ZETA DETERMINANT AND OPERATOR DETERMINANTS

We apply techniques of zeta functions and regularized products theory to study the zeta determinant of a class of abstract operators with compact resolvent, and in particular the relation with other spectral functions.

Minimal Nielsen Root Classes and Roots of Liftings

Given a continuous map f : K -> M from a 2-dimensional CW complex into a closed surface, the Nielsen root number N(f) and the minimal number of roots mu(f) of f satisfy N(f) <= mu(f). But, there is a number mu(C)(f) associated to each Nielsen root class of f, and an important problem is to know when mu(f) = mu(C)(f)N(f). In addition to investigate this problem, we determine a relationship between mu(f) and mu((f) over tilde), when (f) over tilde f is a lifting of f through a covering space, and we find a connection between this problems, with which we answer several questions related to them when the range of the maps is the projective plane.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

Structure of disordered gold-polymer thin films using small angle x-ray scattering

We have investigated the structure of disordered gold-polymer thin films using small angle x-ray scattering and compared the results with the predictions of a theoretical model based on two approaches-a structure form factor approach and the generalized Porod law. The films are formed of polymer-embedded gold nanoclusters and were fabricated by very low energy gold ion implantation into polymethylmethacrylate (PMMA). The composite films span (with dose variation) the transition from electrically insulating to electrically conducting regimes, a range of interest fundamentally and technologically. We find excellent agreement with theory and show that the PMMA-Au films have monodispersive or polydispersive characteristics depending on the implanted ion dose. (C) 2010 American Institute of Physics. [doi:10.1063/1.3493241]

Alfveacuten continuum deformation by kinetic geodesic effect in rotating tokamak plasmas

Using a quasitoroidal set of coordinates with coaxial circular magnetic surfaces, Vlasov equation is solved for collisionless plasmas in drift approach and a perpendicular dielectric tensor is found for large aspect ratio tokamaks in a low frequency band. Taking into account plasma rotation and charge separation parallel electric field, it is found that an ion geodesic effect deform Alfveacuten wave continuum producing continuum minimum at the rational magnetic surfaces, which depends on the plasma rotation and poloidal mode numbers. In kinetic approach, the ion thermal motion defines the geodesic effect but the mode frequency also depends on electron temperature. A geodesic ion Alfveacuten mode predicted below the continuum minimum has a small Landau damping in plasmas with Maxwell distribution but the plasma rotation may drive instability.

Nonlocal magnetorotational instability

An analytical theory of the nonlocal magnetorotational instability (MRI) is developed for the simplest astrophysical plasma model. It is assumed that the rotation frequency profile has a steplike character, so that there are two regions in which it has constant different values, separated by a narrow transition layer. The surface wave approach is employed to investigate the MRI in this configuration. It is shown that the main regularities of the nonlocal MRI are similar to those of the local instability and that driving the nonaxisymmetric MRI is less effective than the axisymmetric one, also for the case of the nonlocal instability. The existence of nonlocal instabilities in nonmagnetized plasma is predicted. (c) 2008 American Institute of Physics.

The influence of adsorption phenomena on the impedance spectroscopy of an electrolytic cell

In this work we investigate the influence of the adsorption of ions on the impedance spectroscopy of an electrolytic cell. We consider that the positive and negative ions present in a dielectric liquid are adsorbed in the electrode surfaces with different adsorption energies. This difference in adsorption energies causes an additional plateaux in the limit of the low-frequency range of the real part of the impedance Z. In the same frequency range, a second minimum in the imaginary part of Z is predicted. The theory is illustrated with measurements of the impedance of an electrolytic solution in the frequency range from 10(-2) Hz to 1 KHz. A comparison between the present model and others from the literature to describe the experimental results is also made.

Search for Lorentz Invariance and CPT Violation with the MINOS Far Detector

We searched for a sidereal modulation in the MINOS far detector neutrino rate. Such a signal would be a consequence of Lorentz and CPT violation as described by the standard-model extension framework. It also would be the first detection of a perturbative effect to conventional neutrino mass oscillations. We found no evidence for this sidereal signature, and the upper limits placed on the magnitudes of the Lorentz and CPT violating coefficients describing the theory are an improvement by factors of 20-510 over the current best limits found by using the MINOS near detector.

Heavy quark production in deep inelastic electron-nucleus scattering

Heavy quark production has been very well studied over the last years both theoretically and experimentally. Theory has been used to study heavy quark production in ep collisions at HERA, in pp collisions at Tevatron and RHIC, in pA and dA collisions at RHIC, and in AA collisions at CERN-SPS and RHIC. However, to the best of our knowledge, heavy quark production in eA has received almost no attention. With the possible construction of a high energy electron-ion collider, updated estimates of heavy quark production are needed. We address the subject from the perspective of saturation physics and compute the heavy quark production cross section with the dipole model. We isolate shadowing and nonlinear effects, showing their impact on the charm structure function and on the transverse momentum spectrum.

Testing Lorentz Invariance and CPT Conservation with NuMI Neutrinos in the MINOS Near Detector

A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).

Electron dephasing scattering rate in two-dimensional GaAs/InGaAs heterostructures with embedded InAs quantum dots

We report a comprehensive study of weak-localization and electron-electron interaction effects in a GaAs/InGaAs two-dimensional electron system with nearby InAs quantum dots, using measurements of the electrical conductivity with and without magnetic field. Although both the effects introduce temperature dependent corrections to the zero magnetic field conductivity at low temperatures, the magnetic field dependence of conductivity is dominated by the weak-localization correction. We observed that the electron dephasing scattering rate tau(-1)(phi), obtained from the magnetoconductivity data, is enhanced by introducing quantum dots in the structure, as expected, and obeys a linear dependence on the temperature and elastic mean free path, which is against the Fermi-liquid model. (c) 2008 American Institute of Physics. [DOI: 10.1063/1.2996034]

Search for the rare decay K(L)->pi(0)pi(0)gamma

The KTeV E799 experiment has conducted a search for the rare decay K(L)->pi(0)pi(0)gamma via the topology K(L)->pi(0)pi(0)(D)gamma (where pi(0)(D)->gamma e(+)e(-)). Because of Bose statistics of the pi(0) pair and the real nature of the photon, the K(L)->pi(0)pi(0)gamma decay is restricted to proceed at lowest order by the CP conserving direct emission (DE) of an E2 electric quadrupole photon. The rate of this decay is interesting theoretically since chiral perturbation theory predicts that this process vanishes at level O(p(4)). Therefore, this mode probes chiral perturbation theory at O(p(6)). In this paper we report a determination of an upper limit of 2.43x10(-7) (90% CL) for K(L)->pi(0)pi(0)gamma. This is approximately a factor of 20 lower than previous results.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Multimode Vibrational Couplings in Resonant Positron Annihilation

The mechanisms for multimode vibrational couplings in resonant positron annihilation are not well understood. We show that these resonances can arise from positron-induced distortions of the potential energy surface (target response to the positron field). Though these distortions can transfer energy into single- and multiquantum vibrations, they have so far been disregarded as a pathway to resonant annihilation. We also compare the existing annihilation theories and show that the currently accepted model can be cast as a special case of the Feshbach annihilation theory.