Kinetics and scaling in ballistic annihilation

We study the simplest irreversible ballistically controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents characterizing the density and typical velocity decay are explicitly worked out in arbitrary dimension. These predictions are in excellent agreement with the complementary results of extensive Monte Carlo and molecular dynamics simulations. We finally discuss the definition of universality classes indexed by a continuous parameter for this far from equilibrium dynamics with no conservation laws.     

Dynamics and growth of particles undergoing ballistic coalescence

The irreversible evolution of a model for ballistic coalescence of spherical particles, whereby colliding particles merge into a single, larger sphere with conservation of mass and momentum, is analyzed on the basis of scaling assumptions, mean-field theory, and kinetic theory for arbitrary dimensionality and size-mass relation. The asymptotic growth regime is characterized by scaling laws associated with the instantaneous mean mass and kinetic energy of the particles. A hyperscaling relation between the mass and energy exponents is derived. The predictions of the theoretical analysis are tested by extensive simulations of the two-dimensional version of the model. Due to multiple coalescence events, the exponents are found to be nonuniversal (i.e., density dependent) and to differ significantly from the mean-field predictions. The distribution of masses turns out to be universal and exponential. Particle energies follow a Boltzmann distribution, with a time-dependent temperature, or relax toward such a distribution, even when the initial distribution is highly non-Maxwellian. In the case where the particles are swollen [i.e., the size-mass relation involves the Flory exponentv=3/(d+2)], an asymptotic scaling regime is observed only for sufficiently low initial packing fractions. At higher densities, the irreversible evolution terminates in a catastrophic coalescence event involving all remaining particles.     

Exact solution of two-species ballistic annihilation with general pair-reaction probability

The reaction processA + B → ∅ is modeled for ballistic reactants on an infinite line with particle velocitiesυ _A =c andυ _B = -c and initially segregated conditions, i.e., allA particles to the left and allB particles to the right of the origin. Previous models of ballistic annihilation have particles that always react on contact, i.e., pair-reaction probabilityp = 1. The evolutions of such systems are wholly determined by the initial distributions of particles and therefore do not have a stochastic dynamics. However, in this paper the generalization is made to p< 1, allowing particles to pass through each other without necessarily reacting. In this way, theA andB particle domains overlap to form a fluctuating, finitesized reaction zone where the product ∅ is created. Fluctuations are also included in the currents ofA andB particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by theintrinsic reaction rate, seen in a single system, and theextrinsic reaction rate, seen in an average over many systems. The intrinsic and extrinsic behaviors are examined and compared to the case of isotropically diffusing reactants     

Parton coalescence and spacetime

The influence of spacetime dynamics in hadronization via parton coalescence at RHIC is investigated using covariant parton transport theory: Key observables, the quark number scaling of elliptic flow and the enhancement of the p/π ratio, show strong dynamical effects and differ from earlier results based on the simple coalescence formulas.     

Hypercharge annihilation

Aspects of the process K^?p → Λ + pions for K^? mesons of momentum 8.25 GeV/c are examined. It is shown that the hypercharge annihilation process can be effectively separated into off-shell baryon (B?B) and strangeness (K?K) annihilation. Both annihilation regions have many features in common and show strong similarities to on-shell annihilation processes; some differences are also noted.     

Diabolo creation and annihilation

A point of circular polarization embedded in a paraxial field of elliptical polarization is a polarization singularity called a C point. At such a point the major axis a and minor axis b of the ellipse become degenerate. Away from the C point this degeneracy is lifted such that surfaces a and b form nonanalytic cones that are joined at their apex (the C point) to produce a double cone called a diabolo. Typically, during propagation diabolo pairs are created or annihilated. We present rules based on geometry and topology that govern these events, provide initial experimental confirmation, and enumerate the allowed configurations in which diabolos can be created or annihilated.     

Hydrodynamics of droplet coalescence

We study droplet coalescence in a molecular system with a variable viscosity and a colloid-polymer mixture with an ultralow surface tension. When either the viscosity is large or the surface tension is small enough, we observe that the opening of the liquid bridge initially proceeds at a constant speed set by the capillary velocity. In the first system we show that inertial effects become dominant at a Reynolds number of about 1.5+/- 0.5 and the neck then grows as the square root of time. In the second system we show that decreasing the surface tension by a factor of 10(5) opens the way to a more complete understanding of the hydrodynamics involved.     

Dynamics of fullerene coalescence

Fullerene coalescence experimentally found in fullerene-embedded single-wall nanotubes under electron-beam irradiation or heat treatment is simulated by minimizing the classical action for many atom systems. The dynamical trajectory for forming a (5,5) C120 nanocapsule from two C60 fullerene molecules consists of thermal motions around potential basins and ten successive Stone-Wales-type bond rotations after the initial cage-opening process for which energy cost is about 8 eV. Dynamical paths for forming large-diameter nanocapsules with (10,0), (6,6), and (12,0) chiral indexes have more bond rotations than 25 with the transition barriers in a range of 10-12 eV.     

Density fluctuations and particle-antiparticle annihilation

With the example of the primordial magnetic monopoles in mind, the time development of a system of particles and antiparticles undergoing irreversible annihilation is studied. The existence of spatial fluctuations in the initial particle and antiparticle densities is shown to lead to constraints on the asymptotic annihilation rate; the most general of these is based on causality considerations. The application of these constraints to several different types of systems is discussed, and computer simulations which were performed in order to test the constraints are described.     

Baryon-antibaryon bound states and annihilation

In order to gain some insight into the problem of the widths of quasi-nuclear levels in the $\text{B}\text{B}$ systems, we investigate a simple multichannel model for the influence of decay channels on a bound state. The shift and width of a bound-state level is found to depend strongly not only on the range of the annihilation and the $\text{B}\text{B}$ wave function at small distances but also on the position of the level relative to the thresholds. We point out a new mechanism through which a level in the vicinity of open thresholds can remain narrow even for strong coupling to the decay channels.     

Antiproton annihilation spectra

Recent data on antiproton (antineutron) spectra from hydrogen, deuterium and nuclear targets are discussed. Special emphasis is given to rare or unusual channels and phenomena. Work supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under grant AF05R87-0246 and U.S. National Science Foundation.     

Cusp values and electron densities at coalescence

The correlation between errors in (a) calculated cusp values and (b) calculated electron densities at coalescence are examined for the electron-nucleus and electron-electron pairs in helium. Calculations for 25 fully optimized variational wavefunctions for the ground state are presented. Although a wide variety of functional forms are represented in the set of wavefunctions studied, a strong correlation between (a) and (b) is obtained in the case of the electron-nucleus pair, and a weaker but still significant correlation is found for the electron-electron pair.     

Decompressing emulsion droplets favors coalescence

The destabilization process of an emulsion under flow is investigated in a microfluidic device. The experimental approach enables us to generate a periodic train of droplet pairs, and thus to isolate and analyze the basic step of the destabilization, namely, the coalescence of two droplets which collide. We demonstrate a counterintuitive phenomenon: coalescence occurs during the separation phase and not during the impact. Separation induces the formation of two facing nipples in the contact area that hastens the connection of the interfaces prior to fusion. Moreover, droplet pairs initially stabilized by surfactants can be destabilized by forcing the separation. Finally, we note that the fusion mechanism is responsible for a cascade of coalescence events in a compact system of droplets where the separation is driven by surface tension.     

Dynamic topology of fullerene coalescence

Atomic rearrangements leading to the coalescence of fullerene cages are revealed by topological analysis. Paths found for nanotubes and C(60) consist exclusively of Stone-Wales bond rotations. Computed intermediate states show gradual evolution from separate clusters to completely fused coherent units. Molecular dynamics simulations follow the predicted routes, overcome the nucleation barrier, and reach a final annealed state. While the overall behavior resembles macroscopic sintering, the nanoscale neck undergoes quantized changes in diameter and crystalline order.     

Correlations in ballistic processes

We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the reaction-controlled limit when particles undergo mostly elastic collisions and therefore are always near equilibrium, the correlations are accounted analytically. For ballistic aggregation, for instance, the density decays as n approximately t(-xi) with xi=2d/(d+3) in the reaction-controlled limit in d dimensions, in contrast with the well-known mean-field prediction xi=2d/(d+2).