Thermal Noise Behavior of the Bridge Circuit

This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the deterministic terminal behavior reduces to that of a single linear resistor. This reduction of the deterministic terminal behavior, in which a natural frequency of a linear circuit does not appear in the driving-point impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper shows that, in addition to the reduction of the deterministic behavior, the thermal noise at the terminals of the network, arising from the usual Nyquist-Johnson noise model associated with each resistor in the network, is also exactly that of a single linear resistor. While this result for the linear time-invariant (LTI) case is a direct consequence of a well-known result for RLC circuits, the nonlinear result is novel. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varyingSupported by the National Science Foundation under Grant 94-23221, by DARPA/ARO under Contract DAAH04-94-G-0342, and by the NEC Research Institute, Princeton, New Jersey

An Ensemble Kalman-Particle Predictor-Corrector Filter for Non-Gaussian Data Assimilation

An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by nonparametric density estimation. It is demonstrated on several numerical examples that the new predictor-corrector filter combines the advantages of the EnKF and the PF and that it is suitable for high dimensional states which are discretizations of solutions of partial differential equations.Comment: ICCS 2009, to appear; 9 pages; minor edit

Boson induced s-wave pairing in dilute boson-fermion mixtures

We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give an analytical method to derive the associated $T_c$ in the limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a $T_c$ of the same order as for a pure Fermi gas with bare attraction.Comment: 12 pages, no figure

A Statistically Modelling Method for Performance Limits in Sensor Localization

In this paper, we study performance limits of sensor localization from a novel perspective. Specifically, we consider the Cramer-Rao Lower Bound (CRLB) in single-hop sensor localization using measurements from received signal strength (RSS), time of arrival (TOA) and bearing, respectively, but differently from the existing work, we statistically analyze the trace of the associated CRLB matrix (i.e. as a scalar metric for performance limits of sensor localization) by assuming anchor locations are random. By the Central Limit Theorems for $U$-statistics, we show that as the number of the anchors increases, this scalar metric is asymptotically normal in the RSS/bearing case, and converges to a random variable which is an affine transformation of a chi-square random variable of degree 2 in the TOA case. Moreover, we provide formulas quantitatively describing the relationship among the mean and standard deviation of the scalar metric, the number of the anchors, the parameters of communication channels, the noise statistics in measurements and the spatial distribution of the anchors. These formulas, though asymptotic in the number of the anchors, in many cases turn out to be remarkably accurate in predicting performance limits, even if the number is small. Simulations are carried out to confirm our results

Nonlinear Lattice Waves in Random Potentials

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.Comment: 45 pages, 19 figure

Technological Devices in the Archives: A Policy Analysis

Doing research in the archive is the cornerstone of humanities scholarship. Various archives institute policies regarding the use of technological devices, such as mobile phones, laptops, and cameras in their reading rooms. Such policies directly affect the scholars as the devices mediate the nature of their interaction with the source materials in terms of capturing, organizing, note taking, and record keeping for future use of found materials. In this paper, we present our analysis of the policies of thirty archives regarding the use of technology in their reading rooms. This policy analysis, along with data from interviews of scholars and archivists, is intended to serve as a basis for developing mobile applications for assisting scholars in their research activities. In this paper we introduce an early prototype of such a mobile application— AMTracker.Informatio

Photoproduction of mesons in nuclei at GeV energies

In a transport model that combines initial state interactions of the photon with final state interactions of the produced particles we present a calculation of inclusive photoproduction of mesons in nuclei in the energy range from 1 to 7 GeV. We give predictions for the photoproduction cross sections of pions, etas, kaons, antikaons, and $\pi^+\pi^-$ invariant mass spectra in ^{12}C and ^{208}Pb. The effects of nuclear shadowing and final state interaction of the produced particles are discussed in detail.Comment: Text added in summary in general reliability of the method, references updated. Phys. Rev. C (2000) in pres

Bcc 4^4He as a Coherent Quantum Solid

In this work we investigate implications of the quantum nature of bcc $^{4}$% He. We show that it is a unique solid phase with both a lattice structure and an Off-Diagonal Long Range Order of coherently oscillating local electric dipole moments. These dipoles arise from the local motion of the atoms in the crystal potential well, and oscillate in synchrony to reduce the dipolar interaction energy. The dipolar ground-state is therefore found to be a coherent state with a well defined global phase and a three-component complex order parameter. The condensation energy of the dipoles in the bcc phase stabilizes it over the hcp phase at finite temperatures. We further show that there can be fermionic excitations of this ground-state and predict that they form an optical-like branch in the (110) direction. A comparison with 'super-solid' models is also discussed.Comment: 12 pages, 8 figure

Testing quantum correlations in a confined atomic cloud by scattering fast atoms

We suggest measuring one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability of the inelastic process, resulting in a pair of outcoming fast atoms for each incoming one, turns out to be given by a Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section. A possible design of the atomic detector is also discussed.Comment: 5 RevTex pages, no figures, submitted to PR

Effect of sedimentary heterogeneities in the sealing formation on predictive analysis of geological CO₂ storage

Numerical models of geologic carbon sequestration (GCS) in saline aquifers use multiphase fluid flow-characteristic curves (relative permeability and capillary pressure) to represent the interactions of the non-wetting CO2 and the wetting brine. Relative permeability data for many sedimentary formations is very scarce, resulting in the utilisation of mathematical correlations to generate the fluid flow characteristics in these formations. The flow models are essential for the prediction of CO2 storage capacity and trapping mechanisms in the geological media. The observation of pressure dissipation across the storage and sealing formations is relevant for storage capacity and geomechanical analysis during CO2 injection. This paper evaluates the relevance of representing relative permeability variations in the sealing formation when modelling geological CO2 sequestration processes. Here we concentrate on gradational changes in the lower part of the caprock, particularly how they affect pressure evolution within the entire sealing formation when duly represented by relative permeability functions. The results demonstrate the importance of accounting for pore size variations in the mathematical model adopted to generate the characteristic curves for GCS analysis. Gradational changes at the base of the caprock influence the magnitude of pressure that propagates vertically into the caprock from the aquifer, especially at the critical zone (i.e. the region overlying the CO2 plume accumulating at the reservoir-seal interface). A higher degree of overpressure and CO2 storage capacity was observed at the base of caprocks that showed gradation. These results illustrate the need to obtain reliable relative permeability functions for GCS, beyond just permeability and porosity data. The study provides a formative principle for geomechanical simulations that study the possibility of pressure-induced caprock failure during CO2 sequestration