Supersymmetry and Supercoherent States of a Nonrelativistic Free Particle

Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an element of this superalgebra which turns out to be a dynamical superalgebra for this system. The supercoherent states, defined by means of a supergroup displacement operator, are explicitly constructed. These are the coordinate representation of the known atypical abstract super group $OSp(2/2)$ coherent states. We interpret obtained results from the classical mechanics viewpoint as a model of classical particle which is immovable in the even sector of the phase superspace and is in rectilinear movement (in the appropriate coordinate system) in its odd sector

Improvement of maneuver aerodynamics by spanwise blowing

Spanwise blowing was used to test a generalized wind-tunnel model to investigate component concepts in order to provide improved maneuver characteristics for advanced fighter aircraft. Primary emphasis was placed on performance, stability, and control at high angles of attack and subsonic speeds. Test data were obtained in the Langley high speed 7 by 10 foot tunnel at free stream Mach numbers up to 0.50 for a range of model angles of attack, jet momentum coefficients, and leading and trailing edge flap deflection angles. Spanwise blowing on a 44 deg swept trapezoidal wing resulted in leading edge vortex enhancement with subsequent large vortex induced lift increments and drag polar improvements at the higher angles of attack. Small deflections of a leading edge flap delayed these lift and drag benefits to higher angles of attack. In addition, blowing was more effective at higher Mach numbers. Spanwise blowing in conjunction with a deflected trailing edge flap resulted in lift and drag benefits that exceeded the summation of the effects of each high lift device acting alone. Asymmetric blowing was an effective lateral control device at the higher angles of attack

Theoretical aerodynamics of upper-surface-blowing jet-wing interaction

A linear, inviscid subsonic compressible flow theory is formulated to treat the aerodynamic interaction between the wing and an inviscid upper-surface-blowing (USB) thick jet with Mach number nonuniformity. The predicted results show reasonably good agreement with some available lift and induced-drag data. It was also shown that the thin-jet-flap theory is inadequate for the USB configurations with thick jet. Additional theoretical results show that the lift and induced drag were reduced by increasing jet temperature and increased by increasing jet Mach number. Reducing jet aspect ratio, while holding jet area constant, caused reductions in lift, induced drag, and pitching moment at a given angle of attack but with a minimal change in the curve of lift coefficient against induced-drag coefficient. The jet-deflection effect was shown to be beneficial to cruise performance. The aerodynamic center was shifted forward by adding power or jet-deflection angle. Moving the jet away from the wing surface resulted in rapid changes in lift and induced drag. Reducing the wing span of a rectangular wing by half decreased the jet-circulation lift by only 24 percent at a thrust coefficient of 2

Theoretical predictions of jet interaction effects for USB and OWB configurations

A wing jet interaction theory is presented for predicting the aerodynamic characteristics of upper surface blowing and over wing blowing configurations. For the latter configurations, a new jet entrainment theory is developed. Comparison of predicted results with some available data showed good agreement. Some applications of the theory are also presented

Effects of spanwise blowing on the surface pressure distribution and vortex-lift characteristics of a trapezoidal wing-strake configuration

The effects of spanwise blowing on the surface pressures of a 44 deg swept trapezoidal wing-strake configuration were measured. Wind tunnel data were obtained at a free stream Mach number of 0.26 for a range of model angle of attack, jet thrust coefficient, and nozzle chordwise location. Results showed that spanwise blowing delayed the leading edge vortex breakdown to larger span distances and increased the lifting pressures. Vortex lift was achieved at span stations immediately outboard of the strake-wing junction with no blowing, but spanwise blowing was necessary to achieve vortex lift at increased span distances. Blowing on the wing in the presence of the strake was not as effective as blowing on the wing alone. Spanwise blowing increased lift throughout the angle-of-attack range, improved the drag polars, and extended the linear pitching moment to higher values of lift. The leading edge suction analogy can be used to estimate the effects of spanwise blowing on the aerodynamic characteristics

Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method

We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated spin-lattice models of interest in quantum magnetism, including their quantum phase transitions. The method itself is described, and it is shown how it may be implemented in practice to high orders in a systematically improvable hierarchy of (so-called LSUB$m$) approximations, by the use of computer-algebraic techniques. The method works from the outset in the thermodynamic limit of an infinite lattice at all levels of approximation, and it is shown both how the "raw" LSUB$m$ results are themselves generally excellent in the sense that they converge rapidly, and how they may accurately be extrapolated to the exact limit, $m \rightarrow \infty$, of the truncation index $m$, which denotes the {\it only} approximation made. All of this is illustrated via a specific application to a two-dimensional, frustrated, spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on a honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$, respectively, where both interactions are of the same anisotropic $XXZ$ type. We show how the method can be used to determine the entire zero-temperature ground-state phase diagram of the model in the range $0 \leq \kappa \leq 1$ of the frustration parameter and $0 \leq \Delta \leq 1$ of the spin-space anisotropy parameter. In particular, we identify a candidate quantum spin-liquid region in the phase space

Spin-1/2 J1J_{1}-J2J_{2} Heisenberg model on a cross-striped square lattice

Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half ($s=1/2$) $J_{1}$-$J_{2}$ Heisenberg model on a cross-striped square lattice. Each site of the square lattice has 4 nearest-neighbour exchange bonds of strength $J_{1}$ and 2 next-nearest-neighbour (diagonal) bonds of strength $J_{2}$. The $J_{2}$ bonds are arranged so that the basic square plaquettes in alternating columns have either both or no $J_{2}$ bonds included. The classical ($s \rightarrow \infty$) version of the model has 4 collinear phases when $J_{1}$ and $J_{2}$ can take either sign. Three phases are antiferromagnetic (AFM), showing so-called N\'{e}el, double N\'{e}el and double columnar striped order respectively, while the fourth is ferromagnetic. For the quantum $s=1/2$ model we use the 3 classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the $s=1/2$ model has 5 phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the 5 quantum critical points are determined with high accuracy. While all 4 phase transitions in the classical model are first order, we find strong evidence that 3 of the 5 quantum phase transitions in the $s=1/2$ model are of continuous deconfined type

A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice

The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half ($s={1}{2}$) $J_{1}$--$J_{2}$ Heisenberg antiferromagnet (HAF) on a 2D chevron-square lattice. Each site on an underlying square lattice has 4 nearest-neighbor exchange bonds of strength $J_{1}>0$ and 2 next-nearest-neighbor (diagonal) bonds of strength $J_{2} \equiv x J_{1}>0$, with each square plaquette having only one diagonal bond. The diagonal bonds form a chevron pattern, and the model thus interpolates smoothly between 2D HAFs on the square ($x=0$) and triangular ($x=1$) lattices, and also extrapolates to disconnected 1D HAF chains ($x \to \infty$). The classical ($s \to \infty$) version of the model has N\'{e}el order for $0 < x < x_{{\rm cl}}$ and a form of spiral order for $x_{{\rm cl}} < x < \infty$, where $x_{{\rm cl}} = {1}{2}$. For the $s={1}{2}$ model we use both these classical states, as well as other collinear states not realized as classical ground-state (GS) phases, as CCM reference states, on top of which the multispin-flip configurations resulting from quantum fluctuations are incorporated in a systematic truncation scheme, which we carry out to high orders and extrapolate to the physical limit. We calculate the GS energy, GS magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order, including plaquette and two different dimer forms. We find that the $s={1}{2}$ model has two quantum critical points, at $x_{c_{1}} \approx 0.72(1)$ and $x_{c_{2}} \approx 1.5(1)$, with N\'{e}el order for $0 < x < x_{c_{1}}$, a form of spiral order for $x_{c_{1}} < x < x_{c_{2}}$ that includes the correct three-sublattice $120^{\circ}$ spin ordering for the triangular-lattice HAF at $x=1$, and parallel-dimer VBC order for $x_{c_{2}} < x < \infty$

The utilization of neural nets in populating an object-oriented database

Existing NASA supported scientific data bases are usually developed, managed and populated in a tedious, error prone and self-limiting way in terms of what can be described in a relational Data Base Management System (DBMS). The next generation Earth remote sensing platforms (i.e., Earth Observation System, (EOS), will be capable of generating data at a rate of over 300 Mbs per second from a suite of instruments designed for different applications. What is needed is an innovative approach that creates object-oriented databases that segment, characterize, catalog and are manageable in a domain-specific context and whose contents are available interactively and in near-real-time to the user community. Described here is work in progress that utilizes an artificial neural net approach to characterize satellite imagery of undefined objects into high-level data objects. The characterized data is then dynamically allocated to an object-oriented data base where it can be reviewed and assessed by a user. The definition, development, and evolution of the overall data system model are steps in the creation of an application-driven knowledge-based scientific information system