A first-order time-domain Green's function approach to supersonic unsteady flow

A time-domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. The Green's function method is employed in order to convert the potential-flow differential equation into an integral one. This integral equation is then discretized, in space through standard finite-element technique, and in time through finite-difference, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. Consistent with the spatial linear (first-order) finite-element approximations, the potential and co-normalwash are assumed to vary linearly in time. The long range goal of our research is to develop a comprehensive theory for unsteady supersonic potential aerodynamics which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range

Universal manifold pairings and positivity

Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p= with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p onto a finite dimensional quotient pairing q with values in C which in physically motivated cases is positive definite. To see if such a "unitary" TQFT can potentially detect any nontrivial x, we ask if is non-zero whenever x is non-zero. If this is the case, we call the pairing p positive. The question arises for each dimension d=0,1,2,.... We find p(d) positive for d=0,1, and 2 and not positive for d=4. We conjecture that p(3) is also positive. Similar questions may be phrased for (manifold, submanifold) pairs and manifolds with other additional structure. The results in dimension 4 imply that unitary TQFTs cannot distinguish homotopy equivalent simply connected 4-manifolds, nor can they distinguish smoothly s-cobordant 4-manifolds. This may illuminate the difficulties that have been met by several authors in their attempts to formulate unitary TQFTs for d=3+1. There is a further physical implication of this paper. Whereas 3-dimensional Chern-Simons theory appears to be well-encoded within 2-dimensional quantum physics, eg in the fractional quantum Hall effect, Donaldson-Seiberg-Witten theory cannot be captured by a 3-dimensional quantum system. The positivity of the physical Hilbert spaces means they cannot see null vectors of the universal pairing; such vectors must map to zero.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper53.abs.htm

A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment

A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range

Atmospheric Sulfur Photochemistry on Hot Jupiters

We develop a new 1D photochemical kinetics code to address stratospheric chemistry and stratospheric heating in hot Jupiters. Here we address optically active S-containing species and CO2 at 1200 < T < 2000 K. HS (mercapto) and S2 are highly reactive species that are generated photochemically and thermochemically from H2S with peak abundances between 1-10 mbar. S2 absorbs UV between 240 and 340 nm and is optically thick for metallicities [SH] > 0 at T > 1200 K. HS is probably more important than S2, as it is generally more abundant than S2 under hot Jupiter conditions and it absorbs at somewhat redder wavelengths. We use molecular theory to compute an HS absorption spectrum from sparse available data and find that HS should absorb strongly between 300 and 460 nm, with absorption at the longer wavelengths being temperature sensitive. When the two absorbers are combined, radiative heating (per kg of gas) peaks at 100 microbars, with a total stratospheric heating of about 8 x 10^4 W/m^2 for a jovian planet orbiting a solar-twin at 0.032 AU. Total heating is insensitive to metallicity. The CO2 mixing ratio is a well-behaved quadratic function of metallicity, ranging from 1.6 x 10^-8 to 1.6 x 10^-4 for -0.3 < [M/H] < 1.7. CO2 is insensitive to insolation, vertical mixing, temperature (1200 < T <2000 K), and gravity. The photochemical calculations confirm that CO2 should prove a useful probe of planetary metallicity.Comment: Astrophysical Journal Lett. in press; important revision includes effect of updated thermodynamic data and a new opacity sourc

Ingestive behaviour and physiology of the medicinal leech

Ingestion lasts 25 min in Hirudo medicinalis and is characterized by pharyngeal peristalsis which fills the crop. This peristalsis has an initial rate of 2.4 Hz which decays smoothly to 1.2 Hz at termination of ingestion. During ingestion, the leech body wall undergoes peristalsis which appears to aid in filling the crop diverticula. Body peristalsis begins at a rate of 10 min^(-1) and decreases linearly to 2 min^(-1) at termination. The body also undergoes dorsoventral flexions when blood flow is occluded. Blood meal size increases slightly with leech size: 8.4 g for 1-g leeches and 9.7 g for 2-g leeches. However, relative meal size decreases markedly with increasing animal size; from 8.15 times body mass for 1-g to 4.80 times for 2-g leeches. When intact leeches were exposed to micromolar concentrations of serotonin, there was an increase in the rate of pharyngeal peristalsis and the size of the blood meals. Leeches excrete the plasma from their ingested blood meals. Excretion is activated during ingestion, which increases feeding efficiency by increasing the proportion of blood cells in the ingestate. Excretion continues for 4–6 days following ingestion, removing all the remaining plasma from the ingestate. Leech ingestion comprises stereotyped muscular movements, secretion of saliva and excretion of plasma. A strikingly similar feeding physiology is seen in the blood-sucking insect Rhodnius, and we suggest that efficient sanguivory may require the convergent evolution of similar ingestive mechanisms

Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.Comment: 19 pages, two figures, latex. v2: reference added, small corrections. v3: corrected unbounded spectrum erro

Three flavour Quark matter in chiral colour dielectric model

We investigate the properties of quark matter at finite density and temperature using the nonlinear chiral extension of Colour Dielectric Model (CCM). Assuming that the square of the meson fields devlop non- zero vacuum expectation value, the thermodynamic potential for interacting three flavour matter has been calculated. It is found that $$and$$ remain zero in the medium whereas $$ changes in the medium. As a result, $u$ and $d$ quark masses decrease monotonically as the temperature and density of the quark matter is increased.In the present model, the deconfinement density and temperature is found to be lower compared to lattice results. We also study the behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.

The Hidden Spatial Geometry of Non-Abelian Gauge Theories

The Gauss law constraint in the Hamiltonian form of the $SU(2)$ gauge theory of gluons is satisfied by any functional of the gauge invariant tensor variable $\phi^{ij} = B^{ia} B^{ja}$. Arguments are given that the tensor $G_{ij} = (\phi^{-1})_{ij}\,\det B$ is a more appropriate variable. When the Hamiltonian is expressed in terms of $\phi$ or $G$, the quantity $\Gamma^i_{jk}$ appears. The gauge field Bianchi and Ricci identities yield a set of partial differential equations for $\Gamma$ in terms of $G$. One can show that $\Gamma$ is a metric-compatible connection for $G$ with torsion, and that the curvature tensor of $\Gamma$ is that of an Einstein space. A curious 3-dimensional spatial geometry thus underlies the gauge-invariant configuration space of the theory, although the Hamiltonian is not invariant under spatial coordinate transformations. Spatial derivative terms in the energy density are singular when $\det G=\det B=0$. These singularities are the analogue of the centrifugal barrier of quantum mechanics, and physical wave-functionals are forced to vanish in a certain manner near $\det B=0$. It is argued that such barriers are an inevitable result of the projection on the gauge-invariant subspace of the Hilbert space, and that the barriers are a conspicuous way in which non-abelian gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223