Operator identities in q-deformed Clifford analysis

In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied

Depinning transition and thermal fluctuations in the random-field Ising model

We analyze the depinning transition of a driven interface in the 3d random-field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111]-direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3d-RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.Comment: 6 pages, including 9 figures, submitted for publicatio

A pattern-recognition theory of search in expert problem solving

Understanding how look-ahead search and pattern recognition interact is one of the important research questions in the study of expert problem-solving. This paper examines the implications of the template theory (Gobet & Simon, 1996a), a recent theory of expert memory, on the theory of problem solving in chess. Templates are "chunks" (Chase & Simon, 1973) that have evolved into more complex data structures and that possess slots allowing values to be encoded rapidly. Templates may facilitate search in three ways: (a) by allowing information to be stored into LTM rapidly; (b) by allowing a search in the template space in addition to a search in the move space; and (c) by compensating loss in the "mind's eye" due to interference and decay. A computer model implementing the main ideas of the theory is presented, and simulations of its search behaviour are discussed. The template theory accounts for the slight skill difference in average depth of search found in chess players, as well as for other empirical data

Spectropolarimetric observations of the Ca II 8498 A and 8542 A lines in the quiet Sun

The Ca II infrared triplet is one of the few magnetically sensitive chromospheric lines available for ground-based observations. We present spectropolarimetric observations of the 8498 A and 8542 A lines in a quiet Sun region near a decaying active region and compare the results with a simulation of the lines in a high plasma-beta regime. Cluster analysis of Stokes V profile pairs shows that the two lines, despite arguably being formed fairly close, often do not have similar shapes. In the network, the local magnetic topology is more important in determining the shapes of the Stokes V profiles than the phase of the wave, contrary to what our simulations show. We also find that Stokes V asymmetries are very common in the network, and the histograms of the observed amplitude and area asymmetries differ significantly from the simulation. Both the network and internetwork show oscillatory behavior in the Ca II lines. It is stronger in the network, where shocking waves, similar to those in the high-beta simulation, are seen and large self-reversals in the intensity profiles are common.Comment: 23 pages, 17 figures, accepted to ApJ some figures are low-res, for high-res email [email protected]

Coulomb field of an accelerated charge: physical and mathematical aspects

The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge invariant "2+2" decomposition is used to see how the Coulomb field of a charge, static in an accelerated frame, has properties that suggest features of electromagnetism which are different from those in an inertial frame. In particular, (1) an illustrative calculation shows that the Larmor radiation reaction equals the electrostatic attraction between the accelerated charge and the charge induced on the surface whose history is the event horizon, and (2) a spectral decomposition of the Coulomb potential in the accelerated frame suggests the possibility that the distortive effects of this charge on the Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at http://www.math.ohio-state.edu/~gerlac

Coupling of frustrated Ising spins to magnetic cycloid in multiferroic TbMnO3

We report on diffraction measurements on multiferroic TbMnO3 which demonstrate that the Tb- and Mn-magnetic orders are coupled below the ferroelectric transition TFE = 28 K. For T < TFE the magnetic propagation vectors (tau) for Tb and Mn are locked so that tauTb = tauMn, while below TNTb = 7 K we find that tauTb and tauMn lock-in to rational values of 3/7 b* and 2/7 b*, respectively, and obey the relation 3tauTb - tauMn = 1. We explain this novel matching of wave vectors within the frustrated ANNNI model coupled to a periodic external field produced by the Mn-spin order. The tauTb = tauMn behavior is recovered when Tb magnetization is small, while the tauTb = 3/7 regime is stabilized at low temperatures by a peculiar arrangement of domain walls in the ordered state of Ising-like Tb spins.Comment: 5 pages, 3 figure

Turbulent convection: comparing the moment equations to numerical simulations

The non-local hydrodynamic moment equations for compressible convection are compared to numerical simulations. Convective and radiative flux typically deviate less than 20% from the 3D simulations, while mean thermodynamic quantities are accurate to at least 2% for the cases we have investigated. The moment equations are solved in minutes rather than days on standard workstations. We conclude that this convection model has the potential to considerably improve the modelling of convection zones in stellar envelopes and cores, in particular of A and F stars.Comment: 10 pages (6 pages of text including figure captions + 4 figures), Latex 2e with AAS Latex 5.0 macros, accepted for publication in ApJ

Comparison of perturbative expansions using different phonon bases for two-site Holstein model

The two-site single-polaron problem is studied within the perturbative expansions using different standard phonon basis obtained through the Lang Firsov (LF), modified LF (MLF) and modified LF transformation with squeezed phonon states (MLFS). The role of these convergent expansions using the above prescriptions in lowering the energy and in determining the correlation functions are compared for different values of coupling strength. The single-electron energy, oscillator wave functions and correlation functions are calculated for the same system. The applicability of different phonon basis in different regimes of the coupling strength as well as in different regimes of hopping are also discussed.Comment: 24 pages (RevTEX), 12 postscript figures, final version accepted in PRB(2000) Jornal Ref: Phys. Rev. B, 61, 4592-4602 (2000

Carrier relaxation in GaAs v-groove quantum wires and the effects of localization

Carrier relaxation processes have been investigated in GaAs/AlGaAs v-groove quantum wires (QWRs) with a large subband separation (46 meV). Signatures of inhibited carrier relaxation mechanisms are seen in temperature-dependent photoluminescence (PL) and photoluminescence-excitation (PLE) measurements; we observe strong emission from the first excited state of the QWR below ~50 K. This is attributed to reduced inter-subband relaxation via phonon scattering between localized states. Theoretical calculations and experimental results indicate that the pinch-off regions, which provide additional two-dimensional confinement for the QWR structure, have a blocking effect on relaxation mechanisms for certain structures within the v-groove. Time-resolved PL measurements show that efficient carrier relaxation from excited QWR states into the ground state, occurs only at temperatures > 30 K. Values for the low temperature radiative lifetimes of the ground- and first excited-state excitons have been obtained (340 ps and 160 ps respectively), and their corresponding localization lengths along the wire estimated.Comment: 9 pages, 8 figures, submitted to Phys. Rev. B Attempted to correct corrupt figure