Exact Green's Function of the reversible diffusion-influenced reaction for an isolated pair in 2D

We derive an exact Green's function of the diffusion equation for a pair of spherical interacting particles in 2D subject to a back-reaction boundary condition.Comment: 6 pages, 1 Figur

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

Dynamical Stability of Witten Rings

The dynamical stability of cosmic rings, or vortons, is investigated for the particular equation of state given by the Witten bosonic model. It is found that there exists a finite range of the state parameter for which the vorton states are actually stable against dynamical perturbations. Inclusion of the electromagnetic self action into the equation of state slightly shrinks the stability region but otherwise yields no qualitative difference. If the Witten bosonic model represents a good approximation for more realistic string models, then the cosmological vorton excess problem can only be solved by assuming either that strings are formed at low energy scales or that some quantum instability may develop at a sufficient rate.Comment: 11 pages, LaTeX-ReVTeX (v.3), 2 figures available upon request, DAMTP R-94/1

Fermionic massive modes along cosmic strings

The influence on cosmic string dynamics of fermionic massive bound states propagating in the vortex, and getting their mass only from coupling to the string forming Higgs field, is studied. Such massive fermionic currents are numerically found to exist for a wide range of model parameters and seen to modify drastically the usual string dynamics coming from the zero mode currents alone. In particular, by means of a quantization procedure, a new equation of state describing cosmic strings with any kind of fermionic current, massive or massless, is derived and found to involve, at least, one state parameter per trapped fermion species. This equation of state exhibits transitions from subsonic to supersonic regimes while the massive modes are filled.Comment: 27 pages, 15 figures, uses ReVTeX. Shortened version, accepted for publication in Phys. Rev.

Quantum Games

In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.Comment: 13 pages (LaTeX), 3 figure

Recent developments in Vorton Theory

This article provides a concise overview of recent theoretical results concerning the theory of vortons, which are defined to be (centrifugally supported) equilibrium configurations of (current carrying) cosmic string loops. Following a presentation of the results of work on the dynamical evolution of small circular string loops, whose minimum energy states are the simplest examples of vortons, recent order of magnitude estimates of the cosmological density of vortons produced in various kinds of theoretical scenario are briefly summarised.Comment: 6 pages Latex. Contribution to 1996 Cosmology Meeting, Peyresq, Franc

Computer simulations of electrorheological fluids in the dipole-induced dipole model

We have employed the multiple image method to compute the interparticle force for a polydisperse electrorheological (ER) fluid in which the suspended particles can have various sizes and different permittivites. The point-dipole (PD) approximation being routinely adopted in computer simulation of ER fluids is shown to err considerably when the particles approach and finally touch due to multipolar interactions. The PD approximation becomes even worse when the dielectric contrast between the particles and the host medium is large. From the results, we show that the dipole-induced-dipole (DID) model yields very good agreements with the multiple image results for a wide range of dielectric contrasts and polydispersity. As an illustration, we have employed the DID model to simulate the athermal aggregation of particles in ER fluids both in uniaxial and rotating fields. We find that the aggregation time is significantly reduced. The DID model accounts for multipolar interaction partially and is simple to use in computer simulation of ER fluids.Comment: 22 pages, 7 figures, submitted to Phys. Rev.

Dark Energy and Modified Gravity

Despite two decades of tremendous experimental and theoretical progress, the riddle of the accelerated expansion of the Universe remains to be solved. On the experimental side, our understanding of the possibilities and limitations of the major dark energy probes has evolved; here we summarize the major probes and their crucial challenges. On the theoretical side, the taxonomy of explanations for the accelerated expansion rate is better understood, providing clear guidance to the relevant observables. We argue that: i) improving statistical precision and systematic control by taking more data, supporting research efforts to address crucial challenges for each probe, using complementary methods, and relying on cross-correlations is well motivated; ii) blinding of analyses is difficult but ever more important; iii) studies of dark energy and modified gravity are related; and iv) it is crucial that R&D for a vibrant dark energy program in the 2030s be started now by supporting studies and technical R&D that will allow embryonic proposals to mature. Understanding dark energy, arguably the biggest unsolved mystery in both fundamental particle physics and cosmology, will remain one of the focal points of cosmology in the forthcoming decade.Comment: 5 pages + references; science white paper submitted to the Astro2020 decadal surve

Equation of state of cosmic strings with fermionic current-carriers

The relevant characteristic features, including energy per unit length and tension, of a cosmic string carrying massless fermionic currents in the framework of the Witten model in the neutral limit are derived through quantization of the spinor fields along the string. The construction of a Fock space is performed by means of a separation between longitudinal modes and the so-called transverse zero energy solutions of the Dirac equation in the vortex. As a result, quantization leads to a set of naturally defined state parameters which are the number densities of particles and anti-particles trapped in the cosmic string. It is seen that the usual one-parameter formalism for describing the macroscopic dynamics of current-carrying vortices is not sufficient in the case of fermionic carriers.Comment: 30 pages, 15 figures, uses ReVTeX, equation of state corrected, comments and references added. Accepted for publication in Phys. Rev.