The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur

Lattice Models of Quantum Gravity

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+\epsilon\sigma$, with $\sigma=\pm 1$, in close analogy to the ancestor of all lattice theories, the Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.Comment: 4 pages, 1 figure

Z_2-Regge versus Standard Regge Calculus in two dimensions

We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z_2 model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the Z_2-Regge Model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the Z_2-Regge Model is analyzed by mean-field theory.Comment: 21 pages, 16 ps-figures, to be published in Phys. Rev.

Tilting mutation of weakly symmetric algebras and stable equivalence

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a weakly symmetric algebra A, presented by a quiver with relations, we give a detailed description of the quiver and relations of the algebra obtained by mutating at a single loopless vertex of the quiver of A. In this form the mutation procedure appears similar to, although significantly more complicated than, the mutation procedure of Derksen, Weyman and Zelevinsky for quivers with potentials. By definition, weakly symmetric algebras connected by a sequence of tilting mutations are derived equivalent, and hence stably equivalent. The second aim of this article is to study these stable equivalences via a result of Okuyama describing the images of the simple modules. As an application we answer a question of Asashiba on the derived Picard groups of a class of self-injective algebras of finite representation type. We conclude by introducing a mutation procedure for maximal systems of orthogonal bricks in a triangulated category, which is motivated by the effect that a tilting mutation has on the set of simple modules in the stable category.Comment: Description and proof of mutated algebra made more rigorous (Prop. 3.1 and 4.2). Okuyama's Lemma incorporated: Theorem 4.1 is now Corollary 5.1, and proof is omitted. To appear in Algebras and Representation Theor

Kinetic and ion pairing contributions in the dielectric spectra of electrolyte aqueous solutions

Understanding dielectric spectra can reveal important information about the dynamics of solvents and solutes from the dipolar relaxation times down to electronic ones. In the late 1970s, Hubbard and Onsager predicted that adding salt ions to a polar solution would result in a reduced dielectric permittivity that arises from the unexpected tendency of solvent dipoles to align opposite to the applied field. So far, this effect has escaped an experimental verification, mainly because of the concomitant appearance of dielectric saturation from which the Hubbard-Onsager decrement cannot be easily separated. Here we develop a novel non-equilibrium molecular dynamics simulation approach to determine this decrement accurately for the first time. Using a thermodynamic consistent all-atom force field we show that for an aqueous solution containing sodium chloride around 4.8 Mol/l, this effect accounts for 12\% of the total dielectric permittivity. The dielectric decrement can be strikingly different if a less accurate force field for the ions is used. Using the widespread GROMOS parameters, we observe in fact an {\it increment} of the dielectric permittivity rather than a decrement. We can show that this increment is caused by ion pairing, introduced by a too low dispersion force, and clarify the microscopic connection between long-living ion pairs and the appearance of specific features in the dielectric spectrum of the solution

A Lagrangian kinetic model for collisionless magnetic reconnection

A new fully kinetic system is proposed for modeling collisionless magnetic reconnection. The formulation relies on fundamental principles in Lagrangian dynamics, in which the inertia of the electron mean flow is neglected in the expression of the Lagrangian, rather then enforcing a zero electron mass in the equations of motion. This is done upon splitting the electron velocity into its mean and fluctuating parts, so that the latter naturally produce the corresponding pressure tensor. The model exhibits a new Coriolis force term, which emerges from a change of frame in the electron dynamics. Then, if the electron heat flux is neglected, the strong electron magnetization limit yields a hybrid model, in which the electron pressure tensor is frozen into the electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio

Laboratoriumstandaardisasie en kwaliteitskontrole in antistolterapie

The original publication is available at http://www.samj.org.za[No abstract available]Publishers' versio

Monte Carlo Study of Topological Defects in the 3D Heisenberg Model

We use single-cluster Monte Carlo simulations to study the role of topological defects in the three-dimensional classical Heisenberg model on simple cubic lattices of size up to $80^3$. By applying reweighting techniques to time series generated in the vicinity of the approximate infinite volume transition point $K_c$, we obtain clear evidence that the temperature derivative of the average defect density $d\langle n \rangle/dT$ behaves qualitatively like the specific heat, i.e., both observables are finite in the infinite volume limit. This is in contrast to results by Lau and Dasgupta [{\em Phys. Rev.\/} {\bf B39} (1989) 7212] who extrapolated a divergent behavior of $d\langle n \rangle/dT$ at $K_c$ from simulations on lattices of size up to $16^3$. We obtain weak evidence that $d\langle n \rangle/dT$ scales with the same critical exponent as the specific heat.As a byproduct of our simulations, we obtain a very accurate estimate for the ratio $\alpha/\nu$ of the specific-heat exponent with the correlation-length exponent from a finite-size scaling analysis of the energy.Comment: pages ,4 ps-figures not included, FUB-HEP 10/9

The 1981 outburst of the old nova GK Persei

Old nova GK Per was observed in 1981 with the IUE, during its rise, maximum, and subsequent return to minimum. In outburst, GK Per is luminous but much redder than dwarf novae or standard model accretion disks. The observed spectrum can be explained qualitatively with the Ghosh and Lamb (1979) model for the interaction of an accretion disk with the magnetic field of the accreting white dwarf. The N V and He2 are enhanced relative to other emission lines during outburst. This can be understood with photoionization by very soft X-rays having a luminosity comparable to that of the hard X-rays

Many-body GW calculations of ground-state properties: Quasi-2D electron systems and van der Waals forces

We present GW many-body results for ground-state properties of two simple but very distinct families of inhomogeneous systems in which traditional implementations of density-functional theory (DFT) fail drastically. The GW approach gives notably better results than the well-known random-phase approximation, at a similar computational cost. These results establish GW as a superior alternative to standard DFT schemes without the expensive numerical effort required by quantum Monte Carlo simulations