Grad's Distribution Function for 13 Moments based Moment Gas Kinetic Solver for Steady and Unsteady Rarefied flows: Discrete and Explicit Forms

Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of discrete Boltzmann equation in the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann integration equation at surrounding points of the cell interface directly, so the complicated partial differential equations with tedious implementation of boundary conditions in the moment method can be avoided. Meanwhile, the explicit expression of numerical fluxes is proposed, which could release the present solver the from the discretization and numerical summation in molecular velocity space. To evaluate the Grad's distribution function for 13 moments in the present framework, the G13-MGKS with the discrete and explicit form of numerical fluxes are examined by several test cases covering the steady and unsteady rarefied flows. Numerical results indicate that the G13-MGKS could simulate continuum flows accurately and present reasonable prediction for rarefied flows at moderate Knudsen number. Moreover, the tests of computations and memory costs demonstrate that the present framework could preserve the highly efficient feature

Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection of a Stiefel U(N)-bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this geometric phase captures the inherent geometric feature of the state evolution. Moreover, the geometric phase in the evolution of the eigenspace of an adiabatic action operator is also addressed, which is elaborated by a pullback U(N)-bundle. Several intriguing physical examples are illustrated.Comment: Added Refs. and corrected typos; 4 page

Optimal design of orders of DFrFTs for sparse representations

This paper proposes to use a set of discrete fractional Fourier transform (DFrFT) matrices with different rotational angles to construct an overcomplete kernel for sparse representations of signals. The design of the rotational angles is formulated as an optimization problem as follows. The sum of the L1 norms of both the real part and the imaginary part of transformed vectors is minimized subject to different values of the optimal rotational angles. In order to avoid all the optimal rotational angles within a small neighbourhood, constraints on the sum of the L1 norms of both the real part and the imaginary part of the product of the individual optimal DFrFT matrices and training vectors being either stationary or nondifferentiable are imposed. Solving this optimization problem is very challenging not only because of the nonsmooth and the nonconvex nature of the problem, but also due to expressing the optimization problem in a nonstandard form. To solve the problem, first it is shown in this paper that this design problem is equivalent to an optimal sampling problem as follows. The absolute sum of the L1 norms of both the real part and the imaginary part of the frequency responses of a set of filters at the optimal sampling frequencies is minimized subject to similar constraints. Second, it is further shown that the optimal sampling frequencies are the roots of a set of harmonic functions. As the frequency responses of the filters are required to be computed only at frequencies in a discrete set, the globally optimal rotational angles can be found very efficiently and effectively

The control parameterization method for nonlinear optimal control: A survey

The control parameterization method is a popular numerical technique for solving optimal control problems. The main idea of control parameterization is to discretize the control space by approximating the control function by a linear combination of basis functions. Under this approximation scheme, the optimal control problem is reduced to an approximate nonlinear optimization problem with a finite number of decision variables. This approximate problem can then be solved using nonlinear programming techniques. The aim of this paper is to introduce the fundamentals of the control parameterization method and survey its various applications to non-standard optimal control problems. Topics discussed include gradient computation, numerical convergence, variable switching times, and methods for handling state constraints. We conclude the paper with some suggestions for future research

Effects of uniaxial strain in LaMnO_3

The effects of uniaxial strain on the structural, orbital, optical, and magnetic properties of LaMnO_3 are calculated using a general elastic energy expression, along with a tight-binding parameterization of the band theory. Tensile uniaxial strain of the order of 2 % (i.e., of the order of magnitude of those induced in thin films by lattice mismatch with substrates) is found to lead to changes in the magnetic ground state, leading to dramatic changes in the band structure and optical conductivity spectrum. The magnetostriction effect associated with the Neel transition of bulk(unstrained) LaMnO_3 is also determined. Due to the Jahn-Teller coupling, the uniform tetragonal distortion mode is softer in LaMnO_3 than in doped cubic manganates. Reasons why the observed (\pi \pi 0) orbital ordering is favored over a (\pi \pi \pi) periodicity are discussed.Comment: 9 figures, submitted in Phys. Rev.

Parents, individualism and education: three paradigms and four countries

The UN Convention on the Rights of the Child (1989) is an important indicator of the increased global importance of education. It defines the goal of education at the level of the child rather than the state, the community or household. The requirement that each child be treated as an individual who can expect to see their 'personality, talents and mental and physical abilities' fully developed, is an example of the individualism which features in three important theoretical paradigms for understanding the rise of education and training. We compare accounts of the global growth of education produced by functionalism, neoinstitutionalism and political economy with the help of qualitative research on children's experience of parental influences. The research is drawn from semi-structured interviews with millennial graduates in Portugal, Singapore, the United Kingdom, and the United States. It reveals weaknesses in the paradigms which are related to the way each theorises individualism and the role it plays in parental influence on education. The functionalist and neoinstitutionalist conceptions of individualism limit the usefulness of these paradigms for understanding changes in the way families around the world prepare children for education. The political economy paradigm is more promising; however, an approach which identifies only one, neoliberal, version of individualism has limited purchase on international differences in parental influences and the way these influences are changing. An approach which can draw on the contrast between a cognitive individualism associated with neoliberalism, and sentimental individualism which originates in social movements, is more promising.info:eu-repo/semantics/publishedVersio

Grain boundary effects on magnetotransport in bi-epitaxial films of La0.7_{0.7}Sr0.3_{0.3}MnO3_3

The low field magnetotransport of La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO) films grown on SrTiO$_3$ substrates has been investigated. A high qualtity LSMO film exhibits anisotropic magnetoresistance (AMR) and a peak in the magnetoresistance close to the Curie temperature of LSMO. Bi-epitaxial films prepared using a seed layer of MgO and a buffer layer of CeO$_2$ display a resistance dominated by grain boundaries. One film was prepared with seed and buffer layers intact, while a second sample was prepared as a 2D square array of grain boundaries. These films exhibit i) a low temperature tail in the low field magnetoresistance; ii) a magnetoconductance with a constant high field slope; and iii) a comparably large AMR effect. A model based on a two-step tunneling process, including spin-flip tunneling, is discussed and shown to be consistent with the experimental findings of the bi-epitaxial films.Comment: REVTeX style; 14 pages, 9 figures. Figure 1 included in jpeg format (zdf1.jpg); the eps was huge. Accepted to Phys. Rev.

Inpatient COVID-19 mortality has reduced over time: Results from an observational cohort

BACKGROUND: The Covid-19 pandemic in the United Kingdom has seen two waves; the first starting in March 2020 and the second in late October 2020. It is not known whether outcomes for those admitted with severe Covid were different in the first and second waves. METHODS: The study population comprised all patients admitted to a 1,500-bed London Hospital Trust between March 2020 and March 2021, who tested positive for Covid-19 by PCR within 3-days of admissions. Primary outcome was death within 28-days of admission. Socio-demographics (age, sex, ethnicity), hypertension, diabetes, obesity, baseline physiological observations, CRP, neutrophil, chest x-ray abnormality, remdesivir and dexamethasone were incorporated as co-variates. Proportional subhazards models compared mortality risk between wave 1 and wave 2. Cox-proportional hazard model with propensity score adjustment were used to compare mortality in patients prescribed remdesivir and dexamethasone. RESULTS: There were 3,949 COVID-19 admissions, 3,195 hospital discharges and 733 deaths. There were notable differences in age, ethnicity, comorbidities, and admission disease severity between wave 1 and wave 2. Twenty-eight-day mortality was higher during wave 1 (26.1% versus 13.1%). Mortality risk adjusted for co-variates was significantly lower in wave 2 compared to wave 1 [adjSHR 0.49 (0.37, 0.65) p<0.001]. Analysis of treatment impact did not show statistically different effects of remdesivir [HR 0.84 (95%CI 0.65, 1.08), p = 0.17] or dexamethasone [HR 0.97 (95%CI 0.70, 1.35) p = 0.87]. CONCLUSION: There has been substantial improvements in COVID-19 mortality in the second wave, even accounting for demographics, comorbidity, and disease severity. Neither dexamethasone nor remdesivir appeared to be key explanatory factors, although there may be unmeasured confounding present

Ripple modulated electronic structure of a 3D topological insulator

3D topological insulators, similar to the Dirac material graphene, host linearly dispersing states with unique properties and a strong potential for applications. A key, missing element in realizing some of the more exotic states in topological insulators is the ability to manipulate local electronic properties. Analogy with graphene suggests a possible avenue via a topographic route by the formation of superlattice structures such as a moir\'e patterns or ripples, which can induce controlled potential variations. However, while the charge and lattice degrees of freedom are intimately coupled in graphene, it is not clear a priori how a physical buckling or ripples might influence the electronic structure of topological insulators. Here we use Fourier transform scanning tunneling spectroscopy to determine the effects of a one-dimensional periodic buckling on the electronic properties of Bi2Te3. By tracking the spatial variations of the scattering vector of the interference patterns as well as features associated with bulk density of states, we show that the buckling creates a periodic potential modulation, which in turn modulates the surface and the bulk states. The strong correlation between the topographic ripples and electronic structure indicates that while doping alone is insufficient to create predetermined potential landscapes, creating ripples provides a path to controlling the potential seen by the Dirac electrons on a local scale. Such rippled features may be engineered by strain in thin films and may find use in future applications of topological insulators.Comment: Nature Communications (accepted

Two-dimensional Dirac fermions in a topological insulator: transport in the quantum limit

Pulsed magnetic fields of up to 55T are used to investigate the transport properties of the topological insulator Bi_2Se_3 in the extreme quantum limit. For samples with a bulk carrier density of n = 2.9\times10^16cm^-3, the lowest Landau level of the bulk 3D Fermi surface is reached by a field of 4T. For fields well beyond this limit, Shubnikov-de Haas oscillations arising from quantization of the 2D surface state are observed, with the \nu =1 Landau level attained by a field of 35T. These measurements reveal the presence of additional oscillations which occur at fields corresponding to simple rational fractions of the integer Landau indices.Comment: 5 pages, 4 figure