Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal

Thermal expansion and magnetostriction of pure and doped RAgSb2 (R = Y, Sm, La) single crystals

Data on temperature-dependent, anisotropic thermal expansion in pure and doped RAgSb2 (R = Y, Sm, La) single crystals are presented. Using the Ehrenfest relation and heat capacity measurements, uniaxial pressure derivatives for long range magnetic ordering and charge density wave transition temperatures are evaluated and compared with the results of the direct measurements under hydrostatic pressure. In-plane and c-axis pressure have opposite effect on the phase transitions in these materials, with in-plane effects being significantly weaker. Quantum oscillations in magnetostriction were observed for the three pure compounds, with the possible detection of new frequencies in SmAgSb2 and LaAgSb2. The uniaxial (along the c-axis) pressure derivatives of the dominant extreme orbits (beta) were evaluated for YAgSb2 and LaAgSb2

Atom-photon entanglement generation and distribution

We extend an earlier model by Law {\it et al.} \cite{law} for a cavity QED based single-photon-gun to atom-photon entanglement generation and distribution. We illuminate the importance of a small critical atom number on the fidelity of the proposed operation in the strong coupling limit. Our result points to a promisingly high purity and efficiency using currently available cavity QED parameters, and sheds new light on constructing quantum computing and communication devices with trapped atoms and high Q optical cavities.Comment: 7 fig

A Bayesian analysis of classical shadows

The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations -- such as high-fidelity ground truth states -- which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.Comment: 8 pages, 5 figure

Entangled quantum tunneling of two-component Bose-Einstein condensates

We examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We discover the condition under which particles of different species can tunnel as pairs through the potential barrier between two wells in opposition directions. This novel form of tunneling is due to the interspecies interaction that eliminates the self- trapping effect. The correlated motion of tunneling atoms leads to the generation of quantum entanglement between two macroscopically coherent systems.Comment: 4 pages, 3 figure

The golden circle: A way of arguing and acting about technology in the London ambulance service

This paper analyses the way in which the London Ambulance Service recovered from the events of October 1992, when it implemented a computer-aided despatch system (LASCAD) that remained in service for less than two weeks. It examines the enactment of a programme of long-term organizational change, focusing on the implementation of an alternative computer system in 1996. The analysis in this paper is informed by actor-network theory, both by an early statement of this approach developed by Callon in the sociology of translation, and also by concepts and ideas from Latour’s more recent restatement of his own position. The paper examines how alternative interests emerged and were stabilized over time, in a way of arguing and acting among key players in the change programme, christened the Golden Circle. The story traces four years in the history of the London Ambulance Service, from the aftermath of October 1992 through the birth of the Golden Circle to the achievement of National Health Service (NHS) trust status. LASCAD was the beginning of the story, this is the middle, an end lies in the future, when the remaining elements of the change programme are enacted beyond the Golden Circle

Electron-hole asymmetry in Co- and Mn-doped SrFe2As2

Phase diagram of electron and hole-doped SrFe2As2 single crystals is investigated using Co and Mn substitution at the Fe-sites. We found that the spin-density-wave state is suppressed by both dopants, but the superconducting phase appears only for Co (electron)-doping, not for Mn (hole)-doping. Absence of the superconductivity by Mn-doping is in sharp contrast to the hole-doped system with K-substitution at the Sr sites. Distinct structural change, in particular the increase of the Fe-As distance by Mn-doping is important to have a magnetic and semiconducting ground state as confirmed by first principles calculations. The absence of electron-hole symmetry in the Fe-site-doped SrFe2As2 suggests that the occurrence of high-Tc superconductivity is sensitive to the structural modification rather than the charge doping.Comment: 7 pages, 6 figure

Engineering cavity-field states by projection synthesis

We propose a reliable scheme for engineering a general cavity-field state. This is different from recently presented strategies,where the cavity is supposed to be initially empty and the field is built up photon by photon through resonant atom-field interactions. Here, a coherent state is previously injected into the cavity. So, the Wigner distribution function of the desired state is constructed from that of the initially coherent state. Such an engineering process is achieved through an adaptation of the recently proposed technique of projection synthesis to cavity QED phenomena.Comment: 5 ps pages plus 3 included figure

Participation in physical play and leisure : developing a theory- and evidence-based intervention for children with motor impairments

Peer reviewedPublisher PD