Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology

Finite difference grid generation by multivariate blending function interpolation

The General Interpolants Method (GIM) code which solves the multidimensional Navier-Stokes equations for arbitrary geometric domains is described. The geometry module in the GIM code generates two and three dimensional grids over specified flow regimes, establishes boundary condition information and computes finite difference analogs for use in the GIM code numerical solution module. The technique can be classified as an algebraic equation approach. The geometry package uses multivariate blending function interpolation of vector-values functions which define the shapes of the edges and surfaces bounding the flow domain. By employing blending functions which conform to the cardinality conditions the flow domain may be mapped onto a unit square (2-D) or unit cube (3-D), thus producing an intrinsic coordinate system for the region of interest. The intrinsic coordinate system facilitates grid spacing control to allow for optimum distribution of nodes in the flow domain

Ground state projection of quantum spin systems in the valence bond basis

A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations of the method to fermion systems are also discussed.Comment: 4+ pages, accepted for publication in Phys. Rev. Let

Vacuum Polarisation and the Black Hole Singularity

In order to investigate the effects of vacuum polarisation on mass inflation singularities, we study a simple toy model of a charged black hole with cross flowing radial null dust which is homogeneous in the black hole interior. In the region $r^2 \ll e^2$ we find an approximate analytic solution to the classical field equations. The renormalized stress-energy tensor is evaluated on this background and we find the vacuum polarisation backreaction corrections to the mass function $m(r)$. Asymptotic analysis of the semiclassical mass function shows that the mass inflation singularity is much stronger in the presence of vacuum polarisation than in the classical case.Comment: 12 pages, RevTe

Spontaneous superconductivity and optical properties of high-Tc cuprates

We suggest that the high temperature superconductivity in cuprate compounds may emerge due to interaction between copper-oxygen layers mediated by in-plane plasmons. The strength of the interaction is determined by the c-axis geometry and by the ab-plane optical properties. Without making reference to any particular in-plane mechanism of superconductivity, we show that the interlayer interaction favors spontaneous appearance of the superconductivity in the layers. At a qualitative level the model describes correctly the dependence of the transition temperature on the interlayer distance, and on the number of adjacent layers in multilayered homologous compounds. Moreover, the model has a potential to explain (i) a mismatch between the optimal doping levels for critical temperature and superconducting density and (ii) a universal scaling relation between the dc-conductivity, the superfluid density, and the superconducting transition temperature.Comment: 4.4 pages, 2 figures; v2 matches the published version (clarifying remarks and references are added

c-axis transport and phenomenology of the pseudo-gap state in Bi2Sr2CaCu2O8+δBi_2Sr_2CaCu_2O_{8+\delta}

We measure and analyze the resistivity of $Bi_2Sr_2CaCu_2O_{8+\delta}$ crystals for different doping $\delta$. We obtain the fraction of carrier $\eta(T,\delta) = n_g/n_{TOT}$ that do not participate to the c-axis conductivity. All the curves $\eta(T,\delta)$ collapse onto a universal curve when plotted against a reduced temperature $x=[T-\Theta(\delta)]/\Delta^{*}(\delta)$. We find that at the superconducting transition $n_g$ is doping independent. We also show that a magnetic field up to 14 T does not affect the degree of localization in the (a,b) planes but widens the temperature range of the x-scaling by suppressing the superconducting phase coherence.Comment: 11 pages, 5 figures, submitted to Phys.Rev.

Experimental investigation of a swept-strut fuel-injector concept for scramjet application

Results are presented of an experiment to investigate the behavior at Mach 4 flight conditions of the swept-strut fuel-injector concept employed in the Langley integrated modular scramjet engine design. Autoignition of the hydrogen fuel was not achieved at stagnation temperatures corresponding to a flight Mach number of 4; however, once ignition was achieved, stable combustion was maintained. Pressure disturbances upstream of the injector location, which were caused by fuel injection and combustion, were generally not observed; this indicates the absence of serious adverse combustor-inlet interactions. Mixing performance and reaction performance determined from probe surveys and wall pressure data indicate that high combustion efficiency should be obtained with the combustor length provided in the scramjet engine design. No adverse interaction between the perpendicular and parallel fuel-injection modes was observed

Large-UU limit of a Hubbard model in a magnetic field: chiral spin interactions and paramagnetism

We consider the large-$U$ limit of the one-band Hubbard model at half-filling on a non-bipartite two-dimensional lattice. An external magnetic field can induce a three-spin chiral interaction at order $1 / U^2 ~$. We discuss situations in which, at low temperatures, the chiral term may have a larger effect than the Pauli coupling of electron spins to a magnetic field. We present a model which explicitly demonstrates this. The ground state is a singlet with a gap; hence the spin susceptibility is zero while the chiral susceptibility is finite and paramagnetic.Comment: 12 pages, plain TeX, one figure available on request, to appear in Phys. Rev.

What is moving in silica at 1 K? A computer study of the low-temperature anomalies

Though the existence of two-level systems (TLS) is widely accepted to explain low temperature anomalies in many physical observables, knowledge about their properties is very rare. For silica which is one of the prototype glass-forming systems we elucidate the properties of the TLS via computer simulations by applying a systematic search algorithm. We get specific information in the configuration space, i.e. about relevant energy scales, the absolute number of TLS and electric dipole moments. Furthermore important insight about the real-space realization of the TLS can be obtained. Comparison with experimental observations is included