Natural Rolling Responses of a Delta Wing in Transonic and Subsonic Flows

The unsteady, three-dimensional, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the natural rolling response of slender delta wings of zero thickness at moderate to high angles of attack, to transonic and subsonic flows. The governing equations of fluid flow and dynamics of the present multi-disciplinary problem are solved using the time-accurate solution of the NS equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The main focus is to analyze the effect of Mach number and angle of attack on the leading edge vortices and their breakdown, the resultant rolling motion, and overall aerodynamic response of the wing. Three cases demonstrate the natural response of a 65 deg swept, cropped delta wing in a transonic flow with breakdown of the leading edge vortices and an 80 deg swept delta wing in a subsonic flow undergoing either damped or self-excited limit-cycle rolling oscillations as a function of angle of attack. Comparisons with an experimental investigation completes this study, validating the analysis and illustrating the complex details afforded by computational investigations

Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews, Scotland, U

The geosystem services concept – What is it and can it support subsurface planning?

The subsurface is a multifunctional natural resource. However, a mindset of “out of sight, out of mind” and a first-come-first-served principle are prevalent when accessing these resources, compromising fair intergenerational and intragenerational distribution and sustainable development. As with the ecosystem services (ES) concept, which acknowledges the contribution of the living part of nature to human well-being, the concept of geosystem services (GS) has been suggested as a way to highlight abiotic services and services provided by the subsurface. The overall aim of this study was to review current definitions of GS and their categorisation, and to suggest how the concept of GS can support subsurface planning. A systematic literature review on GS was carried out following the PRISMA protocol drawing from the Scopus database. The emerging picture from the reviewed articles is that the GS concept is both one of novelty and one currently showing inconsistency, with two prominent definitions: A) GS are abiotic services that are the direct result of the planet\u27s geodiversity, independent of the interactions with biotic nature – there is no differentiation between suprasurface and subsurface features, and B) GS provide benefits specifically resulting from the subsurface. Thirty-one out of thirty-nine GS listed in the reviewed literature are included in the abiotic extension of the common ES framework CICES v5.1, but some essential services are omitted. A unified definition of GS is desirable to build a common framework for classifying and describing GS, potentially following the CICES structure for ES. Such a framework can support systematic inclusion of GS in planning processes and contribute to improved subsurface planning. In planning practice, there are examples of important GS that are already included under the ES umbrella because planners are aware of their importance but a comprehensive framework to handle these services is lacking

The Hydrogen Atom in Combined Electric and Magnetic Fields with Arbitrary Mutual Orientations

For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields. Resonance energies and oscillator strengths are obtained by exact diagonalization of the Hamiltonian in a complete basis set, even far above the ionization threshold. At high excitation energies around the Stark saddle point the eigenenergies exhibit strong level repulsions when the angle between the fields is varied. The large avoided crossings occur between states with the same approximately conserved principal quantum number, n, and this intramanifold mixing of states cannot be explained, not even qualitatively, by conventional perturbation theory. However, it is well reproduced by an extended perturbation theory which takes into account all couplings between the angular momentum and Runge-Lenz vector. The large avoided crossings are interpreted as a quantum manifestation of classical intramanifold chaos. This interpretation is supported by both classical Poincar\'e surfaces of section, which reveal a mixed regular-chaotic intramanifold dynamics, and the statistical analysis of nearest-neighbor-spacingComment: two-column version, 10 pages, REVTeX, 10 figures, uuencoded, submitted to Rhys. Rev.

Microwave study of quantum n-disk scattering

We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin 2-D microwave cavities. Two, three, and four-disk scattering are investigated in detail. The experiments, which are able to probe the stationary Green's function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, non-universal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include

Mutant torsinA in the heterozygous DYT1 state compromises HSV propagation in infected neurons and fibroblasts

Most cases of early onset torsion dystonia (DYT1) are caused by a 3-base pair deletion in one allele of the TOR1A gene causing loss of a glutamate in torsinA, a luminal protein in the nuclear envelope. This dominantly inherited neurologic disease has reduced penetrance and no other medical manifestations. It has been challenging to understand the neuronal abnormalities as cells and mouse models which are heterozygous (Het) for the mutant allele are quite similar to wild-type (WT) controls. Here we found that patient fibroblasts and mouse neurons Het for this mutation showed significant differences from WT cells in several parameters revealed by infection with herpes simplex virus type 1 (HSV) which replicates in the nucleus and egresses out through the nuclear envelope. Using a red fluorescent protein capsid to monitor HSV infection, patient fibroblasts showed decreased viral plaque formation as compared to controls. Mouse Het neurons had a decrease in cytoplasmic, but not nuclear HSV fluorescence, and reduced numbers of capsids entering axons as compared to infected WT neurons. These findings point to altered dynamics of the nuclear envelope in cells with the patient genotype, which can provide assays to screen for therapeutic agents that can normalize these cells

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package