Sparse Bayesian Nonlinear System Identification using Variational Inference

IEEE Bayesian nonlinear system identification for one of the major classes of dynamic model, the nonlinear autoregressive with exogenous input (NARX) model, has not been widely studied to date. Markov chain Monte Carlo (MCMC) methods have been developed, which tend to be accurate but can also be slow to converge. In this contribution, we present a novel, computationally efficient solution to sparse Bayesian identification of the NARX model using variational inference, which is orders of magnitude faster than MCMC methods. A sparsity-inducing hyper-prior is used to solve the structure detection problem. Key results include: 1. successful demonstration of the method on low signal-to-noise ratio signals (down to 2dB); 2. successful benchmarking in terms of speed and accuracy against a number of other algorithms: Bayesian LASSO, reversible jump MCMC, forward regression orthogonalisation, LASSO and simulation error minimisation with pruning; 3. accurate identification of a real world system, an electroactive polymer; and 4. demonstration for the first time of numerically propagating the estimated nonlinear time-domain model parameter uncertainty into the frequency-domain

Trapping of Projectiles in Fixed Scatterer Calculations

We study multiple scattering off nuclei in the closure approximation. Instead of reducing the dynamics to one particle potential scattering, the scattering amplitude for fixed target configurations is averaged over the target groundstate density via stochastic integration. At low energies a strong coupling limit is found which can not be obtained in a first order optical potential approximation. As its physical explanation, we propose it to be caused by trapping of the projectile. We analyse this phenomenon in mean field and random potential approximations. (PACS: 24.10.-i)Comment: 15 page

Radiative charge transfer lifetime of the excited state of (NaCa)+^+

New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom--ion trap under high vacuum conditions. The collisional cooling of laser pre-cooled Ca$^+$ ions by ultracold Na atoms is being studied. Modeling this process requires knowledge of the radiative lifetime of the excited singlet A$^1\Sigma^+$ state of the (NaCa)$^+$ molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using Complete Active Space Self-Consistent field and M\"oller-Plesset second order perturbation theory (CASSCF/MP2) with an extended Gaussian basis, 6-311+G(3df). The semiclassical charge transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be $2.3\times 10^{-16}$ cm$^3$/sec, while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher ($1.1\times 10^{-8}$ cm$^3$/sec and $2.3\times 10^{-9}$ cm$^3$/sec, respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms is favorable with the respect to low loss of calcium ions due to the charge transfer.Comment: 4 pages, 5 figures; v.2 - conceptual change

Effectiveness of summer applications of Trifluralin

Non-Peer Reviewe

Transverse spin dynamics in a spin-polarized Fermi liquid

The linear equations for transverse spin dynamics in weakly polarised degenerate Fermi liquid with arbitrary relationship between temperature and polarization are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at T=0. The analogy between temperature dependences of spin waves attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented. We also discuss spin-polarized Fermi liquid in the general context of the Fermi-liquid theory and compare it with "Fermi liquid" with spontaneous magnetization.Comment: 10 page

Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators

An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are suitably handled with quaternions and octonions in order to obtain their generators, commutation rules and symmetry properties. Accordingly, Casimir operators for SU(2)and SU(3) flavor symmetries are also constructed for the proper testing of these symmetries in terms of quaternions and octonions

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

Atom focusing by far-detuned and resonant standing wave fields: Thin lens regime

The focusing of atoms interacting with both far-detuned and resonant standing wave fields in the thin lens regime is considered. The thin lens approximation is discussed quantitatively from a quantum perspective. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\theta$: the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible ($\theta \gg 1$). Within the diffraction theory analytical expressions show that the focused atoms in the far detuned case have an approximately constant background density $0.5(1-0.635\theta ^{- 1/2})$ while the peak density behaves as $$, the focal distance or time as $\theta ^{-1}(1+1.27\theta ^{- 1/2})$, the focal spot size as $0.744\theta ^{-3/4}$, and the depth of focus as $1.91\theta ^{- 3/2}$. Focusing by the resonant standing wave field leads to a new effect, a Rabi- like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.Comment: 21 pages, 11 figure

Eureka and beyond: mining's impact on African urbanisation

This collection brings separate literatures on mining and urbanisation together at a time when both artisanal and large-scale mining are expanding in many African economies. While much has been written about contestation over land and mineral rights, the impact of mining on settlement, notably its catalytic and fluctuating effects on migration and urban growth, has been largely ignored. African nation-states’ urbanisation trends have shown considerable variation over the past half century. The current surge in ‘new’ mining countries and the slow-down in ‘old’ mining countries are generating some remarkable settlement patterns and welfare outcomes. Presently, the African continent is a laboratory of national mining experiences. This special issue on African mining and urbanisation encompasses a wide cross-section of country case studies: beginning with the historical experiences of mining in Southern Africa (South Africa, Zambia, Zimbabwe), followed by more recent mineralizing trends in comparatively new mineral-producing countries (Tanzania) and an established West African gold producer (Ghana), before turning to the influence of conflict minerals (Angola, the Democratic Republic of Congo and Sierra Leone)

The Frequency Dependent Conductivity of Electron Glasses

Results of DC and frequency dependent conductivity in the quantum limit, i.e. hw > kT, for a broad range of dopant concentrations in nominally uncompensated, crystalline phosphorous doped silicon and amorphous niobium-silicon alloys are reported. These materials fall under the general category of disordered insulating systems, which are referred to as electron glasses. Using microwave resonant cavities and quasi-optical millimeter wave spectroscopy we are able to study the frequency dependent response on the insulating side of the metal-insulator transition. We identify a quantum critical regime, a Fermi glass regime and a Coulomb glass regime. Our phenomenological results lead to a phase diagram description, or taxonomy, of the electrodynamic response of electron glass systems