for one-sided Brownian initial velocity

We study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial velocity on the right side is a Brownian motion that starts from the origin x=0). We consider the cases where the left side is either at rest or empty at t=0. We derive explicit expressions for the velocity distribution and the mean density and current profiles built by this out-of-equilibrium system. We find that on the right side the mean density remains constant whereas the mean current is uniform and grows linearly with time. All quantities show an exponential decay on the far left. We also obtain the properties of the leftmost cluster that travels towards the left. We find that in both cases relevant lengths and masses scale as t² and the evolution is self-similar.     

Ballistic annihilation and deterministic surface growth

A model of deterministic surface growth studied by Krug and Spohn, a model of the annihilating reactionA+Binert studied by Elskens and Frisch, a one-dimensional three-color cyclic cellular automaton studied by Fisch, and a particular automaton that has the number 184 in the classification of Wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation. This automaton is defined by the following rules: At timet=0, one particle is put at each integer point of . To each particle, a velocity is assigned in such a way that it may be either +1 or –1 with probabilities 1/2, independent of the velocities of the other particles. As time goes on, each particle moves along at the velocity assigned to it and annihilates when it collides with another particle. In the present paper we compute the distribution of this automaton for each timet . We then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above. We also show the relation of this limit process to the process which we call moving local minimum of Brownian motion. The latter is the processB _x ^min ,x , defined byB _x ^min min{B _y ;x–1yx+1} for everyx , whereB _x ,x , is the standard Brownian motion withB ₀=0.     

Diffraction gratings of isotropic negative-phase velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric-magnetic half-spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive- or the negative-phase velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings — the Rayleigh-hypothesis method, a perturbative approach, and the C formalism — are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half-space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.     

Constraints on dark matter annihilation and decay from the isotropic gamma-ray background

We study the constraints on dark matter(DM) annihilation/decay from the Fermi-LAT Isotropic Gamma-Ray Background(IGRB) observation.We consider the contributions from both extragalactic and galactic DM components.For DM annihilation,the evolution of extragalactic DM halos is taken into account.We find that the IGRB annihilation constraints under some DM subhalo models can be comparable to those derived from the observations of dwarf spheroidal galaxies and CMB.We also use the IGRB results to constrain the parameter regions accounting for the latest AMS-02 electron-positron anomaly.We find that the majority of DM annihilation/decay channels are strongly disfavored by the latest Fermi-LAT IGRB observation;only DM decays to μ~+μ~-and 4μ channels may be valid.     

Phase transitions for two-dimensional models with isotropic short-range interactions and continuous symmetries

Using the powerful method of reflection-positivity and chess-board estimates, we prove the existence of phase transition for certain class of isotropic short-range interactions with continuous symmetry, provided that the dimension of the lattice is at least two, and the temperature is low enough.     

Bohm velocity with a two-temperature distribution of negativeparticles

A one-dimensional simulation of a low-pressure RF-driven discharge is used to verify the theoretical prediction of the Bohm velocity of ions at the sheath edge for a two-temperature electron distribution. Simulation results indicate that the Bohm velocity is geared to the cooler species, provided that it contains most of the electrons. A similar comparison is performed for an electronegative plasma     

Pion multiplicity distribution in antiproton-proton annihilation at rest

The pion multiplicity distribution is widely believed to reflect the statistical aspects of annihilation at rest. We try to reproduce it in a grand canonical picture with explicit conservation of electric charge, isospin, total angular momentum, and the parity quantum numbersP, C, andG via the projection operator formalism. Bose statistics is found to be non-negligible, particularly in fixing the interaction volume. The calculated pion multiplicity distribution for n =5 turns out to depend strongly on the conservation of the angular momentum and connected quantum numbers, as well as on the spin state occupation inS-wave annihilation. However, the empirical Gaussian pion multiplicity distribution cannot be reproduced. This calls in question either the statistical ansatz or the rather old data themselves.Work supported in part by DFG, BMFT and GSI     

Correlation decay of Lagrangian velocity differences in locally isotropic turbulence

The dynamical correlation decay of eddies in fully developed turbulent flows is considered. Eddies of different sizesr are represented by Galilei invariant velocity differences of two fluid elements moving along with the flow, which start a distancer apart. The equal-time statistical properties of the flow are used as partly theoretical, partly experimental input. The method used is the continued fraction representation of the time evolution operator's resolvent. Neglecting memory effects we find the decay rate in the inertial subrange being determined by the ratio of the energy dissipation and the eddy fluctuation strength (represented by the static second order structure function). The decay rate for small eddies,r0, tends to a Reynolds number dependent constant. The influence of intermittency on the dynamics via statics is evaluated. Inadequate experimental and theoretical information about higher order static structure functions renders an evaluation of the memory contribution impossible. Scaling arguments indicate decreasing relative importance of memory effects in the inertial subrange with increasingr.     

Effect of space charge and the initial electron velocity on the potential distribution in a plane diode

The problem of the potential distribution in a plane vacuum diode is solved for arbitrary values of the space charge density and the initial electron velocity. The resultant solution makes it possible to study the conditions for the potential minimum appearing near the cathode, to determine the position and depth of this minimum, to derive analytic formulas for the potential distribution in the entire space between the cathode and the anode, and to analyze the problem of an infinitely high space charge density.     

Angular distribution of two observed hadrons in electron-position annihilation

I discuss the angular structure of the cross section fore ⁺+e ^?→A+B+X and the closely related energy-energy correlation function.     

Energy velocity and quality factor of poroelastic waves in isotropic media

The energy velocity and Q factor of poroelastic acoustic waves in the context of classical isotropic Biot's theory are revisited. Special attention is paid to the high frequency regime when interphase interaction is viscoelastic. The analogy with viscoelastic behavior is emphasized in derivation of the energy balance equations which relate kinetic energy, potential energy, viscous power dissipation, and elastic energy stored associated with each wave. These lead to exact closed form expressions for the energy velocity and Q factor for both longitudinal and shear waves from energy principles. Most notably, the analysis of the resulting expressions reveals that the energy velocity of both longitudinal and shear waves equals (exceeds) the corresponding phase velocity in the case of the low (full) frequency range theory, and that the exact expression for the Q factor contains an additive correction due to viscoelastic interphase interaction.     

Quantum measurement theory including initial correlations and observables with continuous spectra

In the framework of the quantum mechanical measurement theory we study measurements where the state of the object and the state of the apparatus are initially already correlated. We show that the usual difficulties extend to the measuring schemes considered here. The general structure of the theory is clarified.     

On the velocity and dissipation signature of vortex tubes in isotropic turbulence

The properties of vortex tubes are extracted and analyzed from a DNS database at various Re_λ, with the objective to characterize the associated distributions of induced velocity and kinetic energy dissipation. The induced velocity exhibits an inverse power-law scaling in the far field, different from Burgers’ r⁻¹ scaling, supporting the interpretation that tubes are the remnants of vortex sheets after roll-up, and suggesting a possible link with the Kolmogorov k^−5/3 spectral scaling. The energy dissipation signature is characterized by a local maximum near the edge of the vortex core, and an absolute peak at its center, which can be tentatively explained appealing to the occurrence of a bi-axial configuration of the strain-rate tensor.     

Second-order QCD corrections to the thrust distribution in electron-positron annihilation

We compute the next-to-next-to-leading-order (NNLO) QCD corrections to the thrust distribution in electron-positron annihilation. The corrections turn out to be sizable, enhancing the previously known next-to-leading-order prediction by about 15%. Inclusion of the NNLO corrections significantly reduces the theoretical renormalization scale uncertainty on the prediction of the thrust distribution.     

Chapman-Enskog velocity distribution for tracer diffusion

The Chapman-Enskog method is used to obtain an approximate velocity distribution function for tracer diffusion in dilute hard-sphere mixtures. Different ratios of the mass of the tracer to that of the excess component (including the well-known limiting cases of the Lorentz and the Rayleigh models) are considered and the corresponding diffusion coefficients are also evaluated. A comparison with the recent results of Tompson and Loyalka for both the diffusion coefficients and the distribution functions provides a perspective on the usefulness and nature of the approximate method.     

Radiating gravitational collapse with an initial inhomogeneous energy density distribution

A new model is proposed to a collapsing star consisting of an initial inhomogeneous energy density and anisotropic pressure fluid with shear, radial heat flow and outgoing radiation. In previous papers one of us has always assumed an initial star with homogeneous energy density. The aim of this work is to generalize the previous models by introducing an initial inhomogeneous energy density and compare it to the initial homogeneous energy density collapse model. We will show the differences between these models in the evolution of all physical quantities that characterizes the gravitational collapse. The behavior of the energy density, pressure, mass, luminosity and the effective adiabatic index is analyzed. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied, in contrast of the previous model where a black hole is formed. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. In contrast of the former model where the luminosity also increases exponentially, reaching a maximum and after it decreases until the formation of the black hole. The effective adiabatic index is always positive without any discontinuity in contrast of the former model where there is a discontinuity around the time of maximum luminosity. The collapse is about three thousand times slower than in the case where the energy density is initially homogeneous.