Coarse-grained dynamics of an activity bump in a neural field model

We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a pitchfork bifurcation in bump speed as a parameter (the strength of adaptation) is changed; yet increasing the noise intensity effectively slowed the motion of the bump. Here we revisit the system from the point of view of describing the high-dimensional stochastic dynamics in terms of the effective dynamics of a single scalar "coarse" variable. We show that such a reduced description in the form of an effective Langevin equation characterized by a double-well potential is quantitatively successful. The effective potential can be extracted using short, appropriately-initialized bursts of direct simulation. We demonstrate this approach in terms of (a) an experience-based "intelligent" choice of the coarse observable and (b) an observable obtained through data-mining direct simulation results, using a diffusion map approach.Comment: Corrected aknowledgement

On the evaluation formula for Jack polynomials with prescribed symmetry

The Jack polynomials with prescribed symmetry are obtained from the nonsymmetric polynomials via the operations of symmetrization, antisymmetrization and normalization. After dividing out the corresponding antisymmetric polynomial of smallest degree, a symmetric polynomial results. Of interest in applications is the value of the latter polynomial when all the variables are set equal. Dunkl has obtained this evaluation, making use of a certain skew symmetric operator. We introduce a simpler operator for this purpose, thereby obtaining a new derivation of the evaluation formula. An expansion formula of a certain product in terms of Jack polynomials with prescribed symmetry implied by the evaluation formula is used to derive a generalization of a constant term identity due to Macdonald, Kadell and Kaneko. Although we don't give the details in this work, the operator introduced here can be defined for any reduced crystallographic root system, and used to provide an evaluation formula for the corresponding Heckman-Opdam polynomials with prescribed symmetry.Comment: 18 page

Evidence for magnetic clusters in Ni1−x_{1-x}Vx_{x} close to the quantum critical concentration

The d-metal alloy Ni$_{1-x}$V$_{x}$ undergoes a quantum phase transition from a ferromagnetic ground state to a paramagnetic ground state as the vanadium concentration $x$ is increased. We present magnetization, ac-susceptibility and muon-spin relaxation data at several vanadium concentrations near the critical concentration $x_c \approx11.6$ at which the onset of ferromagnetic order is suppressed to zero temperature. Below $x_c$, the muon data reveal a broad magnetic field distribution indicative of long-range ordered ferromagnetic state with spatial disorder. We show evidence of magnetic clusters in the ferromagnetic phase and close to the phase boundary in this disordered itinerant system as an important generic ingredient of a disordered quantum phase transition. In contrast, the temperature dependence of the magnetic susceptibility above $x_c$ is best described in terms of a magnetic quantum Griffiths phase with a power-law distribution of fluctuation rates of dynamic magnetic clusters. At the lowest temperatures, the onset of a short-range ordered cluster-glass phase is recognized by an increase in the muon depolarization in transverse fields and maxima in ac-susceptibility.Comment: 6 pages, 5 figures, submitted to Proceedings of SCES 201

Strain in epitaxial MnSi films on Si(111) in the thick film limit studied by polarization-dependent extended x-ray absorption fine structure

We report a study of the strain state of epitaxial MnSi films on Si(111) substrates in the thick film limit (100-500~\AA) as a function of film thickness using polarization-dependent extended x-ray absorption fine structure (EXAFS). All films investigated are phase-pure and of high quality with a sharp interface between MnSi and Si. The investigated MnSi films are in a thickness regime where the magnetic transition temperature $T_\mathrm{c}$ assumes a thickness-independent enhanced value of $\geq$43~K as compared with that of bulk MnSi, where $T_\mathrm{c} \approx 29~{\rm K}$. A detailed refinement of the EXAFS data reveals that the Mn positions are unchanged, whereas the Si positions vary along the out-of-plane [111]-direction, alternating in orientation from unit cell to unit cell. Thus, for thick MnSi films, the unit cell volume is essentially that of bulk MnSi --- except in the vicinity of the interface with the Si substrate (thin film limit). In view of the enhanced magnetic transition temperature we conclude that the mere presence of the interface, and its specific characteristics, strongly affects the magnetic properties of the entire MnSi film, even far from the interface. Our analysis provides invaluable information about the local strain at the MnSi/Si(111) interface. The presented methodology of polarization dependent EXAFS can also be employed to investigate the local structure of other interesting interfaces.Comment: 11 pages, 10 figure

Fine-time energetic electron behavior observed by Cluster/RAPID in the magnetotail associated with X-line formation and subsequent current disruption

Energetic electrons with 90deg pitch angle have been observed in the magnetotail at ~19 <i>R<sub>E</sub></i> near local midnight during the recovery phase of a substorm event on 27 August 2001 (Baker et al., 2002). Based on auroral images Baker et al. (2002) placed the substorm expansion phase between ~04:06:16 and ~04:08:19 UT. The electron enhancements perpendicular to the ambient magnetic field occurred while the Cluster spacecraft were on closed field lines in the central plasma sheet approaching the neutral sheet. Magnetic field and energetic particle measurements have been employed from a number of satellites, in order to determine the source and the subsequent appearance of these electrons at the Cluster location. It is found that ~7.5 min after an X-line formation observed by Cluster (Baker et al., 2002) a current disruption event took place inside geosynchronous orbit and subsequently expanded both in local time and tailward, giving rise to field-aligned currents and the formation of a current wedge. A synthesis of tail reconnection and the cross-tail current disruption scenario is proposed for the substorm global initiation process: When a fast flow with northward magnetic field, produced by magnetic reconnection in the midtail, abruptly decelerates at the inner edge of the plasma sheet, it compresses the plasma populations earthward of the front, altering dynamically the B<sub>z</sub> magnetic component in the current sheet. This provides the necessary and sufficient conditions for the kinetic cross-field streaming/current (KCSI/CFCI) instability (Lui et al., 1990, 1991) to initiate. As soon as the ionospheric conductance increases over a threshold level, the auroral electrojet is greatly intensified (see Fig. 2 in Baker et al., 2002), which leads to the formation of the substorm current wedge and dipolarization of the magnetic field. This substorm scenario combines the near-Earth neutral line and the current disruption for the initiation of substorms, at least during steady southward IMF. One can conclude the following: The observations suggest that the anisotropic electron increases observed by Cluster are not related to an acceleration mechanism associated with the X-line formation in the midtail, but rather these particles are generated in the dusk magnetospheric sector due to the longitudinal and tailward expansion of a current disruption region and subsequently observed at the Cluster location with no apparent energy dispersion.<br><br> <b>Keywords.</b> Magnetospheric physics (Magnetotail; Plasma convection; Storms and substorms

Thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets in an external magnetic field within Green function formalism

The thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets (HFM) in an external magnetic field is investigated within a second-order two-time Green function formalism in the wide temperature and field range. A crucial point of the proposed scheme is a proper account of the analytical properties for the approximate transverse commutator Green function obtained as a result of the decoupling procedure. A good quantitative description of the correlation functions, magnetization, susceptibility, and heat capacity of the HFM on a chain, square and triangular lattices is found for both infinite and finite-sized systems. The dependences of the thermodynamic functions of 2D HFM on the cluster size are studied. The obtained results agree well with the corresponding data found by Bethe ansatz, exact diagonalization, high temperature series expansions, and quantum Monte Carlo simulations.Comment: 11 pages, 14 figure

Probing for evolutionary links between local ULIRGs and QSOs from NIR spectroscopy

We present a study of the dynamical evolution of Ultraluminous Infrared Galaxies (ULIRGs), merging galaxies of infrared luminosity >10^12 L_sun. During our Very Large Telescope large program, we have obtained ISAAC near-infrared, high-resolution spectra of 54 ULIRGs (at several merger phases) and 12 local Palomar-Green QSOs to investigate whether ULIRGs go through a QSO phase during their evolution. One possible evolutionary scenario is that after nuclear coalescence, the black hole radiates close to Eddington to produce QSO luminosities. The mean stellar velocity dispersion that we measure from our spectra is similar (~160 km/s) for 30 post-coalescence ULIRGs and 7 IR-bright QSOs. The black holes in both populations have masses of order 10^7-10^8 M_sun (calculated from the relation to the host dispersion) and accrete at rates >0.5 Eddington. Placing ULIRGs and IR-bright QSOs on the fundamental plane of early-type galaxies shows that they are located on a similar region (that of moderate-mass ellipticals), in contrast to giant ellipticals and radio-loud QSOs. While this preliminary comparison of the ULIRG and QSO host kinematical properties indicates that (some) ULIRGs may undergo a QSO phase in their evolutionary history before they settle down as ellipticals, further data on non-IR excess QSOs are necessary to test this scenario.Comment: To appear in the "QSO Host Galaxies: Evolution and Environment" conference proceedings; meeting held in Leiden, August 200

Random matrix ensembles with an effective extensive external charge

Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two such ensembles have been encounted: an ensemble of unitary matrices specified by the so-called Poisson kernel, and the Laguerre ensemble of positive definite matrices. Here we consider various properties of these ensembles. Jack polynomial theory is used to prove a reproducing property of the Poisson kernel, and a certain unimodular mapping is used to demonstrate that the variance of a linear statistic is the same as in the Dyson circular ensemble. For the Laguerre ensemble, the scaled global density is calculated exactly for all even values of the parameter $\beta$, while for $\beta = 2$ (random matrices with unitary symmetry), the neighbourhood of the smallest eigenvalue is shown to be in the soft edge universality class.Comment: LaTeX209, 17 page