Geometry of matrix product states: Metric, parallel transport, and curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haegeman, Jutho, E-mail: jutho.haegeman@gmail.com; Verstraete, Frank; Faculty of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, 9000 Gent

2014-02-15

We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold,more » which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.« less

Investigation of the spinfoam path integral with quantum cuboid intertwiners

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Steinhaus, Sebastian

2016-05-01

In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.

Geometry of the Gene Expression Space of Individual Cells

PubMed Central

Korem, Yael; Szekely, Pablo; Hart, Yuval; Sheftel, Hila; Hausser, Jean; Mayo, Avi; Rothenberg, Michael E.; Kalisky, Tomer; Alon, Uri

2015-01-01

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks. PMID:26161936

Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goto, Shin-itiro, E-mail: sgoto@ims.ac.jp

It has been proposed that equilibrium thermodynamics is described on Legendre submanifolds in contact geometry. It is shown in this paper that Legendre submanifolds embedded in a contact manifold can be expressed as attractors in phase space for a certain class of contact Hamiltonian vector fields. By giving a physical interpretation that points outside the Legendre submanifold can represent nonequilibrium states of thermodynamic variables, in addition to that points of a given Legendre submanifold can represent equilibrium states of the variables, this class of contact Hamiltonian vector fields is physically interpreted as a class of relaxation processes, in which thermodynamicmore » variables achieve an equilibrium state from a nonequilibrium state through a time evolution, a typical nonequilibrium phenomenon. Geometric properties of such vector fields on contact manifolds are characterized after introducing a metric tensor field on a contact manifold. It is also shown that a contact manifold and a strictly convex function induce a lower dimensional dually flat space used in information geometry where a geometrization of equilibrium statistical mechanics is constructed. Legendre duality on contact manifolds is explicitly stated throughout.« less

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

Motivated by uncertainty quantification and inference of quantum information systems, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural sample spaces and probability distributions upon these spaces that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation. This project was supported by the Intelligence Advanced Research Projects Activity via Department of Interior National Business Center Contract Number 2012-12050800010.

Solar-pumped solid state Nd lasers

NASA Technical Reports Server (NTRS)

Williams, M. D.; Zapata, L.

1985-01-01

Solid state neodymium lasers are considered candidates for space-based polar-pumped laser for continuous power transmission. Laser performance for three different slab laser configurations has been computed to show the excellent power capability of such systems if heat problems can be solved. Ideas involving geometries and materials are offered as potential solutions to the heat problem.

A new method for acoustic containerless processing of materials

NASA Technical Reports Server (NTRS)

Barmatz, M.

1984-01-01

The development of an acoustic positioner, which uses only one acoustic mode in chambers of rectangular, cylindrical, and spherical geometries, for high-temperature containerless processing of materials in space is described. The objective of the single-mode positioner is to develop sufficient acoustic forces to stably localize and manipulate molten materials. In order to attain this goal the transducer power, energy transfer medium, and chamber geometry and dimensions need to be optimized. The use of a variable frequency compression driver or solid-state piezoelectric transducer to optimize these properties is investigated; it is determined that a solid-state transducer would be most applicable for optimizing the positioner. The positioning capabilities of this single-mode positioner are discussed. The dependence of the acoustic forces on temperature and ambient pressure is studied. The development of a levitator to process a molten sample at 1500 C in the space environment using the cylindrical (011) mode is illustrated.

The Modeling and Control of Acoustic/Structure Interaction Problems via Piezoceramic Actuators: 2-D Numerical Examples

DTIC Science & Technology

1992-04-01

the voltage applied to the it" patch, K ’ is a parameter which depends on the geometry and piezoceramic...in the state space II L 2(fQ) x L2 (F0 ). Here L2(Q) is the quotient space of L2 over the constant functions. The use of the quotient space results...form of the problem, we also define the Hilbert space V = fti(Q) x H(F 0 ) where h!(Q) is the quotient space of Il’ over the constant functions

EBQ code: Transport of space-charge beams in axially symmetric devices

NASA Astrophysics Data System (ADS)

Paul, A. C.

1982-11-01

Such general-purpose space charge codes as EGUN, BATES, WODF, and TRANSPORT do not gracefully accommodate the simulation of relativistic space-charged beams propagating a long distance in axially symmetric devices where a high degree of cancellation has occurred between the self-magnetic and self-electric forces of the beam. The EBQ code was written specifically to follow high current beam particles where space charge is important in long distance flight in axially symmetric machines possessing external electric and magnetic field. EBQ simultaneously tracks all trajectories so as to allow procedures for charge deposition based on inter-ray separations. The orbits are treated in Cartesian geometry (position and momentum) with z as the independent variable. Poisson's equation is solved in cylindrical geometry on an orthogonal rectangular mesh. EBQ can also handle problems involving multiple ion species where the space charge from each must be included. Such problems arise in the design of ion sources where different charge and mass states are present.

Prediction of electronic structure of organic radicaloid anions using efficient, economical multireference gradient approach.

PubMed

Chattopadhyay, Sudip; Chaudhuri, Rajat K; Freed, Karl F

2011-04-28

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method enables an economical and reasonably accurate treatment of static correlation in systems with significant multireference character, even when using a moderate basis set. This IVO-CASCI method supplants the computationally more demanding complete active space self-consistent field (CASSCF) method by producing comparable accuracy with diminished computational effort because the IVO-CASCI approach does not require additional iterations beyond an initial SCF calculation, nor does it encounter convergence difficulties or multiple solutions that may be found in CASSCF calculations. Our IVO-CASCI analytical gradient approach is applied to compute the equilibrium geometry for the ground and lowest excited state(s) of the theoretically very challenging 2,6-pyridyne, 1,2,3-tridehydrobenzene and 1,3,5-tridehydrobenzene anionic systems for which experiments are lacking, accurate quantum calculations are almost completely absent, and commonly used calculations based on single reference configurations fail to provide reasonable results. Hence, the computational complexity provides an excellent test for the efficacy of multireference methods. The present work clearly illustrates that the IVO-CASCI analytical gradient method provides a good description of the complicated electronic quasi-degeneracies during the geometry optimization process for the radicaloid anions. The IVO-CASCI treatment produces almost identical geometries as the CASSCF calculations (performed for this study) at a fraction of the computational labor. Adiabatic energy gaps to low lying excited states likewise emerge from the IVO-CASCI and CASSCF methods as very similar. We also provide harmonic vibrational frequencies to demonstrate the stability of the computed geometries.

Connes distance function on fuzzy sphere and the connection between geometry and statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devi, Yendrembam Chaoba, E-mail: chaoba@bose.res.in; Chakraborty, Biswajit, E-mail: biswajit@bose.res.in; Prajapat, Shivraj, E-mail: shraprajapat@gmail.com

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which ismore » shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2.« less

Metric on the space of quantum states from relative entropy. Tomographic reconstruction

NASA Astrophysics Data System (ADS)

Man'ko, Vladimir I.; Marmo, Giuseppe; Ventriglia, Franco; Vitale, Patrizia

2017-08-01

In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N=2, N=3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher-Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.

Spontaneous ordering and vortex states of active fluids in circular confinement

NASA Astrophysics Data System (ADS)

Theillard, Maxime; Ezhilan, Barath; Saintillan, David

2015-11-01

Recent experimental, theoretical and simulation studies have shown that confinement can profoundly affect self-organization in active suspensions leading to striking features such as directed fluid pumping in planar confinement, formation of steady and spontaneous vortices in radial confinement. Motivated by this, we study the dynamics in a suspension of biologically active particles confined in spherical geometries using a mean-field kinetic theory for which we developed a novel numerical solver. In the case of circular confinement, we conduct a systematic exploration of the entire parameter space and distinguish 3 broad states: no-flow, stable vortex and chaotic and several interesting sub-states. Our efficient numerical framework is also employed to study 3D effects and dynamics in more complex geometries.

Duality constructions from quantum state manifolds

NASA Astrophysics Data System (ADS)

Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.

2015-11-01

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

Horizon as critical phenomenon

NASA Astrophysics Data System (ADS)

Lee, Sung-Sik

2016-09-01

We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U( N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

Stabilizing embedology: Geometry-preserving delay-coordinate maps

NASA Astrophysics Data System (ADS)

Eftekhari, Armin; Yap, Han Lun; Wakin, Michael B.; Rozell, Christopher J.

2018-02-01

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the tradeoff between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.

Stabilizing embedology: Geometry-preserving delay-coordinate maps.

PubMed

Eftekhari, Armin; Yap, Han Lun; Wakin, Michael B; Rozell, Christopher J

2018-02-01

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the tradeoff between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.

Handy elementary algebraic properties of the geometry of entanglement

NASA Astrophysics Data System (ADS)

Blair, Howard A.; Alsing, Paul M.

2013-05-01

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

Evaluating transition state structures of vanadium-phosphatase protein complexes using shape analysis.

PubMed

Sánchez-Lombardo, Irma; Alvarez, Santiago; McLauchlan, Craig C; Crans, Debbie C

2015-06-01

Shape analysis of coordination complexes is well-suited to evaluate the subtle distortions in the trigonal bipyramidal (TBPY-5) geometry of vanadium coordinated in the active site of phosphatases and characterized by X-ray crystallography. Recent studies using the tau (τ) analysis support the assertion that vanadium is best described as a trigonal bipyramid, because this geometry is the ideal transition state geometry of the phosphate ester substrate hydrolysis (C.C. McLauchlan, B.J. Peters, G.R. Willsky, D.C. Crans, Coord. Chem. Rev. http://dx.doi.org/10.1016/j.ccr.2014.12.012 ; D.C. Crans, M.L. Tarlton, C.C. McLauchlan, Eur. J. Inorg. Chem. 2014, 4450-4468). Here we use continuous shape measures (CShM) analysis to investigate the structural space of the five-coordinate vanadium-phosphatase complexes associated with mechanistic transformations between the tetrahedral geometry and the five-coordinate high energy TBPY-5 geometry was discussed focusing on the protein tyrosine phosphatase 1B (PTP1B) enzyme. No evidence for square pyramidal geometries was observed in any vanadium-protein complexes. The shape analysis positioned the metal ion and the ligands in the active site reflecting the mechanism of the cleavage of the organic phosphate in a phosphatase. We identified the umbrella distortions to be directly on the reaction path between tetrahedral phosphate and the TBPY-5-types of high-energy species. The umbrella distortions of the trigonal bipyramid are therefore identified as being the most relevant types of transition state structures for the phosphoryl group transfer reactions for phosphatases and this may be related to the possibility that vanadium is an inhibitor for enzymes that support both exploded and five-coordinate transition states. Copyright © 2015 Elsevier Inc. All rights reserved.

Theoretical study of electronic structures and spectroscopic properties of Ga3Sn, GaSn3, and their ions.

PubMed

Zhu, Xiaolei

2007-01-01

Ground and excited states of mixed gallium stannide tetramers (Ga3Sn, Ga3Sn+, Ga3Sn-, GaSn3, GaSn3+, and GaSn3-) are investigated employing the complete active space self-consistent-field (CASSCF), density function theory (DFT), and the coupled-cluster single and double substitution (including triple excitations) (CCSD(T)) methods. The ground states of Ga3Sn, Ga3Sn+, and Ga3Sn- are found to be the 2A1, 3B1, and 1A1 states in C2v symmetry with a planar quadrilateral geometry, respectively. The ground states of GaSn3 and GaSn3- is predicted to be the 2A1 and 1A1 states in C2v point group with a planar quadrilateral structure, respectively, while the ground state of GaSn3+ is the 1A1 state with ideal triangular pyramid C3v geometry. Equilibrium geometries, vibrational frequencies, binding energies, electron affinities, ionization energies, and other properties of Ga3Sn and GaSn3 are computed and discussed. The anion photoelectron spectra of Ga3Sn- and GaSn3- are also predicted. It is interesting to find that the amount of charge transfer between Ga and Sn2 atoms in the 1A1 state of GaSn3+ greatly increases upon electron ionization from the 2A1 state of GaSn3, which may be caused by large geometry change. On the other hand, the results of the low-lying states of Ga3Sn and GaSn3 are compared with those of Ga3Si and GaSi3.

Theoretical study of electronic structures and spectroscopic properties of Ga 3Sn, GaSn 3, and their ions

NASA Astrophysics Data System (ADS)

Zhu, Xiaolei

2007-01-01

Ground and excited states of mixed gallium stannide tetramers (Ga 3Sn, Ga 3Sn +, Ga 3Sn -, GaSn 3, GaSn 3+, and GaSn 3-) are investigated employing the complete active space self-consistent-field (CASSCF), density function theory (DFT), and the coupled-cluster single and double substitution (including triple excitations) (CCSD(T)) methods. The ground states of Ga 3Sn, Ga 3Sn +, and Ga 3Sn - are found to be the 2A 1, 3B 1, and 1A 1 states in C2v symmetry with a planar quadrilateral geometry, respectively. The ground states of GaSn 3 and GaSn 3- is predicted to be the 2A 1 and 1A 1 states in C2v point group with a planar quadrilateral structure, respectively, while the ground state of GaSn 3+ is the 1A 1 state with ideal triangular pyramid C3v geometry. Equilibrium geometries, vibrational frequencies, binding energies, electron affinities, ionization energies, and other properties of Ga 3Sn and GaSn 3 are computed and discussed. The anion photoelectron spectra of Ga 3Sn - and GaSn 3- are also predicted. It is interesting to find that the amount of charge transfer between Ga and Sn 2 atoms in the 1A 1 state of GaSn 3+ greatly increases upon electron ionization from the 2A 1 state of GaSn 3, which may be caused by large geometry change. On the other hand, the results of the low-lying states of Ga 3Sn and GaSn 3 are compared with those of Ga 3Si and GaSi 3.

Lorenz, Gödel and Penrose: new perspectives on determinism and causality in fundamental physics

NASA Astrophysics Data System (ADS)

Palmer, T. N.

2014-07-01

Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of Lorenz's fractal invariant set relate space-time calculus to deep areas of mathematics such as Gödel's Incompleteness Theorem. Could such properties also provide new perspectives on deep unsolved issues in fundamental physics? Recent developments in cosmology motivate what is referred to as the 'cosmological invariant set postulate': that the universe ? can be considered a deterministic dynamical system evolving on a causal measure-zero fractal invariant set ? in its state space. Symbolic representations of ? are constructed explicitly based on permutation representations of quaternions. The resulting 'invariant set theory' provides some new perspectives on determinism and causality in fundamental physics. For example, while the cosmological invariant set appears to have a rich enough structure to allow a description of (quantum) probability, its measure-zero character ensures it is sparse enough to prevent invariant set theory being constrained by the Bell inequality (consistent with a partial violation of the so-called measurement independence postulate). The primacy of geometry as embodied in the proposed theory extends the principles underpinning general relativity. As a result, the physical basis for contemporary programmes which apply standard field quantisation to some putative gravitational lagrangian is questioned. Consistent with Penrose's suggestion of a deterministic but non-computable theory of fundamental physics, an alternative 'gravitational theory of the quantum' is proposed based on the geometry of ?, with new perspectives on the problem of black-hole information loss and potential observational consequences for the dark universe.

A Vector Approach to Euclidean Geometry: Inner Product Spaces, Euclidean Geometry and Trigonometry, Volume 2. Teacher's Edition.

ERIC Educational Resources Information Center

Vaughan, Herbert E.; Szabo, Steven

This is the teacher's edition of a text for the second year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…

Boundary kinematic space

DOE PAGES

Karch, Andreas; Sully, James; Uhlemann, Christoph F.; ...

2017-08-10

We extend kinematic space to a simple scenario where the state is not fixed by conformal invariance: the vacuum of a conformal field theory with a boundary (bCFT). We identify the kinematic space associated with the boundary operator product expansion (bOPE) as a subspace of the full kinematic space. In addition, we establish representations of the corresponding bOPE blocks in a dual gravitational description. We show how the new kinematic dictionary and the dynamical data in bOPE allows one to reconstruct the bulk geometry. This is evidence that kinematic space may be a useful construction for understanding bulk physics beyondmore » just kinematics.« less

Boundary kinematic space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karch, Andreas; Sully, James; Uhlemann, Christoph F.

We extend kinematic space to a simple scenario where the state is not fixed by conformal invariance: the vacuum of a conformal field theory with a boundary (bCFT). We identify the kinematic space associated with the boundary operator product expansion (bOPE) as a subspace of the full kinematic space. In addition, we establish representations of the corresponding bOPE blocks in a dual gravitational description. We show how the new kinematic dictionary and the dynamical data in bOPE allows one to reconstruct the bulk geometry. This is evidence that kinematic space may be a useful construction for understanding bulk physics beyondmore » just kinematics.« less

Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

NASA Astrophysics Data System (ADS)

Qin, Tao; Hofstetter, Walter

2017-08-01

We present a systematic study of the spectral functions of a time-periodically driven Falicov-Kimball Hamiltonian. In the high-frequency limit, this system can be effectively described as a Harper-Hofstadter-Falicov-Kimball model. Using real-space Floquet dynamical mean-field theory (DMFT), we take into account the interaction effects and contributions from higher Floquet bands in a nonperturbative way. Our calculations show a high degree of similarity between the interacting driven system and its effective static counterpart with respect to spectral properties. However, as also illustrated by our results, one should bear in mind that Floquet DMFT describes a nonequilibrium steady state, while an effective static Hamiltonian describes an equilibrium state. We further demonstrate the possibility of using real-space Floquet DMFT to study edge states on a cylinder geometry.

Role of interface states on electron transport in a-Si:H/nc-Si:H multilayer structures

NASA Astrophysics Data System (ADS)

Yadav, Asha; Kumari, Juhi; Agarwal, Pratima

2018-05-01

In this paper we report, I-V characteristic of a-Si:H/nc-Si:H multilayer structures in lateral as well as transverse direction. In lateral geometry, where the interfaces are parallel to the direction of electronic transport, residual photo conductivity (persistent photoconductivity) is observed after the light was turned off. On the other hand, in transverse geometry, where interfaces are along the direction of electronic transport, the space charge limited currents are affected and higher density of states is obtained. The PPC was more in the structures where numbers of such interface were more. These results have been understood in terms of the charge carriers trapped at the interface, which influence the electronic transport.

The protonation of N2O reexamined - A case study on the reliability of various electron correlation methods for minima and transition states

NASA Technical Reports Server (NTRS)

Martin, J. M. L.; Lee, Timothy J.

1993-01-01

The protonation of N2O and the intramolecular proton transfer in N2OH(+) are studied using various basis sets and a variety of methods, including second-order many-body perturbation theory (MP2), singles and doubles coupled cluster (CCSD), the augmented coupled cluster (CCSD/T/), and complete active space self-consistent field (CASSCF) methods. For geometries, MP2 leads to serious errors even for HNNO(+); for the transition state, only CCSD/T/ produces a reliable geometry due to serious nondynamical correlation effects. The proton affinity at 298.15 K is estimated at 137.6 kcal/mol, in close agreement with recent experimental determinations of 137.3 +/- 1 kcal/mol.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bianchi, Eugenio; Speziale, Simone; Dona, Pietro

Intertwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in R{sup 3}: A polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: We give formulas for the edge lengths, the volume, and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner withmore » the state of a quantum polyhedron, thus generalizing the notion of the quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spin foams with nonsimplicial graphs.« less

Fuel Injector Design Optimization for an Annular Scramjet Geometry

NASA Technical Reports Server (NTRS)

Steffen, Christopher J., Jr.

2003-01-01

A four-parameter, three-level, central composite experiment design has been used to optimize the configuration of an annular scramjet injector geometry using computational fluid dynamics. The computational fluid dynamic solutions played the role of computer experiments, and response surface methodology was used to capture the simulation results for mixing efficiency and total pressure recovery within the scramjet flowpath. An optimization procedure, based upon the response surface results of mixing efficiency, was used to compare the optimal design configuration against the target efficiency value of 92.5%. The results of three different optimization procedures are presented and all point to the need to look outside the current design space for different injector geometries that can meet or exceed the stated mixing efficiency target.

Evaluation of SIR-A space radar for geologic interpretation: United States, Panama, Colombia, and New Guinea

NASA Technical Reports Server (NTRS)

Macdonald, H.; Waite, W. P.; Kaupp, V. H.; Bridges, L. C.; Storm, M.

1983-01-01

Comparisons between LANDSAT MSS imagery, and aircraft and space radar imagery from different geologic environments in the United States, Panama, Colombia, and New Guinea demonstrate the interdependence of radar system geometry and terrain configuration for optimum retrieval of geologic information. Illustrations suggest that in the case of space radars (SIR-A in particular), the ability to acquire multiple look-angle/look-direction radar images of a given area is more valuable for landform mapping than further improvements in spatial resolution. Radar look-angle is concluded to be one of the most important system parameters of a space radar designed to be used for geologic reconnaissance mapping. The optimum set of system parameters must be determined for imaging different classes of landform features and tailoring the look-angle to local topography.

A scalable and accurate method for classifying protein-ligand binding geometries using a MapReduce approach.

PubMed

Estrada, T; Zhang, B; Cicotti, P; Armen, R S; Taufer, M

2012-07-01

We present a scalable and accurate method for classifying protein-ligand binding geometries in molecular docking. Our method is a three-step process: the first step encodes the geometry of a three-dimensional (3D) ligand conformation into a single 3D point in the space; the second step builds an octree by assigning an octant identifier to every single point in the space under consideration; and the third step performs an octree-based clustering on the reduced conformation space and identifies the most dense octant. We adapt our method for MapReduce and implement it in Hadoop. The load-balancing, fault-tolerance, and scalability in MapReduce allow screening of very large conformation spaces not approachable with traditional clustering methods. We analyze results for docking trials for 23 protein-ligand complexes for HIV protease, 21 protein-ligand complexes for Trypsin, and 12 protein-ligand complexes for P38alpha kinase. We also analyze cross docking trials for 24 ligands, each docking into 24 protein conformations of the HIV protease, and receptor ensemble docking trials for 24 ligands, each docking in a pool of HIV protease receptors. Our method demonstrates significant improvement over energy-only scoring for the accurate identification of native ligand geometries in all these docking assessments. The advantages of our clustering approach make it attractive for complex applications in real-world drug design efforts. We demonstrate that our method is particularly useful for clustering docking results using a minimal ensemble of representative protein conformational states (receptor ensemble docking), which is now a common strategy to address protein flexibility in molecular docking. Copyright © 2012 Elsevier Ltd. All rights reserved.

Quantum fluctuating geometries and the information paradox

NASA Astrophysics Data System (ADS)

Eyheralde, Rodrigo; Campiglia, Miguel; Gambini, Rodolfo; Pullin, Jorge

2017-12-01

We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking’s original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering a back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell. More work will be needed to determine whether all the information can be recovered. The calculations show that non-trivial quantum effects can occur in regions of low curvature when horizons are involved, as is proposed in the firewall scenario, for instance.

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

DOE PAGES

Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; ...

2015-06-11

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as dualsmore » of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.« less

Influence of matter geometry on shocked flows-I: Accretion in the Schwarzschild metric

NASA Astrophysics Data System (ADS)

Tarafdar, Pratik; Das, Tapas K.

2018-07-01

This work presents a comprehensive and extensive study to illustrate how the geometrical configurations of low angular momentum axially symmetric general relativistic matter flow in the Schwarzschild metric may influence the formation of energy-preserving shocks for adiabatic/polytropic accretion as well as of temperature-preserving dissipative shocks for the isothermal accretion onto non-rotating astrophysical black holes. The dynamical and thermodynamic states of post-shock polytropic and isothermal flow have been studied extensively for three possible matter geometries, and it has been thoroughly discussed about how such states depend on the flow structure, even when the self gravity and the back reaction on the metric are not taken into account. Main purpose of this paper is thus to mathematically demonstrate that for non-self gravitating accretion, various matter geometries, in addition to the corresponding space-time geometry, control the shock induced phenomena as observed within the black hole accretion discs. This work is expected to reveal how the shock generated phenomena (emergence of the outflows/flare in the associated light curves) observed at the close proximity of the horizon depend on the physical environment of the source harbouring a supermassive black hole.

Hyperbolic geometry of Kuramoto oscillator networks

NASA Astrophysics Data System (ADS)

Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato

2017-09-01

Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space T N (the N-fold torus). This result has been used to explain the existence of the N-3 constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this Möbius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk \

3D glasma initial state for relativistic heavy ion collisions

DOE PAGES

Schenke, Björn; Schlichting, Sören

2016-10-13

We extend the impact-parameter-dependent Glasma model to three dimensions using explicit small-x evolution of the two incoming nuclear gluon distributions. We compute rapidity distributions of produced gluons and the early-time energy momentum tensor as a function of space-time rapidity and transverse coordinates. Finally, we study rapidity correlations and fluctuations of the initial geometry and multiplicity distributions and make comparisons to existing models for the three-dimensional initial state.

Comparison of Space Radiation Calculations from Deterministic and Monte Carlo Transport Codes

NASA Technical Reports Server (NTRS)

Adams, J. H.; Lin, Z. W.; Nasser, A. F.; Randeniya, S.; Tripathi, r. K.; Watts, J. W.; Yepes, P.

2010-01-01

The presentation outline includes motivation, radiation transport codes being considered, space radiation cases being considered, results for slab geometry, results from spherical geometry, and summary. ///////// main physics in radiation transport codes hzetrn uprop fluka geant4, slab geometry, spe, gcr,

Probing quantum state space: does one have to learn everything to learn something?

PubMed

Carmeli, Claudio; Heinosaari, Teiko; Schultz, Jussi; Toigo, Alessandro

2017-05-01

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.

Probing quantum state space: does one have to learn everything to learn something?

PubMed Central

Carmeli, Claudio; Schultz, Jussi; Toigo, Alessandro

2017-01-01

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task. PMID:28588404

Controls on the spacing and geometry of rill networks on hillslopes: Rainsplash detachment, initial hillslope roughness, and the competition between fluvial and colluvial transport

USDA-ARS?s Scientific Manuscript database

Rill networks have been a focus of study for many decades but we still lack a complete understanding of what variables control the spacing of rills and the geometry of rill networks (e.g. parallel or dendritic) on hillslopes. In this paper we investigate the controls on the spacing and geometry of ...

Ab initio coupled-cluster and multi-reference configuration interaction studies of the low-lying electronic states of 1,2,3,4-cyclobutanetetraone

DOE PAGES

Hansen, Jared A.; Bauman, Nicholas P.; Shen, Jun; ...

2015-12-09

In this paper, the four, closely spaced, lowest energy electronic states of the challenging, D 4h-symmetric, 1,2,3,4-cyclobutanetetraone (C 4O 4) molecule have been investigated using high-level ab initio methods. The calculated states include the closed-shell singlet 8π( 1A 1g) state, the singlet 10π( 1A 1g) state, in which the π-type lowest unoccupied molecular orbital (LUMO) of the 8π( 1A 1g) reference is doubly occupied and the σ-type highest occupied molecular orbital (HOMO) is empty, and the open-shell singlet and triplet states, designated as 9π( 1B 2u) and 9π( 3B 2u), respectively, originating from single occupancy of the HOMO and LUMO.more » Our focus is on single-reference coupled-cluster (CC) approaches capable of handling electronic near-degeneracies in diradicals, especially the completely renormalised CR-CC(2,3) and active-space CCSDt methods, along with their CCSD and EOMCCSD counterparts. The internally contracted multi-reference configuration interaction calculations with a quasi-degenerate Davidson correction are performed as well. Our computations demonstrate that the state ordering is 9π( 3B 2u) < 8π( 1A 1g) < 9π( 1B 2u) < 10π( 1A 1g) and that the 8π( 1A 1g) - 9π( 3B 2u) gap is in the 7–11 kJ/mol range, in reasonable agreement with the negative ion photoelectron spectroscopy measurements, which give 6.27 ± 0.5 kJ/mol. Finally, in addition to the theory level used, geometry relaxation and basis set play a significant role in determining the state ordering and energy spacings. In particular, it is unsafe to use lower level, non-CC geometries and smaller basis sets.« less

Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)

NASA Astrophysics Data System (ADS)

Berland, K.; Einstein, T. L.; Hyldgaard, P.

2012-01-01

The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wave functions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.

Theoretical study of actinide monocarbides (ThC, UC, PuC, and AmC)

NASA Astrophysics Data System (ADS)

Pogány, Peter; Kovács, Attila; Visscher, Lucas; Konings, Rudy J. M.

2016-12-01

A study of four representative actinide monocarbides, ThC, UC, PuC, and AmC, has been performed with relativistic quantum chemical calculations. The two applied methods were multireference complete active space second-order perturbation theory (CASPT2) including the Douglas-Kroll-Hess Hamiltonian with all-electron basis sets and density functional theory with the B3LYP exchange-correlation functional in conjunction with relativistic pseudopotentials. Beside the ground electronic states, the excited states up to 17 000 cm-1 have been determined. The molecular properties explored included the ground-state geometries, bonding properties, and the electronic absorption spectra. According to the occupation of the bonding orbitals, the calculated electronic states were classified into three groups, each leading to a characteristic bond distance range for the equilibrium geometry. The ground states of ThC, UC, and PuC have two doubly occupied π orbitals resulting in short bond distances between 1.8 and 2.0 Å, whereas the ground state of AmC has significant occupation of the antibonding orbitals, causing a bond distance of 2.15 Å.

Stability of Granular Packings Jammed under Gravity: Avalanches and Unjamming

NASA Astrophysics Data System (ADS)

Merrigan, Carl; Birwa, Sumit; Tewari, Shubha; Chakraborty, Bulbul

Granular avalanches indicate the sudden destabilization of a jammed state due to a perturbation. We propose that the perturbation needed depends on the entire force network of the jammed configuration. Some networks are stable, while others are fragile, leading to the unpredictability of avalanches. To test this claim, we simulated an ensemble of jammed states in a hopper using LAMMPS. These simulations were motivated by experiments with vibrated hoppers where the unjamming times followed power-law distributions. We compare the force networks for these simulated states with respect to their overall stability. The states are classified by how long they remain stable when subject to continuous vibrations. We characterize the force networks through both their real space geometry and representations in the associated force-tile space, extending this tool to jammed states with body forces. Supported by NSF Grant DMR1409093 and DGE1068620.

Geometric descriptions of entangled states by auxiliary varieties

NASA Astrophysics Data System (ADS)

Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-01

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n + 1), for n ⩾ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.

Euclidean sections of protein conformation space and their implications in dimensionality reduction

PubMed Central

Duan, Mojie; Li, Minghai; Han, Li; Huo, Shuanghong

2014-01-01

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality–reduction methods using the pairwise root–mean–square deviation as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality–reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N-dimensional Euclidean space R3N. We formally define the protein conformation space as the quotient space of R3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise root–mean–square deviation is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean-based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra-peptide and β–hairpin systems. PMID:24913095

Potential energy surfaces of the ground and low-lying states of HCCS and NCS: CASSCF, MRCI and CCSD(T) studies

NASA Astrophysics Data System (ADS)

Li, Yumin; Iwata, Suehiro

1997-07-01

For astronomically interesting molecules, HCCS and NCS, the equilibrium geometries and potential energy curves of three states (X 2Π, A 2Π and B 2Σ+) as well as vertical excitation energies are studied using complete active space SCF (CASSCF), multi-reference configuration interaction (MRCI) and coupled cluster (CCSD(T)) methods with cc-pVTZ basis sets. The difference and similarity in the three states of HCCS and NCS are illustrated. The results obtained are in good agreement with available experimental data.

Synthetic Landau Levels and Spinor Vortex Matter on a Haldane Spherical Surface with a Magnetic Monopole.

PubMed

Zhou, Xiang-Fa; Wu, Congjun; Guo, Guang-Can; Wang, Ruquan; Pu, Han; Zhou, Zheng-Wei

2018-03-30

We present a flexible scheme to realize exact flat Landau levels on curved spherical geometry in a system of spinful cold atoms. This is achieved by applying the Floquet engineering of a magnetic quadrupole field to create a synthetic monopole field in real space. The system can be exactly mapped to the electron-monopole system on a sphere, thus realizing Haldane's spherical geometry for fractional quantum Hall physics. This method works for either bosons or fermions. We investigate the ground-state vortex pattern for an s-wave interacting atomic condensate by mapping this system to the classical Thompson's problem. The distortion and stability of the vortex pattern are further studied in the presence of dipolar interaction. Our scheme is compatible with the current experimental setup, and may serve as a promising route of investigating quantum Hall physics and exotic spinor vortex matter on curved space.

Synthetic Landau Levels and Spinor Vortex Matter on a Haldane Spherical Surface with a Magnetic Monopole

NASA Astrophysics Data System (ADS)

Zhou, Xiang-Fa; Wu, Congjun; Guo, Guang-Can; Wang, Ruquan; Pu, Han; Zhou, Zheng-Wei

2018-03-01

We present a flexible scheme to realize exact flat Landau levels on curved spherical geometry in a system of spinful cold atoms. This is achieved by applying the Floquet engineering of a magnetic quadrupole field to create a synthetic monopole field in real space. The system can be exactly mapped to the electron-monopole system on a sphere, thus realizing Haldane's spherical geometry for fractional quantum Hall physics. This method works for either bosons or fermions. We investigate the ground-state vortex pattern for an s -wave interacting atomic condensate by mapping this system to the classical Thompson's problem. The distortion and stability of the vortex pattern are further studied in the presence of dipolar interaction. Our scheme is compatible with the current experimental setup, and may serve as a promising route of investigating quantum Hall physics and exotic spinor vortex matter on curved space.

A defect in holographic interpretations of tensor networks

NASA Astrophysics Data System (ADS)

Czech, Bartlomiej; Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan

2017-03-01

We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.

Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry

NASA Astrophysics Data System (ADS)

Bredthauer, Andreas

2007-01-01

In this thesis, two aspects of string theory are discussed, tensionless strings and supersymmetric sigma models. The equivalent to a massless particle in string theory is a tensionless string. Even almost 30 years after it was first mentioned, it is still quite poorly understood. We discuss how tensionless strings give rise to exact solutions to supergravity and solve closed tensionless string theory in the ten dimensional maximally supersymmetric plane wave background, a contraction of AdS(5)xS(5) where tensionless strings are of great interest due to their proposed relation to higher spin gauge theory via the AdS/CFT correspondence. For a sigma model, the amount of supersymmetry on its worldsheet restricts the geometry of the target space. For N=(2,2) supersymmetry, for example, the target space has to be bi-hermitian. Recently, with generalized complex geometry, a new mathematical framework was developed that is especially suited to discuss the target space geometry of sigma models in a Hamiltonian formulation. Bi-hermitian geometry is so-called generalized Kaehler geometry but the relation is involved. We discuss various amounts of supersymmetry in phase space and show that this relation can be established by considering the equivalence between the Hamilton and Lagrange formulation of the sigma model. In the study of generalized supersymmetric sigma models, we find objects that favor a geometrical interpretation beyond generalized complex geometry.

Entanglement entropy and correlations in loop quantum gravity

NASA Astrophysics Data System (ADS)

Feller, Alexandre; Livine, Etera R.

2018-02-01

Black hole entropy is one of the few windows into the quantum aspects of gravitation, and its study over the years has highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into an analysis of the correlations between the regions of the spin network states defining the quantum state of the geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physics, satisfying an area law for entanglement entropy and having non-trivial correlations. We highlight that entanglement comes from holonomy operators acting on loops crossing the boundary of the region.

Veronese geometry and the electroweak vacuum moduli space

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Jejjala, Vishnu; Matti, Cyril; Nelson, Brent D.

2014-09-01

We explain the origin of the Veronese surface in the vacuum moduli space geometry of the MSSM electroweak sector. While this result appeared many years ago using techniques of computational algebraic geometry, it has never been demonstrated analytically. Here, we present an analytical derivation of the vacuum geometry of the electroweak theory by understanding how the F- and D-term relations lead to the Veronese surface. We moreover give a detailed description of this geometry, realising an extra branch as a zero-dimensional point when quadratic Higgs lifting deformations are incorporated into the superpotential.

Response of the Shockley surface state on Cu(111) to an external electrical field: A density-functional theory study

NASA Astrophysics Data System (ADS)

Berland, Kristian; Hyldgaard, Per; Einstein, T. L.

2011-03-01

We study the response of the Cu(111) Shockley surface state to an external electrical field E by combining a density-functional theory calculation for a finite slab geometry with an analysis of the Kohn-Sham wavefunctions to obtain a well-converged characterization. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We find that the shift in band minimum and effective mass depend linearly on E. Most change in electrostatic potential profile, and charge transfer occurs outside the outermost copper atoms, and most of the screening is due to bulk electrons. Our analysis is facilitated by a method used to decouple the Kohn-Sham states due to the finite slab geometry, using a rotation in Hilbert space. We discuss applications to tuning the Fermi wavelength and so the many patterns attributed to metallic surface states. Supported by (KB and PH) Swedish Vetenskapsrådet VR 621-2008-4346 and (TLE) NSF CHE 07-50334 & UMD MRSEC DMR 05-20471.

The physics of solid-state neutron detector materials and geometries.

PubMed

Caruso, A N

2010-11-10

Detection of neutrons, at high total efficiency, with greater resolution in kinetic energy, time and/or real-space position, is fundamental to the advance of subfields within nuclear medicine, high-energy physics, non-proliferation of special nuclear materials, astrophysics, structural biology and chemistry, magnetism and nuclear energy. Clever indirect-conversion geometries, interaction/transport calculations and modern processing methods for silicon and gallium arsenide allow for the realization of moderate- to high-efficiency neutron detectors as a result of low defect concentrations, tuned reaction product ranges, enhanced effective omnidirectional cross sections and reduced electron-hole pair recombination from more physically abrupt and electronically engineered interfaces. Conversely, semiconductors with high neutron cross sections and unique transduction mechanisms capable of achieving very high total efficiency are gaining greater recognition despite the relative immaturity of their growth, lithographic processing and electronic structure understanding. This review focuses on advances and challenges in charged-particle-based device geometries, materials and associated mechanisms for direct and indirect transduction of thermal to fast neutrons within the context of application. Calorimetry- and radioluminescence-based intermediate processes in the solid state are not included.

Path Toward a Unified Geometry for Radiation Transport

NASA Astrophysics Data System (ADS)

Lee, Kerry

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex CAD models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN (high charge and energy transport code developed by NASA LaRC), are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading to the creation and maintenance of toolkit specific simplistic geometry models. The work presented here builds on the Direct Accelerated Geometry Monte Carlo (DAGMC) toolkit developed for use with the Monte Carlo N-Particle (MCNP) transport code. The work-flow for doing radiation transport on CAD models using MCNP and FLUKA has been demonstrated and the results of analyses on realistic spacecraft/habitats will be presented. Future work is planned that will further automate this process and enable the use of multiple radiation transport codes on identical geometry models imported from CAD. This effort will enhance the modeling tools used by NASA to accurately evaluate the astronaut space radiation risk and accurately determine the protection provided by as-designed exploration mission vehicles and habitats.

Methods of space radiation dose analysis with applications to manned space systems

NASA Technical Reports Server (NTRS)

Langley, R. W.; Billings, M. P.

1972-01-01

The full potential of state-of-the-art space radiation dose analysis for manned missions has not been exploited. Point doses have been overemphasized, and the critical dose to the bone marrow has been only crudely approximated, despite the existence of detailed man models and computer codes for dose integration in complex geometries. The method presented makes it practical to account for the geometrical detail of the astronaut as well as the vehicle. Discussed are the major assumptions involved and the concept of applying the results of detailed proton dose analysis to the real-time interpretation of on-board dosimetric measurements.

Generic isolated horizons in loop quantum gravity

NASA Astrophysics Data System (ADS)

Beetle, Christopher; Engle, Jonathan

2010-12-01

Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of all generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one-quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface.

New Techniques in Time-Frequency Analysis: Adaptive Band, Ultra-Wide Band and Multi-Rate Signal Processing

DTIC Science & Technology

2016-03-02

Nyquist tiles and sampling groups in Euclidean geometry, and discussed the extension of these concepts to hyperbolic and spherical geometry and...hyperbolic or spherical spaces. We look to develop a structure for the tiling of frequency spaces in both Euclidean and non-Euclidean domains. In particular...we establish Nyquist tiles and sampling groups in Euclidean geometry, and discuss the extension of these concepts to hyperbolic and spherical geometry

Analysis instrument test on mathematical power the material geometry of space flat side for grade 8

NASA Astrophysics Data System (ADS)

Kusmaryono, Imam; Suyitno, Hardi; Dwijanto, Karomah, Nur

2017-08-01

The main problem of research to determine the quality of test items on the material side of flat geometry to assess students' mathematical power. The method used is quantitative descriptive. The subjects were students of class 8 as many as 20 students. The object of research is the quality of test items in terms of the power of mathematics: validity, reliability, level of difficulty and power differentiator. Instrument mathematical power ratings are tested include: written tests and questionnaires about the disposition of mathematical power. Data were obtained from the field, in the form of test data on the material geometry of space flat side and questionnaires. The results of the test instrument to the reliability of the test item is influenced by many factors. Factors affecting the reliability of the instrument is the number of items, homogeneity test questions, the time required, the uniformity of conditions of the test taker, the homogeneity of the group, the variability problem, and motivation of the individual (person taking the test). Overall, the evaluation results of this study stated that the test instrument can be used as a tool to measure students' mathematical power.

Methods of treating complex space vehicle geometry for charged particle radiation transport

NASA Technical Reports Server (NTRS)

Hill, C. W.

1973-01-01

Current methods of treating complex geometry models for space radiation transport calculations are reviewed. The geometric techniques used in three computer codes are outlined. Evaluations of geometric capability and speed are provided for these codes. Although no code development work is included several suggestions for significantly improving complex geometry codes are offered.

BPS Jumping Loci are Automorphic

NASA Astrophysics Data System (ADS)

Kachru, Shamit; Tripathy, Arnav

2018-06-01

We show that BPS jumping loci-loci in the moduli space of string compactifications where the number of BPS states jumps in an upper semi-continuous manner—naturally appear as Fourier coefficients of (vector space-valued) automorphic forms. For the case of T 2 compactification, the jumping loci are governed by a modular form studied by Hirzebruch and Zagier, while the jumping loci in K3 compactification appear in a story developed by Oda and Kudla-Millson in arithmetic geometry. We also comment on some curious related automorphy in the physics of black hole attractors and flux vacua.

a Web Service Approach for Linking Sensors and Cellular Spaces

NASA Astrophysics Data System (ADS)

Isikdag, U.

2013-09-01

More and more devices are starting to be connected to the Internet. In the future the Internet will not only be a communication medium for people, it will in fact be a communication environment for devices. The connected devices which are also referred as Things will have an ability to interact with other devices over the Internet, i.) provide information in interoperable form and ii.) consume /utilize such information with the help of sensors embedded in them. This overall concept is known as Internet-of- Things (IoT). This requires new approaches to be investigated for system architectures to establish relations between spaces and sensors. The research presented in this paper elaborates on an architecture developed with this aim, i.e. linking spaces and sensors using a RESTful approach. The objective is making spaces aware of (sensor-embedded) devices, and making devices aware of spaces in a loosely coupled way (i.e. a state/usage/function change in the spaces would not have effect on sensors, similarly a location/state/usage/function change in sensors would not have any effect on spaces). The proposed architecture also enables the automatic assignment of sensors to spaces depending on space geometry and sensor location.

Deeply-Integrated Feature Tracking for Embedded Navigation

DTIC Science & Technology

2009-03-01

metric would result in increased feature strength, but a decrease in repeatability. The feature spacing also helped with repeatability of strong...locations in the second frame. This relationship is a constraint of projective geometry and states that the cross product of a point with itself (when...integrated refers to the incorporation of inertial information into the image processing, rather than just

Biological Individuality of Man

DTIC Science & Technology

1974-12-01

levels of a specific chemical substance in blood, urine, digestive juices , or tissues of "normal" persons. These are cited as the extremes of...physiological state, blood sugar level and nutritional status of the individual have been identified as significant. Studies on oxygen deprivation...in great detail. These include; geometry and composition of the cochlear partition, riensf.ty and spacing of epithelial hair cells, size and

Uncertainty relations as Hilbert space geometry

NASA Technical Reports Server (NTRS)

Braunstein, Samuel L.

1994-01-01

Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.

E-Invariant Quantized Motion of Valence Quarks

NASA Astrophysics Data System (ADS)

Kreymer, E. L.

2018-06-01

In sub-proton space wave processes are impossible. The analog of the Klein-Gordon equation in sub-proton space is elliptical and describes a stationary system with a constant number of particles. For dynamical processes, separation of variables is used and in each quantum of motion of the quark two states are distinguished: a localization state and a translation state with infinite velocity. Alternation of these states describes the motion of a quark. The mathematical expectations of the lifetimes of the localization states and the spatial extents of the translation states for a free quark and for a quark in a centrally symmetric potential are found. The action after one quantum of motion is equal to the Planck constant. The one-sided Laplace transform is used to determine the Green's function. Use of path integrals shows that the quantized trajectory of a quark is a broken line enveloping the classical trajectory of oscillation of the quark. Comparison of the calculated electric charge distribution in a proton with its experimental value gives satisfactory results. A hypothesis is formulated, according to which the three Grand Geometries of space correspond to the three main interactions of elementary particles.

Complex quantum network geometries: Evolution and phase transitions

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Complex quantum network geometries: Evolution and phase transitions.

PubMed

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Perceptual geometry of space and form: visual perception of natural scenes and their virtual representation

NASA Astrophysics Data System (ADS)

Assadi, Amir H.

2001-11-01

Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form and space are among fundamental problems in vision science. In recent cognitive and computational models of human perception, natural scenes are used systematically as preferred visual stimuli. Among key problems in perception of form and space, we have examined perception of geometry of natural surfaces and curves, e.g. as in the observer's environment. Besides a systematic mathematical foundation for a remarkably general framework, the advantages of the Gestalt theory of natural surfaces include a concrete computational approach to simulate or recreate images whose geometric invariants and quantities might be perceived and estimated by an observer. The latter is at the very foundation of understanding the nature of perception of space and form, and the (computer graphics) problem of rendering scenes to visually invoke virtual presence.

The Influence of Hierarchy and Layout Geometry in the Design of Learning Spaces

ERIC Educational Resources Information Center

Smith, Charlie

2017-01-01

For a number of years, higher education has moved away from didactic teaching toward collaborative and self-directed learning. This paper discusses how the configuration and spatial geometry of learning spaces influences engagement and interaction, with a particular focus on hierarchies between people within the space. Layouts, presented as…

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

NASA Astrophysics Data System (ADS)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Conventionalism and integrable Weyl geometry

NASA Astrophysics Data System (ADS)

Pucheu, M. L.

2015-03-01

Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.

Dynamic Tasking of Networked Sensors Using Covariance Information

DTIC Science & Technology

2010-09-01

has been created under an effort called TASMAN (Tasking Autonomous Sensors in a Multiple Application Network). One of the first studies utilizing this...environment was focused on a novel resource management approach, namely covariance-based tasking. Under this scheme, the state error covariance of...resident space objects (RSO), sensor characteristics, and sensor- target geometry were used to determine the effectiveness of future observations in

Geometric descriptions of entangled states by auxiliary varieties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-15

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete themore » approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.« less

En Route Spacing System and Method

NASA Technical Reports Server (NTRS)

Erzberger, Heinz (Inventor); Green, Steven M. (Inventor)

2002-01-01

A method of and computer software for minimizing aircraft deviations needed to comply with an en route miles-in-trail spacing requirement imposed during air traffic control operations via establishing a spacing reference geometry, predicting spatial locations of a plurality of aircraft at a predicted time of intersection of a path of a first of said plurality of aircraft with the spacing reference geometry, and determining spacing of each of the plurality of aircraft based on the predicted spatial locations.

En route spacing system and method

NASA Technical Reports Server (NTRS)

Erzberger, Heinz (Inventor); Green, Steven M. (Inventor)

2002-01-01

A method of and computer software for minimizing aircraft deviations needed to comply with an en route miles-in-trail spacing requirement imposed during air traffic control operations via establishing a spacing reference geometry, predicting spatial locations of a plurality of aircraft at a predicted time of intersection of a path of a first of said plurality of aircraft with the spacing reference geometry, and determining spacing of each of the plurality of aircraft based on the predicted spatial locations.

High resolution observations: The state of the art and beyond

NASA Technical Reports Server (NTRS)

Title, A.; Tarbell, T.; Shine, R.; Topka, K.; Frank, Z.

1992-01-01

The meaning of high resolution and its scientific importance with regard to solar observations is discussed. The state of the art is reviewed, looking into Solar Optical Universal Polarimeter (SOUP) observations, image selection techniques, and adaptive optics. It is concluded that until there are observations in space, complete understanding of processes in the solar photosphere, chromosphere, transition region, and corona will be impossible. The importance of high resolution is considered with regard to solar surface and convection, solar photosphere inside and outside magnetic fields, and sunspot geometry.

Solar energy

NASA Technical Reports Server (NTRS)

Rapp, D.

1981-01-01

The book opens with a review of the patterns of energy use and resources in the United States, and an exploration of the potential of solar energy to supply some of this energy in the future. This is followed by background material on solar geometry, solar intensities, flat plate collectors, and economics. Detailed attention is then given to a variety of solar units and systems, including domestic hot water systems, space heating systems, solar-assisted heat pumps, intermediate temperature collectors, space heating/cooling systems, concentrating collectors for high temperatures, storage systems, and solar total energy systems. Finally, rights to solar access are discussed.

Path Toward a Unifid Geometry for Radiation Transport

NASA Technical Reports Server (NTRS)

Lee, Kerry; Barzilla, Janet; Davis, Andrew; Zachmann

2014-01-01

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading to the creation and maintenance of toolkit-specific simplistic geometry models. The work presented here builds on the Direct Accelerated Geometry Monte Carlo (DAGMC) toolkit developed for use with the Monte Carlo N-Particle (MCNP) transport code. The workflow for achieving radiation transport on CAD models using MCNP and FLUKA has been demonstrated and the results of analyses on realistic spacecraft/habitats will be presented. Future work is planned that will further automate this process and enable the use of multiple radiation transport codes on identical geometry models imported from CAD. This effort will enhance the modeling tools used by NASA to accurately evaluate the astronaut space radiation risk and accurately determine the protection provided by as-designed exploration mission vehicles and habitats

Quantum Correlation Properties in Composite Parity-Conserved Matrix Product States

NASA Astrophysics Data System (ADS)

Zhu, Jing-Min

2016-09-01

We give a new thought for constructing long-range quantum correlation in quantum many-body systems. Our proposed composite parity-conserved matrix product state has long-range quantum correlation only for two spin blocks where their spin-block length larger than 1 compared to any subsystem only having short-range quantum correlation, and we investigate quantum correlation properties of two spin blocks varying with environment parameter and spacing spin number. We also find that the geometry quantum discords of two nearest-neighbor spin blocks and two next-nearest-neighbor spin blocks become smaller and for other conditions the geometry quantum discord becomes larger than that in any subcomponent, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation compared to the corresponding classical correlation and total correlation having no any characteristic of regulation. For nearest-neighbor and next-nearest-neighbor all the correlations take their maximal values at the same points, while for other conditions no whether for spacing same spin number or for different spacing spin numbers all the correlations taking their maximal values are respectively at different points which are very close. We believe that our work is helpful to comprehensively and deeply understand the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems; and further helpful for the classification, the depiction and the measure of quantum correlation of quantum many-body systems.

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

ERIC Educational Resources Information Center

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Synthesis, characterization, single crystal X-ray and DFT analysis of disubstituted phosphorodithioates

NASA Astrophysics Data System (ADS)

Kour, Mandeep; Kumar, Sandeep; Feddag, Ahmed; Andotra, Savit; Chouaih, Abdelkader; Gupta, Vivek K.; Kant, Rajni; Pandey, Sushil K.

2018-04-01

Disubstituted phosphorodithioates of the type [{(2,5-CH3)2C6H3O}2PS2HNEt3] (1) and [{(3,5-CH3)2C6H3O)2(PS2)}2] (2) were synthesized and characterized by IR and NMR (1H,13C and 31P) spectroscopic studies and as single crystal X-ray analysis. The compound 1 crystallizes in monoclinic space group P21/c whereas compound 2 crystallizes in triclinic space group Pbar1. The X-ray analysis reveals that in compound 1 phosphorus atom is coordinated to the two S and two O atoms to form tetrahedral geometry. The structure is stabilized by cation-anion Nsbnd H⋯S hydrogen bonded interactions. In compound 2, the two phosphorus atoms have a distorted tetrahedral geometry coordinated to two (3,5-CH3)2C6H3O groups. The molecule possesses a crystallographic center of symmetry and consists of zig-zag array of Sdbnd Psbnd Ssbnd Ssbnd Pdbnd S linkages with two diphenyldithiophosphate moieties in the trans configuration. Molecular geometries, HOMO-LUMO analysis and molecular electrostatic potential of compounds 1 and 2 are investigated by theoretical calculations using B3LYP functional with the 6-311G basis combination set in the ground state and compared with the experimental values.

Phase space methods in HMD systems

NASA Astrophysics Data System (ADS)

Babington, James

2017-06-01

We consider using phase space techniques and methods in analysing optical ray propagation in head mounted display systems. Two examples are considered that illustrate the concepts and methods. Firstly, a shark tooth freeform geometry, and secondly, a waveguide geometry that replicates a pupil in one dimension. Classical optics and imaging in particular provide a natural stage to employ phase space techniques, albeit as a constrained system. We consider how phase space provides a global picture of the physical ray trace data. As such, this gives a complete optical world history of all of the rays propagating through the system. Using this data one can look at, for example, how aberrations arise on a surface by surface basis. These can be extracted numerically from phase space diagrams in the example of a freeform imaging prism. For the waveguide geometry, phase space diagrams provide a way of illustrating how replicated pupils behave and what these imply for design considerations such as tolerances.

Dynamic Regimes of El Niño Southern Oscillation and Influenza Pandemic Timing

PubMed Central

Oluwole, Olusegun Steven Ayodele

2017-01-01

El Niño southern oscillation (ENSO) dynamics has been shown to drive seasonal influenza dynamics. Severe seasonal influenza epidemics and the 2009–2010 pandemic were coincident with chaotic regime of ENSO dynamics. ENSO dynamics from 1876 to 2016 were characterized to determine if influenza pandemics are coupled to chaotic regimes. Time-varying spectra of southern oscillation index (SOI) and sea surface temperature (SST) were compared. SOI and SST were decomposed to components using the algorithm of noise-assisted multivariate empirical mode decomposition. The components were Hilbert transformed to generate instantaneous amplitudes and phases. The trajectories and attractors of components were characterized in polar coordinates and state space. Influenza pandemics were mapped to dynamic regimes of SOI and SST joint recurrence of annual components. State space geometry of El Niños lagged by influenza pandemics were characterized and compared with other El Niños. Timescales of SOI and SST components ranged from sub-annual to multidecadal. The trajectories of SOI and SST components and the joint recurrence of annual components were dissipative toward chaotic attractors. Periodic, quasi-periodic, and chaotic regimes were present in the recurrence of trajectories, but chaos–chaos transitions dominated. Influenza pandemics occurred during chaotic regimes of significantly low transitivity dimension (p < 0.0001). El Niños lagged by influenza pandemics had distinct state space geometry (p < 0.0001). Chaotic dynamics explains the aperiodic timing, and varying duration and strength of El Niños. Coupling of all influenza pandemics of the past 140 years to chaotic regimes of low transitivity indicate that ENSO dynamics drives influenza pandemic dynamics. Forecasts models from ENSO dynamics should compliment surveillance for novel influenza viruses. PMID:29218303

Thermodynamics of confined gallium clusters.

PubMed

Chandrachud, Prachi

2015-11-11

We report the results of ab initio molecular dynamics simulations of Ga13 and Ga17 clusters confined inside carbon nanotubes with different diameters. The cluster-tube interaction is simulated by the Lennard-Jones (LJ) potential. We discuss the geometries, the nature of the bonding and the thermodynamics under confinement. The geometries as well as the isomer spectra of both the clusters are significantly affected. The degree of confinement decides the dimensionality of the clusters. We observe that a number of low-energy isomers appear under moderate confinement while some isomers seen in the free space disappear. Our finite-temperature simulations bring out interesting aspects, namely that the heat capacity curve is flat, even though the ground state is symmetric. Such a flat nature indicates that the phase change is continuous. This effect is due to the restricted phase space available to the system. These observations are supported by the mean square displacement of individual atoms, which are significantly smaller than in free space. The nature of the bonding is found to be approximately jellium-like. Finally we note the relevance of the work to the problem of single file diffusion for the case of the highest confinement.

Positive geometries and canonical forms

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas

2017-11-01

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

Generalized Finsler geometric continuum physics with applications in fracture and phase transformations

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

A theory of deformation of continuous media based on concepts from Finsler differential geometry is presented. The general theory accounts for finite deformations, nonlinear elasticity, and changes in internal state of the material, the latter represented by elements of a state vector of generalized Finsler space whose entries consist of one or more order parameter(s). Two descriptive representations of the deformation gradient are considered. The first invokes an additive decomposition and is applied to problems involving localized inelastic deformation mechanisms such as fracture. The second invokes a multiplicative decomposition and is applied to problems involving distributed deformation mechanisms such as phase transformations or twinning. Appropriate free energy functions are posited for each case, and Euler-Lagrange equations of equilibrium are derived. Solutions are obtained for specific problems of tensile fracture of an elastic cylinder and for amorphization of a crystal under spherical and uniaxial compression. The Finsler-based approach is demonstrated to be more general and potentially more physically descriptive than existing hyperelasticity models couched in Riemannian geometry or Euclidean space, without incorporation of supplementary ad hoc equations or spurious fitting parameters. Predictions for single crystals of boron carbide ceramic agree qualitatively, and in many instances quantitatively, with results from physical experiments and atomic simulations involving structural collapse and failure of the crystal along its c-axis.

Space Object Classification and Characterization Via Multiple Model Adaptive Estimation

DTIC Science & Technology

2014-07-14

BRDF ) which models light distribution scattered from the surface due to the incident light. The BRDF at any point on the surface is a function of two...uu B vu B nu obs I u sun I u I hu (b) Reflection Geometry Fig. 2: Reflection Geometry and Space Object Shape Model of the BRDF is ρdiff(i...Space Object Classification and Characterization Via Multiple Model Adaptive Estimation Richard Linares Director’s Postdoctoral Fellow Space Science

Lorentz symmetric n-particle systems without ``multiple times''

NASA Astrophysics Data System (ADS)

Smith, Felix

2013-05-01

The need for multiple times in relativistic n-particle dynamics is a consequence of Minkowski's postulated symmetry between space and time coordinates in a space-time s = [x1 , . . ,x4 ] = [ x , y , z , ict ] , Eq. (1). Poincaré doubted the need for this space-time symmetry, believing Lorentz covariance could also prevail in some geometries with a three-dimensional position space and a quite different time coordinate. The Hubble expansion observed later justifies a specific geometry of this kind, a negatively curved position 3-space expanding with time at the Hubble rate lH (t) =lH , 0 + cΔt (F. T. Smith, Ann. Fond. L. de Broglie, 30, 179 (2005) and 35, 395 (2010)). Its position 4-vector is not s but q = [x1 , . . ,x4 ] = [ x , y , z , ilH (t) ] , and shows no 4-space symmetry. What is observed is always a difference 4-vector Δq = [ Δx , Δy , Δz , icΔt ] , and this displays the structure of Eq. (1) perfectly. Thus we find the standard 4-vector of special relativity in a geometry that does not require a Minkowski space-time at all, but a quite different geometry with a expanding 3-space symmetry and an independent time. The same Lorentz symmetry with but a single time extends to 2 and n-body systems.

The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gromov, N. A., E-mail: gromov@dm.komisc.r

2009-05-15

More than forty years ago R.I. Pimenov introduced a new geometry-semi-Riemannian one-as a set of geometrical objects consistent with a fibering pr: M{sub n} {yields} M{sub m}. He suggested the heuristic principle according to which the physically different quantities (meter, second, Coulomb, etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple-fibered semi-Riemannian geometry is the most appropriate one for the treatment of more than three different physical quantities as unified geometrical field theory. Semi-Euclideanmore » geometry {sup 3}R{sub 5}{sup 4} with 1-dimensional fiber x{sup 5} and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry {sup 3}V{sub 5}{sup 4} with the general relativity pseudo-Riemannian space-time {sup 3}V{sub 4}, and 1-dimensional fiber x{sup 5}, responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the fifth coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise.« less

Predictor-based multivariable closed-loop system identification of the EXTRAP T2R reversed field pinch external plasma response

NASA Astrophysics Data System (ADS)

Olofsson, K. Erik J.; Brunsell, Per R.; Rojas, Cristian R.; Drake, James R.; Hjalmarsson, Håkan

2011-08-01

The usage of computationally feasible overparametrized and nonregularized system identification signal processing methods is assessed for automated determination of the full reversed-field pinch external plasma response spectrum for the experiment EXTRAP T2R. No assumptions on the geometry of eigenmodes are imposed. The attempted approach consists of high-order autoregressive exogenous estimation followed by Markov block coefficient construction and Hankel matrix singular value decomposition. It is seen that the obtained 'black-box' state-space models indeed can be compared with the commonplace ideal magnetohydrodynamics (MHD) resistive thin-shell model in cylindrical geometry. It is possible to directly map the most unstable autodetected empirical system pole to the corresponding theoretical resistive shell MHD eigenmode.

Hybrid Techniques for Quantum Circuit Simulation

DTIC Science & Technology

2014-02-01

Detailed theorems and proofs describing these results are included in our published manuscript [10]. Embedding of stabilizer geometry in the Hilbert ...space. We also describe how the discrete embedding of stabilizer geometry in Hilbert space complicates several natural geometric tasks. As described...the Hilbert space in which they are embedded, and that they are arranged in a fairly uniform pattern. These factors suggest that, if one seeks a

Bonding and structure of copper nitrenes.

PubMed

Cundari, Thomas R; Dinescu, Adriana; Kazi, Abul B

2008-11-03

Copper nitrenes are of interest as intermediates in the catalytic aziridination of olefins and the amination of C-H bonds. However, despite advances in the isolation and study of late-transition-metal multiply bonded complexes, a bona fide structurally characterized example of a terminal copper nitrene has, to our knowledge, not been reported. In anticipation of such a report, terminal copper nitrenes are studied from a computational perspective. The nitrene complexes studied here are of the form (beta-diketiminate)Cu(NPh). Density functional theory (DFT), complete active space self-consistent-field (CASSCF) electronic structure techniques, and hybrid quantum mechanical/molecular mechanical (QM/MM) methods are employed to study such species. While DFT methods indicate that a triplet (S = 1) is the ground state, CASSCF calculations indicate that a singlet (S = 0) is the ground state, with only a small energy gap between the singlet and triplet. Moreover, the ground-state (open-shell) singlet copper nitrene is found to be highly multiconfigurational (i.e., biradical) and to possess a bent geometry about the nitrene nitrogen, contrasting with the linear nitrene geometry of the triplet copper nitrenes. CASSCF calculations also reveal the existence of a closed-shell singlet state with some degree of multiple bonding character for the copper-nitrene bond.

Risks incurred by hydrogen escaping from containers and conduits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swain, M.R.; Grilliot, E.S.

1998-08-01

This paper is a discussion of a method for hydrogen leak classification. Leaks are classified as; gas escapes into enclosed spaces, gas escapes into partially enclosed spaces (vented), and gas escapes into unenclosed spaces. Each of the three enclosure classifications is further divided into two subclasses; total volume of hydrogen escaped and flow rate of escaping hydrogen. A method to aid in risk assessment determination in partially enclosed spaces is proposed and verified for several enclosure geometries. Examples are discussed for additional enclosure geometries.

Emergence of polysaccharide membrane walls through macro-space partitioning via interfacial instability.

PubMed

Okeyoshi, Kosuke; Okajima, Maiko K; Kaneko, Tatsuo

2017-07-21

Living organisms in drying environments build anisotropic structures and exhibit directionality through self-organization of biopolymers. However, the process of macro-scale assembly is still unknown. Here, we introduce a dissipative structure through a non-equilibrium process between hydration and deposition in the drying of a polysaccharide liquid crystalline solution. By controlling the geometries of the evaporation front in a limited space, multiple nuclei emerge to grow vertical membrane walls with macroscopic orientation. Notably, the membranes are formed through rational orientation of rod-like microassemblies along the dynamic three-phase contact line. Additionally, in the non-equilibrium state, a dissipative structure is ultimately immobilized as a macroscopically partitioned space by multiple vertical membranes. We foresee that such oriented membranes will be applicable to soft biomaterials with direction controllability, and the macroscopic space partitionings will aid in the understanding of the space recognition ability of natural products under drying environments.

Some finite terms from ladder diagrams in three and four loop maximal supergravity

NASA Astrophysics Data System (ADS)

Basu, Anirban

2015-10-01

We consider the finite part of the leading local interactions in the low energy expansion of the four graviton amplitude from the ladder skeleton diagrams in maximal supergravity on T 2, at three and four loops. At three loops, we express the {D}8{{R}}4 and {D}10{{R}}4 amplitudes as integrals over the moduli space of an underlying auxiliary geometry. These amplitudes are evaluated exactly for special values of the the moduli of the auxiliary geometry, where the integrand simplifies. We also perform a similar analysis for the {D}8{{R}}4 amplitude at four loops that arise from the ladder skeleton diagrams for a special value of a parameter in the moduli space of the auxiliary geometry. While the dependence of the amplitudes on the volume of the T 2 is very simple, the dependence on the complex structure of the T 2 is quite intricate. In some of the cases, the amplitude consists of terms each of which factorizes into a product of two {SL}(2,{{Z}}) invariant modular forms. While one of the factors is a non-holomorphic Eisenstein series, the other factor splits into a sum of modular forms each of which satisfies a Poisson equation on moduli space with source terms that are bilinear in the Eisenstein series. This leads to several possible perturbative contributions unto genus 5 in type II string theory on S1. Unlike the one and two loop supergravity analysis, these amplitudes also receive non-perturbative contributions from bound states of three D-(anti)instantons in the IIB theory.

ON THE GEOMETRY OF MEASURABLE SETS IN N-DIMENSIONAL SPACE ON WHICH GENERALIZED LOCALIZATION HOLDS FOR MULTIPLE FOURIER SERIES OF FUNCTIONS IN L_p, p>1

NASA Astrophysics Data System (ADS)

Bloshanskiĭ, I. L.

1984-02-01

The precise geometry is found of measurable sets in N-dimensional Euclidean space on which generalized localization almost everywhere holds for multiple Fourier series which are rectangularly summable.Bibliography: 14 titles.

Effects of anode geometry on forward wide-angle neon ion emissions in 3.5 kJ plasma focus device by novel mega-size panorama polycarbonate image detectors

NASA Astrophysics Data System (ADS)

Sohrabi, M.; Soltani, Z.; Sarlak, Z.

2018-03-01

Forward wide-angle neon ion emissions in a 3.5 kJ plasma focus device (PFD) were studied using 5 different anode top geometries; hollow-end cylinder, solid triangle, solid hemisphere, hollow-end cone and flat-end cone. Position-sensitive mega-size panorama polycarbonate ion image detectors (MS-PCID) developed by dual-cell circular mega-size electrochemical etching (MS-ECE) systems were applied for processesing wide-angle neon ion images on MS-PCIDs exposed on the PFD cylinder top base under a single pinch shot. The images can be simply observed, analyzed and relatively quantified in terms of ion emission angular distributions even by the unaided eyes. By analysis of the forward neon ion emission images, the ion emission yields, ion emission angular distributions, iso-fluence ion contours and solid angles of ion emissions in 4π PFD space were determined. The neon ion emission yields on the PFD cylinder top base are in an increasing order ~2.1×109, ~2.2 ×109, ~2.8×109, ~2.9×109, and ~3.5×109 neon ions/shot for the 5 stated anode top geometries respectively. The panorama neon ion images as diagnosed even by the unaided eyes demonstrate the lowest and highest ion yields from the hollow-end cylinder and flat-end cone anode tops respectively. Relative dynamic qualitative neon ion spectrometry was made by the unaided eyes demonstrating relative neon ion energy as they appear. The study also demonstrates the unique power of the MS-PCID/MS-ECE imaging system as an advanced state-of-the-art ion imaging method for wide-angle dynamic parametric studies in PFD space and other ion study applications.

Minimizing Actuator-Induced Residual Error in Active Space Telescope Primary Mirrors

DTIC Science & Technology

2010-09-01

actuator geometry, and rib-to-facesheet intersection geometry are exploited to achieve improved performance in silicon carbide ( SiC ) mirrors . A...are exploited to achieve improved performance in silicon carbide ( SiC ) mirrors . A parametric finite element model is used to explore the trade space...MOST) finite element model. The move to lightweight actively-controlled silicon carbide ( SiC ) mirrors is traced back to previous generations of space

Momentum-space cigar geometry in topological phases

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2018-01-01

In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.

The Koslowski-Sahlmann representation: quantum configuration space

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Varadarajan, Madhavan

2014-09-01

The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.

Network geometry with flavor: From complexity to quantum geometry

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but its statistical properties reveal the relation to its quantum mechanical description. In fact the δ -dimensional faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann, or Bose-Einstein statistics depending on the flavor s and the dimensions d and δ .

Network geometry with flavor: From complexity to quantum geometry.

PubMed

Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its statistical properties reveal the relation to its quantum mechanical description. In fact the δ-dimensional faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann, or Bose-Einstein statistics depending on the flavor s and the dimensions d and δ.

Feasibility of a 30-meter space based laser transmitter

NASA Technical Reports Server (NTRS)

Berggren, R. R.; Lenertz, G. E.

1975-01-01

A study was made of the application of large expandable mirror structures in future space missions to establish the feasibility and define the potential of high power laser systems for such applications as propulsion and power transmission. Application of these concepts requires a 30-meter diameter, diffraction limited mirror for transmission of the laser energy. Three concepts for the transmitter are presented. These concepts include consideration of continuous as well as segmented mirror surfaces and the major stow-deployment categories of inflatable, variable geometry and assembled-in-space structures. The mirror surface for each concept would be actively monitored and controlled to maintain diffraction limited performance at 10.6 microns during operation. The proposed mirror configurations are based on existing aerospace state-of-the-art technology. The assembled-in-space concept appears to be the most feasible, at this time.

No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox

NASA Astrophysics Data System (ADS)

Perez, Alejandro

2015-04-01

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation can be described by a unitary evolution without the problems encountered by the standard remnant scenario or the schemes where information is assumed to come out with the radiation during evaporation (firewalls and complementarity). The final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler), which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

Topological phases in two-dimensional arrays of parafermionic zero modes

NASA Astrophysics Data System (ADS)

Burrello, M.; van Heck, B.; Cobanera, E.

2013-05-01

It has recently been realized that zero modes with projective non-Abelian statistics, generalizing the notion of Majorana bound states, may exist at the interface between a superconductor and a ferromagnet along the edge of a fractional topological insulator (FTI). Here, we study two-dimensional architectures of these non-Abelian zero modes, whose interactions are generated by the charging and Josephson energies of the superconductors. We derive low-energy Hamiltonians for two different arrays of FTIs on the plane, revealing an interesting interplay between the real-space geometry of the system and its topological properties. On the one hand, in a geometry where the length of the FTI edges is independent on the system size, the array has a topologically ordered phase, giving rise to a qudit toric code Hamiltonian in perturbation theory. On the other hand, in a geometry where the length of the edges scales with system size, we find an exact duality to an Abelian lattice gauge theory and no topological order.

DEM study of granular flow around blocks attached to inclined walls

NASA Astrophysics Data System (ADS)

Samsu, Joel; Zhou, Zongyan; Pinson, David; Chew, Sheng

2017-06-01

Damage due to intense particle-wall contact in industrial applications can cause severe problems in industries such as mineral processing, mining and metallurgy. Studying the flow dynamics and forces on containing walls can provide valuable feedback for equipment design and optimising operations to prolong the equipment lifetime. Therefore, solids flow-wall interaction phenomena, i.e. induced wall stress and particle flow patterns should be well understood. In this work, discrete element method (DEM) is used to study steady state granular flow in a gravity-fed hopper like geometry with blocks attached to an inclined wall. The effects of different geometries, e.g. different wall angles and spacing between blocks are studied by means of a 3D DEM slot model with periodic boundary conditions. The findings of this work include (i) flow analysis in terms of flow patterns and particle velocities, (ii) force distributions within the model geometry, and (iii) wall stress vs. model height diagrams. The model enables easy transfer of the key findings to other industrial applications handling granular materials.

Complex Ordered Patterns in Mechanical Instability Induced Geometrically Frustrated Triangular Cellular Structures

NASA Astrophysics Data System (ADS)

Kang, Sung Hoon; Shan, Sicong; Košmrlj, Andrej; Noorduin, Wim L.; Shian, Samuel; Weaver, James C.; Clarke, David R.; Bertoldi, Katia

2014-03-01

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

The problems in quantum foundations in the light of gauge theories

NASA Astrophysics Data System (ADS)

Ne'Eman, Yuval

1986-04-01

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.

Quantum Limits of Space-to-Ground Optical Communications

NASA Technical Reports Server (NTRS)

Hemmati, H.; Dolinar, S.

2012-01-01

For a pure loss channel, the ultimate capacity can be achieved with classical coherent states (i.e., ideal laser light): (1) Capacity-achieving receiver (measurement) is yet to be determined. (2) Heterodyne detection approaches the ultimate capacity at high mean photon numbers. (3) Photon-counting approaches the ultimate capacity at low mean photon numbers. A number of current technology limits drive the achievable performance of free-space communication links. Approaching fundamental limits in the bandwidth-limited regime: (1) Heterodyne detection with high-order coherent-state modulation approaches ultimate limits. SOA improvements to laser phase noise, adaptive optics systems for atmospheric transmission would help. (2) High-order intensity modulation and photon-counting can approach heterodyne detection within approximately a factor of 2. This may have advantages over coherent detection in the presence of turbulence. Approaching fundamental limits in the photon-limited regime (1) Low-duty cycle binary coherent-state modulation (OOK, PPM) approaches ultimate limits. SOA improvements to laser extinction ratio, receiver dark noise, jitter, and blocking would help. (2) In some link geometries (near field links) number-state transmission could improve over coherent-state transmission

Dynamics of entanglement in expanding quantum fields

NASA Astrophysics Data System (ADS)

Berges, Jürgen; Floerchinger, Stefan; Venugopalan, Raju

2018-04-01

We develop a functional real-time approach to computing the entanglement between spatial regions for Gaussian states in quantum field theory. The entanglement entropy is characterized in terms of local correlation functions on space-like Cauchy hypersurfaces. The framework is applied to explore an expanding light cone geometry in the particular case of the Schwinger model for quantum electrodynamics in 1+1 space-time dimensions. We observe that the entanglement entropy becomes extensive in rapidity at early times and that the corresponding local reduced density matrix is a thermal density matrix for excitations around a coherent field with a time dependent temperature. Since the Schwinger model successfully describes many features of multiparticle production in e + e - collisions, our results provide an attractive explanation in this framework for the apparent thermal nature of multiparticle production even in the absence of significant final state scattering.

Experimental Non-Violation of the Bell Inequality

NASA Astrophysics Data System (ADS)

Palmer, Tim

2018-05-01

A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry $I_U$ in cosmological state space. Consistent with the assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and hence non-classical) metric $g_p$ is defined on cosmological state space, where $p$ is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be $g_p$-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit $p=\\infty$, at which $g_p$ is Euclidean. Broader implications are discussed.

Structure of 1,5-benzodiazepinones in the solid state and in solution: Effect of the fluorination in the six-membered ring

PubMed Central

Pérez-Torralba, Marta; Ángeles García, M; López, Concepción; Torralba, M Carmen; Rosario Torres, M; Alkorta, Ibon; Elguero, José

2013-01-01

Summary Two novel tetrafluorinated 1,5-benzodiazepinones were synthesized and their X-ray structures determined. 6,7,8,9-Tetrafluoro-4-methyl-1,3-dihydro-2H-1,5-benzodiazepin-2-one crystallizes in the monoclinic P21/c space group and 6,7,8,9-tetrafluoro-1,4-dimethyl-1,3-dihydro-2H-1,5-benzodiazepin-2-one in the triclinic P−1 space group. Density functional theory studies at the B3LYP/6-311++G(d,p) level were carried out on these compounds and on four non-fluorinated derivatives, allowing to calculate geometries, tautomeric energies and ring-inversion barriers, that were compared with the experimental results obtained by static and dynamic NMR in solution and in solid state. PMID:24204428

Space Charge Effect in the Sheet and Solid Electron Beam

NASA Astrophysics Data System (ADS)

Song, Ho Young; Kim, Hyoung Suk; Ahn, Saeyoung

1998-11-01

We analyze the space charge effect of two different types of electron beam ; sheet and solid electron beam. Electron gun simulations are carried out using shadow and control grids for high and low perveance. Rectangular and cylindrical geometries are used for sheet and solid electron beam in planar and disk type cathode. The E-gun code is used to study the limiting current and space charge loading in each geometries.

Composite fermions on a torus

NASA Astrophysics Data System (ADS)

Pu, Songyang; Wu, Ying-Hai; Jain, J. K.

2017-11-01

We achieve an explicit construction of the lowest Landau level (LLL) projected wave functions for composite fermions in the periodic (torus) geometry. To this end, we first demonstrate how the vortex attachment of the composite fermion (CF) theory can be accomplished in the torus geometry to produce the "unprojected" wave functions satisfying the correct (quasi)periodic boundary conditions. We then consider two methods for projecting these wave functions into the LLL. The direct projection produces valid wave functions but can be implemented only for very small systems. The more powerful and more useful projection method of Jain and Kamilla fails in the torus geometry because it does not preserve the periodic boundary conditions and thus takes us out of the original Hilbert space. We have succeeded in constructing a modified projection method that is consistent with both the periodic boundary conditions and the general structure of the CF theory. This method is valid for a large class of states of composite fermions, called "proper states," which includes the incompressible ground states at electron filling factors ν =n/2 p n +1 , their charged and neutral excitations, and also the quasidegenerate ground states at arbitrary filling factors of the form ν =ν/*2pν*+1 , where n and p are integers and ν* is the CF filling factor. Comparison with exact results known for small systems for the ground and excited states at filling factors ν =1 /3 , 2/5, and 3/7 demonstrates our LLL-projected wave functions to be extremely accurate representations of the actual Coulomb eigenstates. Our construction enables the study of large systems of composite fermions on the torus, thereby opening the possibility of investigating numerous interesting questions and phenomena.

How Can Polarization States of Reflected Light from Snow Surfaces Inform Us on Surface Normals and Ultimately Snow Grain Size Measurements?

NASA Astrophysics Data System (ADS)

Schneider, A. M.; Flanner, M.; Yang, P.; Yi, B.; Huang, X.; Feldman, D.

2016-12-01

The Snow Grain Size and Pollution (SGSP) algorithm is a method applied to Moderate Resolution Imaging Spectroradiometer data to estimate snow grain size from space-borne measurements. Previous studies validate and quantify potential sources of error in this method, but because it assumes flat snow surfaces, however, large scale variations in surface normals can cause biases in its estimates due to its dependence on solar and observation zenith angles. To address these variations, we apply the Monte Carlo method for photon transport using data containing the single scattering properties of different ice crystals to calculate polarization states of reflected monochromatic light at 1500nm from modeled snow surfaces. We evaluate the dependence of these polarization states on solar and observation geometry at 1500nm because multiple scattering is generally a mechanism for depolarization and the ice crystals are relatively absorptive at this wavelength. Using 1500nm thus results in a higher number of reflected photons undergoing fewer scattering events, increasing the likelihood of reflected light having higher degrees of polarization. In evaluating the validity of the model, we find agreement with previous studies pertaining to near-infrared spectral directional hemispherical reflectance (i.e. black-sky albedo) and similarities in measured bidirectional reflectance factors, but few studies exist modeling polarization states of reflected light from snow surfaces. Here, we present novel results pertaining to calculated polarization states and compare dependences on solar and observation geometry for different idealized snow surfaces. If these dependencies are consistent across different ice particle shapes and sizes, then these findings could inform the SGSP algorithm by providing useful relationships between measurable physical quantities and solar and observation geometry to better understand variations in snow surface normals from remote sensing observations.

Conformal gravity and time

NASA Astrophysics Data System (ADS)

Hazboun, Jeffrey Shafiq

2014-10-01

Cartan geometry provides a rich formalism from which to look at various geometrically motivated extensions to general relativity. In this manuscript, we start by motivating reasons to extend the theory of general relativity. We then introduce the reader to our technique, called the quotient manifold method, for extending the geometry of spacetime. We will specifically look at the class of theories formed from the various quotients of the conformal group. Starting with the conformal symmetries of Euclidean space, we construct a manifold where time manifests as a part of the geometry. Though there is no matter present in the geome- try studied here, geometric terms analogous to dark energy and dark matter appear when we write down the Einstein tensor. Specifically, the quotient of the conformal group of Euclidean four-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and nondegenerate Killing metric. We show the general solution possesses orthogonal Lagrangian submanifolds, with the induced metric and the spin connection on the submanifolds necessarily Lorentzian, despite the Euclidean starting point. By examining the structure equations of the biconformal space in an orthonormal frame adapted to its phase space properties, we also find two new tensor fields exist in this geometry, not present in Riemannian geometry. The first is a combination of the Weyl vector with the scale factor on the metric, and determines the time-like directions on the submanifolds. The second comes from the components of the spin connection, symmetric with respect to the new metric. Though this field comes from the spin connection, it transforms ho- mogeneously. Finally, we show in the absence of Cartan curvature or sources, the configuration space has geometric terms equivalent to a perfect fluid and a cosmological constant. We complete the analysis of this homogeneous space by transforming the known, general solution of the Maurer-Cartan equations into the orthogonal, Lagrangian basis. This results in a signature-changing metric, just as in the work of Spencer and Wheeler, however without any conditions on the curvature of the momentum sector. The Riemannian curvatures of the two submanifolds are directly related. We investigate the case where the curvature on the momentum submanifold vanishes, while the curvature of the configuration submanifold gives an effective energy-momentum tensor corresponding to a perfect fluid. In the second part of this manuscript, we look at the most general curved biconformal geometry dictated by the Wehner-Wheeler action. We use the assemblage of structure equations, Bianchi identities, and field equations to show how the geometry of the manifolds self-organizes into trivial Weyl geometries, which can then be gauged to Riemannian geometries. The Bianchi identities reveal the strong relationships between the various curvatures, torsions, and cotorsions. The discussion of the curved case culminates in a number of simplifying restrictions that show general relativity as the base of the more general theory.

Thin‐ or thick‐skinned faulting in the Yakima fold and thrust belt (WA)? Constraints from kinematic modeling of the saddle mountains anticline

USGS Publications Warehouse

Casale, Gabriele; Pratt, Thomas L.

2015-01-01

The Yakima fold and thrust belt (YFTB) deforms the Columbia River Basalt Group flows of Washington State. The YFTB fault geometries and slip rates are crucial parameters for seismic‐hazard assessments of nearby dams and nuclear facilities, yet there are competing models for the subsurface fault geometry involving shallowly rooted versus deeply rooted fault systems. The YFTB is also thought to be analogous to the evenly spaced wrinkle ridges found on other terrestrial planets. Using seismic reflection data, borehole logs, and surface geologic data, we tested two proposed kinematic end‐member thick‐ and thin‐skinned fault models beneath the Saddle Mountains anticline of the YFTB. Observed subsurface geometry can be produced by 600–800 m of heave along a single listric‐reverse fault or ∼3.5  km of slip along two superposed low‐angle thrust faults. Both models require decollement slip between 7 and 9 km depth, resulting in greater fault areas than sometimes assumed in hazard assessments. Both models require initial slip much earlier than previously thought and may provide insight into the subsurface geometry of analogous comparisons to wrinkle ridges observed on other planets.

Using SpaceClaimTD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

NASA Technical Reports Server (NTRS)

Fabanich, William A., Jr.

2014-01-01

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.

Using SpaceClaim/TD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

NASA Technical Reports Server (NTRS)

Fabanich, William

2014-01-01

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.

Technology in Spherical Geometry Investigations: Reflections on Spontaneous Use and Motivation

ERIC Educational Resources Information Center

Sinclair, Margaret

2010-01-01

Students in a graduate geometry class used items such as paper, ribbon, plastic spheres, cardboard tubes, and markers to carry out investigations in spherical geometry. The hands-on activities helped students develop a new appreciation of geometry as a study of shape and space; however, the difficulty of subduing wayward elastics and drawing lines…

Web-dendritic ribbon growth

NASA Technical Reports Server (NTRS)

Hilborn, R. B., Jr.; Faust, J. W., Jr.

1976-01-01

A web furnace was constructed for pulling dendritic-web samples. The effect of changes in the furnace thermal geometry on the growth of dendritic-web was studied. Several attempts were made to grow primitive dendrites for use as the dendritic seed crystals for web growth and to determine the optimum twin spacing in the dendritic seed crystal for web growth. Mathematical models and computer programs were used to determine the thermal geometries in the susceptor, crucible melt, meniscus, and web. Several geometries were determined for particular furnace geometries and growth conditions. The information obtained was used in conjunction with results from the experimental growth investigations in order to achieve proper conditions for sustained pulling of two dendrite web ribbons. In addition, the facilities for obtaining the following data were constructed: twin spacing, dislocation density, web geometry, resistivity, majority charge carrier type, and minority carrier lifetime.

Geometry, topology, and string theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Varadarajan, Uday

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

Dynamic mapping of conical intersection seams: A general method for incorporating the geometric phase in adiabatic dynamics in polyatomic systems

NASA Astrophysics Data System (ADS)

Xie, Changjian; Malbon, Christopher L.; Yarkony, David R.; Guo, Hua

2017-07-01

The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S1 state of phenol, which is affected by a Cs symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI.

Using 3D Geometric Models to Teach Spatial Geometry Concepts.

ERIC Educational Resources Information Center

Bertoline, Gary R.

1991-01-01

An explanation of 3-D Computer Aided Design (CAD) usage to teach spatial geometry concepts using nontraditional techniques is presented. The software packages CADKEY and AutoCAD are described as well as their usefulness in solving space geometry problems. (KR)

Method of grid generation

DOEpatents

Barnette, Daniel W.

2002-01-01

The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.

Neural-Network Quantum States, String-Bond States, and Chiral Topological States

NASA Astrophysics Data System (ADS)

Glasser, Ivan; Pancotti, Nicola; August, Moritz; Rodriguez, Ivan D.; Cirac, J. Ignacio

2018-01-01

Neural-network quantum states have recently been introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between neural-network quantum states in the form of restricted Boltzmann machines and some classes of tensor-network states in arbitrary dimensions. In particular, we demonstrate that short-range restricted Boltzmann machines are entangled plaquette states, while fully connected restricted Boltzmann machines are string-bond states with a nonlocal geometry and low bond dimension. These results shed light on the underlying architecture of restricted Boltzmann machines and their efficiency at representing many-body quantum states. String-bond states also provide a generic way of enhancing the power of neural-network quantum states and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of tensor networks and the efficiency of neural-network quantum states into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional tensor networks, we show that, because of their nonlocal geometry, neural-network quantum states and their string-bond-state extension can describe a lattice fractional quantum Hall state exactly. In addition, we provide numerical evidence that neural-network quantum states can approximate a chiral spin liquid with better accuracy than entangled plaquette states and local string-bond states. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of string-bond states as a tool in more traditional machine-learning applications.

Geometry of Theory Space and RG Flows

NASA Astrophysics Data System (ADS)

Kar, Sayan

The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor-Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.

Computational Approaches to Image Understanding.

DTIC Science & Technology

1981-10-01

represnting points, edges, surfaces, and volumes to facilitate display. The geometry or perspective and parailcl (or orthographic) projection has...of making the image forming process explicit. This in turn leads to a concern with geometry , such as the properties f the gradient, stereographic, and...dual spaces. Combining geometry and smoothness leads naturally to multi-variate vector analysis, and to differential geometry . For the most part, a

A Hamiltonian approach to Thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldiotti, M.C., E-mail: baldiotti@uel.br; Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br; Molina, C., E-mail: cmolina@usp.br

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensivelymore » used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.« less

Gravity Wave Energetics Determined From Coincident Space-Based and Ground-Based Observations of Airglow Emissions

NASA Technical Reports Server (NTRS)

2000-01-01

Significant progress was made toward the goals of this proposal in a number of areas during the covered period. Section 5.1 contains a copy of the originally proposed schedule. The tasks listed below have been accomplished: (1) Construction of space-based observing geometry gravity wave model. This model has been described in detail in the paper accompanying this report (Section 5.2). It can simulate the observing geometry of both ground-based, and orbital instruments allowing comparisons to be made between them. (2) Comparisons of relative emission intensity, temperatures, and Krassovsky's ratio for space- and ground-based observing geometries. These quantities are used in gravity wave literature to describe the effects of the waves on the airglow. (3) Rejection of Bates [1992], and Copeland [1994] chemistries for gravity wave modeling purposes. Excessive 02(A(sup 13)(Delta)) production led to overproduction of O2(b(sup 1)(Sigma)), the state responsible for the emission of O2. Atmospheric band. Attempts were made to correct for this behavior, but could not adequately compensate for this. (4) Rejection of MSX dataset due to lack of coincident data, and resolution necessary to characterize the waves. A careful search to identify coincident data revealed only four instances, with only one of those providing usable data. Two high latitude overpasses and were contaminated by auroral emissions. Of the remaining two mid-latitude coincidences, one overflight was obscured by cloud, leaving only one ten minute segment of usable data. Aside from the statistical difficulties involved in comparing measurements taken in this short period, the instrument lacks the necessary resolution to determine the vertical wavelength of the gravity wave. This means that the wave cannot be uniquely characterized from space with this dataset. Since no observed wave can be uniquely identified, model comparisons are not possible.

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

NASA Astrophysics Data System (ADS)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

Low-lying excited states of model proteins: Performances of the CC2 method versus multireference methods

NASA Astrophysics Data System (ADS)

Ben Amor, Nadia; Hoyau, Sophie; Maynau, Daniel; Brenner, Valérie

2018-05-01

A benchmark set of relevant geometries of a model protein, the N-acetylphenylalanylamide, is presented to assess the validity of the approximate second-order coupled cluster (CC2) method in studying low-lying excited states of such bio-relevant systems. The studies comprise investigations of basis-set dependence as well as comparison with two multireference methods, the multistate complete active space 2nd order perturbation theory (MS-CASPT2) and the multireference difference dedicated configuration interaction (DDCI) methods. First of all, the applicability and the accuracy of the quasi-linear multireference difference dedicated configuration interaction method have been demonstrated on bio-relevant systems by comparison with the results obtained by the standard MS-CASPT2. Second, both the nature and excitation energy of the first low-lying excited state obtained at the CC2 level are very close to the Davidson corrected CAS+DDCI ones, the mean absolute deviation on the excitation energy being equal to 0.1 eV with a maximum of less than 0.2 eV. Finally, for the following low-lying excited states, if the nature is always well reproduced at the CC2 level, the differences on excitation energies become more important and can depend on the geometry.

Low-lying excited states of model proteins: Performances of the CC2 method versus multireference methods.

PubMed

Ben Amor, Nadia; Hoyau, Sophie; Maynau, Daniel; Brenner, Valérie

2018-05-14

A benchmark set of relevant geometries of a model protein, the N-acetylphenylalanylamide, is presented to assess the validity of the approximate second-order coupled cluster (CC2) method in studying low-lying excited states of such bio-relevant systems. The studies comprise investigations of basis-set dependence as well as comparison with two multireference methods, the multistate complete active space 2nd order perturbation theory (MS-CASPT2) and the multireference difference dedicated configuration interaction (DDCI) methods. First of all, the applicability and the accuracy of the quasi-linear multireference difference dedicated configuration interaction method have been demonstrated on bio-relevant systems by comparison with the results obtained by the standard MS-CASPT2. Second, both the nature and excitation energy of the first low-lying excited state obtained at the CC2 level are very close to the Davidson corrected CAS+DDCI ones, the mean absolute deviation on the excitation energy being equal to 0.1 eV with a maximum of less than 0.2 eV. Finally, for the following low-lying excited states, if the nature is always well reproduced at the CC2 level, the differences on excitation energies become more important and can depend on the geometry.

A systematic construction of microstate geometries with low angular momentum

NASA Astrophysics Data System (ADS)

Bena, Iosif; Heidmann, Pierre; Ramírez, Pedro F.

2017-10-01

We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corre-sponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata [1], and multi-center Gibbons-Hawking spaces have been believed to give rise only to microstate geometries of BMPV black holes with a large angular mo-mentum [2]. We perform a thorough search throughout the parameter space of smooth horizonless solutions with four GH centers and find that these have an angular momentum that is generally larger than 80% of the cosmic censorship bound. However, we find that solutions with three GH centers and one supertube (which are smooth in six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our construction thus gives a recipe to build large classes of microstate geometries for zero-angular-momentum black holes without resorting to superstratum technology.

Nonassociative differential geometry and gravity with non-geometric fluxes

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Ćirić, Marija Dimitrijević; Szabo, Richard J.

2018-02-01

We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory.

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silva, Edilberto O., E-mail: edilbertoo@gmail.com; Ulhoa, Sérgio C., E-mail: sc.ulhoa@gmail.com; Andrade, Fabiano M., E-mail: f.andrade@ucl.ac.uk

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in suchmore » a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions. -- Highlights: •Motion of particle under the influence of magnetic field in curved space. •Bound state for Aharonov–Bohm problem. •Particle describing a circular path. •Determination of the self-adjoint extension parameter.« less

Crystal Melting and Wall Crossing Phenomena

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

This paper summarizes recent developments in the theory of Bogomol'nyi-Prasad-Sommerfield (BPS) state counting and the wall crossing phenomena, emphasizing in particular the role of the statistical mechanical model of crystal melting. This paper is divided into two parts, which are closely related to each other. In the first part, we discuss the statistical mechanical model of crystal melting counting BPS states. Each of the BPS states contributing to the BPS index is in one-to-one correspondence with a configuration of a molten crystal, and the statistical partition function of the melting crystal gives the BPS partition function. We also show that smooth geometry of the Calabi-Yau manifold emerges in the thermodynamic limit of the crystal. This suggests a remarkable interpretation that an atom in the crystal is a discretization of the classical geometry, giving an important clue as such to the geometry at the Planck scale. In the second part, we discuss the wall crossing phenomena. Wall crossing phenomena states that the BPS index depends on the value of the moduli of the Calabi-Yau manifold, and jumps along real codimension one subspaces in the moduli space. We show that by using type IIA/M-theory duality, we can provide a simple and an intuitive derivation of the wall crossing phenomena, furthermore clarifying the connection with the topological string theory. This derivation is consistent with another derivation from the wall crossing formula, motivated by multicentered BPS extremal black holes. We also explain the representation of the wall crossing phenomena in terms of crystal melting, and the generalization of the counting problem and the wall crossing to the open BPS invariants.

Geometric model of topological insulators from the Maxwell algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2017-11-01

We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.

The Holographic Entropy Cone

DOE PAGES

Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; ...

2015-09-21

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phasemore » space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.« less

Dietary protein, aging and nutritional geometry.

PubMed

Simpson, Stephen J; Le Couteur, David G; Raubenheimer, David; Solon-Biet, Samantha M; Cooney, Gregory J; Cogger, Victoria C; Fontana, Luigi

2017-10-01

Nearly a century of research has shown that nutritional interventions can delay aging and age- related diseases in many animal models and possibly humans. The most robust and widely studied intervention is caloric restriction, while protein restriction and restriction of various amino acids (methionine, tryptophan) have also been shown to delay aging. However, there is still debate over whether the major impact on aging is secondary to caloric intake, protein intake or specific amino acids. Nutritional geometry provides new perspectives on the relationship between nutrition and aging by focusing on calories, macronutrients and their interactions across a landscape of diets, and taking into account compensatory feeding in ad libitum-fed experiments. Nutritional geometry is a state-space modelling approach that explores how animals respond to and balance changes in nutrient availability. Such studies in insects and mice have shown that low protein, high carbohydrate diets are associated with longest lifespan in ad libitum fed animals suggesting that the interaction between macronutrients may be as important as their total intake. Copyright © 2017 Elsevier B.V. All rights reserved.

Understanding the Primary School Students' Van Hiele Levels of Geometry Thinking in Learning Shapes and Spaces: A Q-Methodology

ERIC Educational Resources Information Center

Hock, Tan Tong; Tarmizi, Rohani Ahmad; Yunus, Aida Suraya Md.; Ayub, Ahmad Fauzi

2015-01-01

This study was conducted using a new hybrid method of research which combined qualitative and quantitative designs to investigate the viewpoints of primary school students' conceptual understanding in learning geometry from the aspect of shapes and spaces according to van Hiele theory. Q-methodology is used in this research to find out what…

Bidirectional holographic codes and sub-AdS locality

NASA Astrophysics Data System (ADS)

Yang, Zhao; Hayden, Patrick; Qi, Xiaoliang

Tensor networks implementing quantum error correcting codes have recently been used as toy models of the holographic duality which explicitly realize some of the more puzzling features of the AdS/CFT correspondence. These models reproduce the Ryu-Takayanagi entropy formula for boundary intervals, and allow bulk operators to be mapped to the boundary in a redundant fashion. These exactly solvable, explicit models have provided valuable insight but nonetheless suffer from many deficiencies, some of which we attempt to address in this talk. We propose a new class of tensor network models that subsume the earlier advances and, in addition, incorporate additional features of holographic duality, including: (1) a holographic interpretation of all boundary states, not just those in a ''code'' subspace, (2) a set of bulk states playing the role of ''classical geometries'' which reproduce the Ryu-Takayanagi formula for boundary intervals, (3) a bulk gauge symmetry analogous to diffeomorphism invariance in gravitational theories, (4) emergent bulk locality for sufficiently sparse excitations, and the ability to describe geometry at sub-AdS resolutions or even flat space. David and Lucile Packard Foundation.

Bidirectional holographic codes and sub-AdS locality

NASA Astrophysics Data System (ADS)

Yang, Zhao; Hayden, Patrick; Qi, Xiao-Liang

2016-01-01

Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce the Ryu-Takayanagi entropy formula for boundary intervals, and allow bulk operators to be mapped to the boundary in a redundant fashion. These exactly solvable, explicit models have provided valuable insight but nonetheless suffer from many deficiencies, some of which we attempt to address in this article. We propose a new class of tensor network models that subsume the earlier advances and, in addition, incorporate additional features of holographic duality, including: (1) a holographic interpretation of all boundary states, not just those in a "code" subspace, (2) a set of bulk states playing the role of "classical geometries" which reproduce the Ryu-Takayanagi formula for boundary intervals, (3) a bulk gauge symmetry analogous to diffeomorphism invariance in gravitational theories, (4) emergent bulk locality for sufficiently sparse excitations, and (5) the ability to describe geometry at sub-AdS resolutions or even flat space.

Entanglement entropy and entanglement spectrum of triplet topological superconductors.

PubMed

Oliveira, T P; Ribeiro, P; Sacramento, P D

2014-10-22

We analyze the entanglement entropy properties of a 2D p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and we find numerical evidence that for this model the derivative with respect to the magnetization provides a sensible signature of each topological phase. Following the area law for the entanglement entropy, we systematically analyze the contributions that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the finite subsystem. For this model, we show that even though the topological entanglement entropy vanishes, it signals the topological phase transitions in a finite system. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state, as in other topological systems.

Early sex differences in weighting geometric cues.

PubMed

Lourenco, Stella F; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia

2011-11-01

When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when direct non-geometric information (i.e. a beacon) was also available for localizing a hidden object. Children were tested on a disorientation task with multiple phases. Across experiments, boys relied more heavily than girls on geometry to guide localization, as indicated by their errors during the initial phase of the task, and by their search choices following transformations that left only geometry available, or that, under limited conditions, created a conflict between beacon and geometry. Analyses of search times suggested that girls, like boys, had encoded geometry, and testing in a square space ruled out explanations concerned with motivational and methodological variables. Taken together, the findings provide evidence for an early sex difference in the weighting of geometry. This sex difference, we suggest, reflects subtle variation in how boys and girls approach the problem of combining multiple sources of location information. 2011 Blackwell Publishing Ltd.

Grasping versus knitting: A geometric perspective. Comment on "Hand synergies: Integration of robotics and neuroscience for understanding the control of biological and artificial hands" by M. Santello et al.

NASA Astrophysics Data System (ADS)

Laumond, Jean-Paul

2016-07-01

Grasping an object is a matter of first moving a prehensile organ at some position in the world, and then managing the contact relationship between the prehensile organ and the object. Once the contact relationship has been established and made stable, the object is part of the body and it can move in the world. As any action, the action of grasping is ontologically anchored in the physical space while the correlative movement originates in the space of the body. Robots-as any living system-access the physical space only indirectly through sensors and motors. Sensors and motors constitute the space of the body where homeostasis takes place. Physical space and both sensor space and motor space constitute a triangulation, which is the locus of the action embodiment, i.e. the locus of operations allowing the fundamental inversion between world-centered and body-centered frames. Referring to these three fundamental spaces, geometry appears as the best abstraction to capture the nature of action-driven movements. Indeed, a particular geometry is captured by a particular group of transformations of the points of a space such that every point or every direction in space can be transformed by an element of the group to every other point or direction within the group. Quoting mathematician Poincaré, the issue is not find the truest geometry but the most practical one to account for the complexity of the world [1]. Geometry is then the language fostering the dialog between neurophysiology and engineering about natural and artificial movement science and technology. Evolution has found amazing solutions that allow organisms to rapidly and efficiently manage the relationship between their body and the world [2]. It is then natural that roboticists consider taking inspiration of these natural solutions, while contributing to better understand their origin.

Use of Geometry for Spatial Reorientation in Children Applies Only to Symmetric Spaces

ERIC Educational Resources Information Center

Lew, Adina R.; Gibbons, Bryony; Murphy, Caroline; Bremner, J. Gavin

2010-01-01

Proponents of the geometric module hypothesis argue that following disorientation, many species reorient by use of macro-environment geometry. It is suggested that attention to the surface layout geometry of natural terrain features may have been selected for over evolutionary time due to the enduring and unambiguous location information it…

Calabi's conjecture and some new results in algebraic geometry

PubMed Central

Yau, Shing-Tung

1977-01-01

We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kähler structure on a complex projective space is the standard one. PMID:16592394

Asymptotic symmetries and geometry on the boundary in the first order formalism

NASA Astrophysics Data System (ADS)

Korovin, Yegor

2018-03-01

Proper understanding of the geometry on the boundary of a spacetime is a critical step on the way to extending holography to spaces with non-AdS asymptotics. In general the boundary cannot be described in terms of the Riemannian geometry and the first order formalism is more appropriate as we show. We analyze the asymptotic symmetries in the first order formalism for large classes of theories on AdS, Lifshitz or flat space. In all cases the asymptotic symmetry algebra is realized on the first order variables as a gauged symmetry algebra. First order formalism geometrizes and simplifies the analysis. We apply our framework to the issue of scale versus conformal invariance in AdS/CFT and obtain new perspective on the structure of asymptotic expansions for AdS and flat spaces.

The identification of van Hiele level students on the topic of space analytic geometry

NASA Astrophysics Data System (ADS)

Yudianto, E.; Sunardi; Sugiarti, T.; Susanto; Suharto; Trapsilasiwi, D.

2018-03-01

Geometry topics are still considered difficult by most students. Therefore, this study focused on the identification of students related to van Hiele levels. The task used from result of the development of questions related to analytical geometry of space. The results of the work involving 78 students who worked on these questions covered 11.54% (nine students) classified on a visual level; 5.13% (four students) on analysis level; 1.28% (one student) on informal deduction level; 2.56% (two students) on deduction and 2.56% (two students) on rigor level, and 76.93% (sixty students) classified on the pre-visualization level.

Black holes, anti de Sitter space, and topological strings

NASA Astrophysics Data System (ADS)

Yin, Xi

This thesis is devoted to the study of black holes in string theory, their connection to two and three dimensional anti de-Sitter space, and topological strings. We start by proposing a relation between supersymmetric black holes in four and five dimensions, as well as connections between multi-centered black holes in four dimensions and black rings in five dimensions. This connection is then applied to counting supersymmetric dyonic black holes in four dimensional string compactifications with 16 and 32 supersymmetries, respectively. We then turn to the near horizon attractor geometry AdS 2 x S2 x CY 3, and study the classical supersymmetric D-branes in this background. We also find supersymmetric black hole solutions in supergravity in AdS2 x S2, although the solutions have regions of closed timelike curves. Finally we consider the M-theory attractor geometry AdS3 x S2 x CY3, and compute the elliptic genus of the dual (0, 4) CFT by counting wrapped M2-brane states in the bulk in a dilute gas approximation. This leads to a derivation of the conjectured relation between black hole partition function and topological string amplitudes.

High-resolution structures of adenylate kinase from yeast ligated with inhibitor Ap5A, showing the pathway of phosphoryl transfer.

PubMed Central

Abele, U.; Schulz, G. E.

1995-01-01

The structure of adenylate kinase from yeast ligated with the two-substrate-mimicking inhibitor Ap5A and Mg2+ has been refined to 1.96 A resolution. In addition, the refined structure of the same complex with a bound imidazole molecule replacing Mg2+ has been determined at 1.63 A. These structures indicate that replacing Mg2+ by imidazole disturbs the water structure and thus the complex. A comparison with the G-proteins shows that Mg2+ is exactly at the same position with respect to the phosphates. However, although the Mg2+ ligand sphere of the G-proteins is a regular octahedron containing peptide ligands, the reported adenylate kinase has no such ligands and an open octahedron leaving space for the Mg2+ to accompany the transferred phosphoryl group. A superposition of the known crystalline and therefore perturbed phosphoryl transfer geometries in the adenylate kinases demonstrates that all of them are close to the start of the forward reaction with bound ATP and AMP. Averaging all observed perturbed structures gives rise to a close approximation of the transition state, indicating in general how to establish an elusive transition state geometry. The average shows that the in-line phosphoryl transfer is associative, because there is no space for a dissociative metaphosphate intermediate. As a side result, the secondary dipole interaction in the alpha-helices of both protein structures has been quantified. PMID:7670369

Teichmuller Space Resolution of the EPR Paradox

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2013-04-01

The mystery of Newton's action-at-a-distance law of gravity was resolved by Einstein with Riemann's non-Euclidean geometry, which permitted the explanation of the departure from Newton's law for the motion of Mercury. It is here proposed that the similarly mysterious non-local EPR-type quantum correlations may be explained by a Teichmuller space geometry below the Planck length, for which an experiment for its verification is proposed.

Application of the Chimera overlapped grid scheme to simulation of Space Shuttle ascent flows

NASA Technical Reports Server (NTRS)

Buning, Pieter G.; Parks, Steven J.; Chan, William M.; Renze, Kevin J.

1992-01-01

Several issues relating to the application of Chimera overlapped grids to complex geometries and flowfields are discussed. These include the addition of geometric components with different grid topologies, gridding for intersecting pieces of geometry, and turbulence modeling in grid overlap regions. Sample results are presented for transonic flow about the Space Shuttle launch vehicle. Comparisons with wind tunnel and flight measured pressures are shown.

Five dimensional microstate geometries

NASA Astrophysics Data System (ADS)

Wang, Chih-Wei

In this thesis, we discuss the possibility of exploring the statistical mechanics description of a black hole from the point view of supergravity. Specifically, we study five dimensional microstate geometries of a black hole or black ring. At first, we review the method to find the general three-charge BPS supergravity solutions proposed by Bena and Warner. By applying this method, we show the classical merger of a black ring and black hole on [Special characters omitted.] base space in general are irreversible. On the other hand, we review the solutions on ambi-polar Gibbons-Hawking (GH) base which are bubbled geometries. There are many possible microstate geometries among the bubbled geometries. Particularly, we show that a generic blob of GH points that satisfy certain conditions can be either microstate geometry of a black hole or black ring without horizon. Furthermore, using the result of the entropy analysis in classical merger as a guide, we show that one can have a merger of a black-hole blob and a black-ring blob or two black-ring blobs that corresponds to a classical irreversible merger. From the irreversible mergers, we find the scaling solutions and deep microstates which are microstate geometries of a black hole/ring with macroscopic horizon. These solutions have the same AdS throats as classical black holes/rings but instead of having infinite throats, the throat is smoothly capped off at a very large depth with some local structure at the bottom. For solutions that produced from U (1) × U (1) invariant merger, the depth of the throat is limited by flux quantization. The mass gap is related with the depth of this throat and we show the mass gap of these solutions roughly match with the mass gap of the typical conformal-field-theory (CFT) states. Therefore, based on AdS/CFT correspondence, they can be dual geometries of the typical CFT states that contribute to the entropy of a black hole/ring. On the other hand, we show that for the solutions produced from more general merger (without U (1) × U (1) invariance), the throat can be arbitrarily deep. This presents a puzzle from the point view of AdS/CFT correspondence. We propose that this puzzle may be solved by some quantization of the angle or promoting the flux vectors to quantum spins. Finally, we suggest some future directions of further study including the puzzle of arbitrary long AdS throat and a general coarse-graining picture of microstate geometries.

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Quantum detection of wormholes.

PubMed

Sabín, Carlos

2017-04-06

We show how to use quantum metrology to detect a wormhole. A coherent state of the electromagnetic field experiences a phase shift with a slight dependence on the throat radius of a possible distant wormhole. We show that this tiny correction is, in principle, detectable by homodyne measurements after long propagation lengths for a wide range of throat radii and distances to the wormhole, even if the detection takes place very far away from the throat, where the spacetime is very close to a flat geometry. We use realistic parameters from state-of-the-art long-baseline laser interferometry, both Earth-based and space-borne. The scheme is, in principle, robust to optical losses and initial mixedness.

Intrinsic two-dimensional states on the pristine surface of tellurium

NASA Astrophysics Data System (ADS)

Li, Pengke; Appelbaum, Ian

2018-05-01

Atomic chains configured in a helical geometry have fascinating properties, including phases hosting localized bound states in their electronic structure. We show how the zero-dimensional state—bound to the edge of a single one-dimensional helical chain of tellurium atoms—evolves into two-dimensional bands on the c -axis surface of the three-dimensional trigonal bulk. We give an effective Hamiltonian description of its dispersion in k space by exploiting confinement to a virtual bilayer, and elaborate on the diminished role of spin-orbit coupling. These intrinsic gap-penetrating surface bands were neglected in the interpretation of seminal experiments, where two-dimensional transport was otherwise attributed to extrinsic accumulation layers.

Magnetic state selected by magnetic dipole interaction in the kagome antiferromagnet NaBa2Mn3F11

NASA Astrophysics Data System (ADS)

Hayashida, Shohei; Ishikawa, Hajime; Okamoto, Yoshihiko; Okubo, Tsuyoshi; Hiroi, Zenji; Avdeev, Maxim; Manuel, Pascal; Hagihala, Masato; Soda, Minoru; Masuda, Takatsugu

2018-02-01

We haved studied the ground state of the classical kagome antiferromagnet NaBa2Mn3F11 . Strong magnetic Bragg peaks observed for d spacings shorter than 6.0 Å were indexed by the propagation vector of k0=(0 ,0 ,0 ) . Additional peaks with weak intensities in the d -spacing range above 8.0 Å were indexed by the incommensurate vector of k1=[0.3209 (2 ) ,0.3209 (2 ) ,0 ] and k2=[0.3338 (4 ) ,0.3338 (4 ) ,0 ] . Magnetic structure analysis unveils a 120∘ structure with the tail-chase geometry having k0 modulated by the incommensurate vector. A classical calculation of the Heisenberg kagome antiferromagnet with antiferromagnetic second-neighbor interaction, for which the ground state a k0120∘ degenerated structure, reveals that the magnetic dipole-dipole (MDD) interaction including up to the fourth neighbor terms selects the tail-chase structure. The observed modulation of the tail-chase structure is attributed to a small perturbation such as the long-range MDD interaction or the interlayer interaction.

Dynamical initial-state model for relativistic heavy-ion collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Chun; Schenke, Bjorn

We present a fully three-dimensional model providing initial conditions for energy and net-baryon density distributions in heavy ion collisions at arbitrary collision energy. The model includes the dynamical deceleration of participating nucleons or valence quarks, depending on the implementation. The duration of the deceleration continues until the string spanned between colliding participants is assumed to thermalize, which is either after a fixed proper time, or a uctuating time depending on sampled final rapidities. Energy is deposited in space-time along the string, which in general will span a range of space-time rapidities and proper times. We study various observables obtained directlymore » from the initial state model, including net-baryon rapidity distributions, 2-particle rapidity correlations, as well as the rapidity decorrelation of the transverse geometry. Their dependence on the model implementation and parameter values is investigated. Here, we also present the implementation of the model with 3+1 dimensional hydrodynamics, which involves the addition of source terms that deposit energy and net-baryon densities produced by the initial state model at proper times greater than the initial time for the hydrodynamic simulation.« less

Dynamical initial-state model for relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Shen, Chun; Schenke, Björn

2018-02-01

We present a fully three-dimensional model providing initial conditions for energy and net-baryon density distributions in heavy-ion collisions at arbitrary collision energy. The model includes the dynamical deceleration of participating nucleons or valence quarks, depending on the implementation. The duration of the deceleration continues until the string spanned between colliding participants is assumed to thermalize, which is either after a fixed proper time, or a fluctuating time depending on sampled final rapidities. Energy is deposited in space time along the string, which in general will span a range of space-time rapidities and proper times. We study various observables obtained directly from the initial-state model, including net-baryon rapidity distributions, two-particle rapidity correlations, as well as the rapidity decorrelation of the transverse geometry. Their dependence on the model implementation and parameter values is investigated. We also present the implementation of the model with 3+1-dimensional hydrodynamics, which involves the addition of source terms that deposit energy and net-baryon densities produced by the initial-state model at proper times greater than the initial time for the hydrodynamic simulation.

Dynamical initial-state model for relativistic heavy-ion collisions

DOE PAGES

Shen, Chun; Schenke, Bjorn

2018-02-15

We present a fully three-dimensional model providing initial conditions for energy and net-baryon density distributions in heavy ion collisions at arbitrary collision energy. The model includes the dynamical deceleration of participating nucleons or valence quarks, depending on the implementation. The duration of the deceleration continues until the string spanned between colliding participants is assumed to thermalize, which is either after a fixed proper time, or a uctuating time depending on sampled final rapidities. Energy is deposited in space-time along the string, which in general will span a range of space-time rapidities and proper times. We study various observables obtained directlymore » from the initial state model, including net-baryon rapidity distributions, 2-particle rapidity correlations, as well as the rapidity decorrelation of the transverse geometry. Their dependence on the model implementation and parameter values is investigated. Here, we also present the implementation of the model with 3+1 dimensional hydrodynamics, which involves the addition of source terms that deposit energy and net-baryon densities produced by the initial state model at proper times greater than the initial time for the hydrodynamic simulation.« less

Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions.

PubMed

Vlaisavljevich, Bess; Shiozaki, Toru

2016-08-09

We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multistate complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also considered in this work. This is an extension of the fully internally contracted CASPT2 nuclear gradient program recently developed for a state-specific variant by us [MacLeod and Shiozaki, J. Chem. Phys. 2015, 142, 051103]; in this extension, the so-called λ equation is solved to account for the variation of the multistate CASPT2 energies with respect to the change in the amplitudes obtained in the preceding state-specific CASPT2 calculations, and the Z vector equations are modified accordingly. The program is parallelized using the MPI3 remote memory access protocol that allows us to perform efficient one-sided communication. The optimized geometries of the ground and excited states of a copper corrole and benzophenone are presented as numerical examples. The code is publicly available under the GNU General Public License.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

Coupling impedance and wake functions for laminated structures with an application to the Fermilab Booster

DOE PAGES

Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James; ...

2011-06-28

We calculate the impedance and wake functions for laminated structures with parallel-plane and circular geometries. We critically examine the approximations used in the literature for the coupling impedance in laminated chambers and find that most of them are not justified because the wall surface impedance is large. A comparison between flat and circular geometry impedances is presented. We apply our calculation in a state-of-the-art beam dynamics simulation of the Fermilab Booster which includes nonlinear optics, laminated wakefields, and space charge impedance. The latter can have a significant effect away from the ultrarelativistic limit. Even though the simulations and the comparisonmore » with the experiment are done at the Booster injection energy, where the relativistic factor γ = 1.42, we find good agreement between our calculation of the coherent tune shift and recent experimental measurements.« less

Synthesis, crystal structure, biological activity and theoretical calculations of novel isoxazole derivatives

NASA Astrophysics Data System (ADS)

Jin, R. Y.; Sun, X. H.; Liu, Y. F.; Long, W.; Chen, B.; Shen, S. Q.; Ma, H. X.

2016-01-01

Series of isoxazole derivatives were synthesized by substituted chalcones and 2-chloro-6-fluorobenzene formaldehyde oxime with 1,3-dipolar cycloaddition. The target compounds were determined by melting point, IR, 1H NMR, elemental analyses and HRMS. The crystal structure of compound 3a was detected by X-ray diffraction and it crystallizes in the triclinic space group p2(1)/c with z = 4. The molecular geometry of compound 3a was optimized using density functional theory (DFT/B3LYP) method with the 6-31G+(d,p) basis set in the ground state. From the optimized geometry of the molecule, FT-IR, FT-Raman, HOMO-LUMO and natural bond orbital (NBO) were calculated at B3LYP/6-31G+(d,p) level. Finally, the antifungal activity of the synthetic compounds were evaluated against Pythium solani, Gibberella nicotiancola, Fusarium oxysporium f.sp. niveum and Gibberella saubinetii.

Estimation of attitude sensor timetag biases

NASA Technical Reports Server (NTRS)

Sedlak, J.

1995-01-01

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Towards the Geometry of Reproducing Kernels

NASA Astrophysics Data System (ADS)

Galé, J. E.

2010-11-01

It is shown here how one is naturally led to consider a category whose objects are reproducing kernels of Hilbert spaces, and how in this way a differential geometry for such kernels may be settled down.

Joint U.S./Japan Conference on Adaptive Structures, 1st, Maui, HI, Nov. 13-15, 1990, Proceedings

NASA Technical Reports Server (NTRS)

Wada, Ben K. (Editor); Fanson, James L. (Editor); Miura, Koryo (Editor)

1991-01-01

The present volume of adaptive structures discusses the development of control laws for an orbiting tethered antenna/reflector system test scale model, the sizing of active piezoelectric struts for vibration suppression on a space-based interferometer, the control design of a space station mobile transporter with multiple constraints, and optimum configuration control of an intelligent truss structure. Attention is given to the formulation of full state feedback for infinite order structural systems, robustness issues in the design of smart structures, passive piezoelectric vibration damping, shape control experiments with a functional model for large optical reflectors, and a mathematical basis for the design optimization of adaptive trusses in precision control. Topics addressed include approaches to the optimal adaptive geometries of intelligent truss structures, the design of an automated manufacturing system for tubular smart structures, the Sandia structural control experiments, and the zero-gravity dynamics of space structures in parabolic aircraft flight.

Joint U.S./Japan Conference on Adaptive Structures, 1st, Maui, HI, Nov. 13-15, 1990, Proceedings

NASA Astrophysics Data System (ADS)

Wada, Ben K.; Fanson, James L.; Miura, Koryo

1991-11-01

The present volume of adaptive structures discusses the development of control laws for an orbiting tethered antenna/reflector system test scale model, the sizing of active piezoelectric struts for vibration suppression on a space-based interferometer, the control design of a space station mobile transporter with multiple constraints, and optimum configuration control of an intelligent truss structure. Attention is given to the formulation of full state feedback for infinite order structural systems, robustness issues in the design of smart structures, passive piezoelectric vibration damping, shape control experiments with a functional model for large optical reflectors, and a mathematical basis for the design optimization of adaptive trusses in precision control. Topics addressed include approaches to the optimal adaptive geometries of intelligent truss structures, the design of an automated manufacturing system for tubular smart structures, the Sandia structural control experiments, and the zero-gravity dynamics of space structures in parabolic aircraft flight.

Self-report captures 27 distinct categories of emotion bridged by continuous gradients.

PubMed

Cowen, Alan S; Keltner, Dacher

2017-09-19

Emotions are centered in subjective experiences that people represent, in part, with hundreds, if not thousands, of semantic terms. Claims about the distribution of reported emotional states and the boundaries between emotion categories-that is, the geometric organization of the semantic space of emotion-have sparked intense debate. Here we introduce a conceptual framework to analyze reported emotional states elicited by 2,185 short videos, examining the richest array of reported emotional experiences studied to date and the extent to which reported experiences of emotion are structured by discrete and dimensional geometries. Across self-report methods, we find that the videos reliably elicit 27 distinct varieties of reported emotional experience. Further analyses revealed that categorical labels such as amusement better capture reports of subjective experience than commonly measured affective dimensions (e.g., valence and arousal). Although reported emotional experiences are represented within a semantic space best captured by categorical labels, the boundaries between categories of emotion are fuzzy rather than discrete. By analyzing the distribution of reported emotional states we uncover gradients of emotion-from anxiety to fear to horror to disgust, calmness to aesthetic appreciation to awe, and others-that correspond to smooth variation in affective dimensions such as valence and dominance. Reported emotional states occupy a complex, high-dimensional categorical space. In addition, our library of videos and an interactive map of the emotional states they elicit (https://s3-us-west-1.amazonaws.com/emogifs/map.html) are made available to advance the science of emotion.

Self-report captures 27 distinct categories of emotion bridged by continuous gradients

PubMed Central

Keltner, Dacher

2017-01-01

Emotions are centered in subjective experiences that people represent, in part, with hundreds, if not thousands, of semantic terms. Claims about the distribution of reported emotional states and the boundaries between emotion categories—that is, the geometric organization of the semantic space of emotion—have sparked intense debate. Here we introduce a conceptual framework to analyze reported emotional states elicited by 2,185 short videos, examining the richest array of reported emotional experiences studied to date and the extent to which reported experiences of emotion are structured by discrete and dimensional geometries. Across self-report methods, we find that the videos reliably elicit 27 distinct varieties of reported emotional experience. Further analyses revealed that categorical labels such as amusement better capture reports of subjective experience than commonly measured affective dimensions (e.g., valence and arousal). Although reported emotional experiences are represented within a semantic space best captured by categorical labels, the boundaries between categories of emotion are fuzzy rather than discrete. By analyzing the distribution of reported emotional states we uncover gradients of emotion—from anxiety to fear to horror to disgust, calmness to aesthetic appreciation to awe, and others—that correspond to smooth variation in affective dimensions such as valence and dominance. Reported emotional states occupy a complex, high-dimensional categorical space. In addition, our library of videos and an interactive map of the emotional states they elicit (https://s3-us-west-1.amazonaws.com/emogifs/map.html) are made available to advance the science of emotion. PMID:28874542

Nd:YAG end pumped by semiconductor laser arrays for free space optical communications

NASA Technical Reports Server (NTRS)

Sipes, D. L., Jr.

1985-01-01

Preliminary experimental results are reported for a diode-pumped Nd:YAG laser employing a tightly focused end-pump geometry. The resonator configuration is planoconcave, with the pumped end of the Nd:YAG rod being coated for high reflection at 1.06 microns. This geometry rectifies nearly all the inefficiencies plaguing side-pumped schemes. This laser is further considered as a candidate for optical communication over the deep space channel.

Testing the limits of sensitivity in a solid-state structural investigation by combined X-ray powder diffraction, solid-state NMR, and molecular modelling.

PubMed

Filip, Xenia; Borodi, Gheorghe; Filip, Claudiu

2011-10-28

A solid state structural investigation of ethoxzolamide is performed on microcrystalline powder by using a multi-technique approach that combines X-ray powder diffraction (XRPD) data analysis based on direct space methods with information from (13)C((15)N) solid-state Nuclear Magnetic Resonance (SS-NMR) and molecular modeling. Quantum chemical computations of the crystal were employed for geometry optimization and chemical shift calculations based on the Gauge Including Projector Augmented-Wave (GIPAW) method, whereas a systematic search in the conformational space was performed on the isolated molecule using a molecular mechanics (MM) approach. The applied methodology proved useful for: (i) removing ambiguities in the XRPD crystal structure determination process and further refining the derived structure solutions, and (ii) getting important insights into the relationship between the complex network of non-covalent interactions and the induced supra-molecular architectures/crystal packing patterns. It was found that ethoxzolamide provides an ideal case study for testing the accuracy with which this methodology allows to distinguish between various structural features emerging from the analysis of the powder diffraction data. This journal is © the Owner Societies 2011

Deconstructing field-induced ketene isomerization through Lagrangian descriptors.

PubMed

Craven, Galen T; Hernandez, Rigoberto

2016-02-07

The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter-Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.

Reply to ``Comment on `Relative locality and the soccer ball problem'''

NASA Astrophysics Data System (ADS)

Amelino-Camelia, Giovanni; Freidel, Laurent; Kowalski-Glikman, Jerzy; Smolin, Lee

2013-07-01

In a Comment [S. Hossenfelder Phys. Rev. D 88, 028701 (2013)], Hossenfelder proposes a generalization of the results we reported in [Phys. Rev. D 84, 087702 (2011)] and argues that thermal fluctuations introduce incurable pathologies for the description of macroscopic bodies in the relative-locality framework. We here show that Hossenfelder’s analysis, while raising a very interesting point, is incomplete and leads to incorrect conclusions. Her estimate for the fluctuations did not take into account some contributions from the geometry of momentum space, which must be included at the relevant order of approximation. Using the full expression here derived, one finds that thermal fluctuations are not, in general, large for macroscopic bodies in the relative-locality framework. We find that such corrections can be unexpectedly large only for some choices of momentum-space geometry, and we comment on the possibility of developing a phenomenology suitable for possibly ruling out such geometries of momentum space.

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

NASA Astrophysics Data System (ADS)

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-05-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.

Marginal deformations of heterotic G 2 sigma models

NASA Astrophysics Data System (ADS)

Fiset, Marc-Antoine; Quigley, Callum; Svanes, Eirik Eik

2018-02-01

Recently, the infinitesimal moduli space of heterotic G 2 compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST operator. This BRST operator is nilpotent if and only if the target space geometry satisfies the heterotic supersymmetry conditions. We relate this to the supergravity approach by showing that the corresponding cohomologies are indeed isomorphic. We work at tree-level in α' perturbation theory and study general geometries, in particular with non-vanishing torsion.

A crystallographic investigation of GaN nanostructures by reciprocal space mapping in a grazing incidence geometry.

PubMed

Lee, Sanghwa; Sohn, Yuri; Kim, Chinkyo; Lee, Dong Ryeol; Lee, Hyun-Hwi

2009-05-27

Reciprocal space mapping with a two-dimensional (2D) area detector in a grazing incidence geometry was applied to determine crystallographic orientations of GaN nanostructures epitaxially grown on a sapphire substrate. By using both unprojected and projected reciprocal space mapping with a proper coordinate transformation, the crystallographic orientations of GaN nanostructures with respect to that of a substrate were unambiguously determined. In particular, the legs of multipods in the wurtzite phase were found to preferentially nucleate on the sides of tetrahedral cores in the zinc blende phase.

Dynamics and control of state-dependent networks for probing genomic organization

PubMed Central

Rajapakse, Indika; Groudine, Mark; Mesbahi, Mehran

2011-01-01

A state-dependent dynamic network is a collection of elements that interact through a network, whose geometry evolves as the state of the elements changes over time. The genome is an intriguing example of a state-dependent network, where chromosomal geometry directly relates to genomic activity, which in turn strongly correlates with geometry. Here we examine various aspects of a genomic state-dependent dynamic network. In particular, we elaborate on one of the important ramifications of viewing genomic networks as being state-dependent, namely, their controllability during processes of genomic reorganization such as in cell differentiation. PMID:21911407

Natural polypeptide scaffolds: beta-sheets, beta-turns, and beta-hairpins.

PubMed

Rotondi, Kenneth S; Gierasch, Lila M

2006-01-01

This paper provides an introduction to fundamental conformational states of polypeptides in the beta-region of phi,psi space, in which the backbone is extended near to its maximal length, and to more complex architectures in which extended segments are linked by turns and loops. There are several variants on these conformations, and they comprise versatile scaffolds for presentation of side chains and backbone amides for molecular recognition and designed catalysts. In addition, the geometry of these fundamental folds can be readily mimicked in peptidomimetics. Copyright 2005 Wiley Periodicals, Inc.

Covalent Electron Transfer Theory of Superconductivity

DTIC Science & Technology

1992-06-19

carriers. This situation is analogous to a vacuum diode without space charge, where each electron emitted from the cathode arrives at the anode before...Generic MO energy level diagram for a do cation in an oxygen octahedral complex. 89 53 Band model approximation of the MO states of a Cu perovskite ...C2) CuO4 complex. 94 57 p-type 3d 2,2-2p a Cu2+-O-Cu3+ covalent transfer in I 80-deg perovskite bond 95 geometry for d9 - d8(low-spin). xi LIST OF

OPS MCC level B/C formulation requirements: Area targets and space volumes processor

NASA Technical Reports Server (NTRS)

Bishop, M. J., Jr.

1979-01-01

The level B/C mathematical specifications for the area targets and space volumes processor (ATSVP) are described. The processor is designed to compute the acquisition-of-signal (AOS) and loss-of-signal (LOS) times for area targets and space volumes. The characteristics of the area targets and space volumes are given. The mathematical equations necessary to determine whether the spacecraft lies within the area target or space volume are given. These equations provide a detailed model of the target geometry. A semianalytical technique for predicting the AOS and LOS time periods is disucssed. This technique was designed to bound the actual visibility period using a simplified target geometry model and unperturbed orbital motion. Functional overview of the ATSVP is presented and it's detailed logic flow is described.

Influence of geometry on pressure and velocity distribution in packed-bed methanol steam reforming reactor

NASA Astrophysics Data System (ADS)

Ivanović, Ivana; Sedmak, Aleksandar; Milošević, Miloš; Cvetković, Ivana; Pohar, Andrej; Likozar, Blaž

2017-07-01

The main tasks of this research is to propose several changes in the packed bed micro methanol steam reformer geometry in order to ensure its performance. The reformer is an integral part of the existing indirect internal reforming high temperature PEMFC and most of its geometry is already defined. The space for remodeling is very limited.

The role of geometry in 4-vertex origami mechanics

NASA Astrophysics Data System (ADS)

Waitukaitis, Scott; Dieleman, Peter; van Hecke, Martin

Origami offers an interesting design platform metamaterials because it strongly couples mechanics with geometry. Even so, most research carried out so far has been limited to one or two particular patterns. I will discuss the full geometrical space of the most common origami building block, the 4-vertex, and show how exotic geometries can have dramatic effects on the mechanics.

Making Conjectures in Dynamic Geometry: The Potential of a Particular Way of Dragging

ERIC Educational Resources Information Center

Mariotti, Maria Alessandra; Baccaglini-Frank, Anna

2011-01-01

When analyzing what has changed in the geometry scenario with the advent of dynamic geometry systems (DGS), one can notice a transition from the traditional graphic environment made of paper-and-pencil, and the classical construction tools like the ruler and compass, to a virtual graphic space, made of a computer screen, graphical tools that are…

Understanding the On-Off Switching Mechanism in Cationic Tetravalent Group-V-Based Fluoride Molecular Sensors Using Orbital Analysis.

PubMed

Usui, Kosuke; Ando, Mikinori; Yokogawa, Daisuke; Irle, Stephan

2015-12-24

The precise control of on-off switching is essential to the design of ideal molecular sensors. To understand the switching mechanism theoretically, we selected as representative example a 9-anthryltriphenylstibonium cation, which was reported as a fluoride ion sensor. In this molecule, the first excited singlet state exhibits two minimum geometries, where one of them is emissive and the other one dark. The excited state at the geometry with bright emission is of π-π* character, whereas it is of π-σ* character at the "dark" geometry. Geometry changes in the excited state were identified by geometry optimization and partial potential energy surface (PES) mapping. We also studied Group V homologues of this molecule. A barrierless relaxation pathway after vertical excitation to the "dark" geometry was found for the Sb-containing compound on the excited-states PES, whereas barriers appear in the case of P and As. Molecular orbital analysis suggests that the σ* orbital of the antimony compound is stabilized along such relaxation and that the excited state changes its nature correspondingly. Our results indicate that the size of the central atom is crucial for the design of fluoride sensors with this ligand framework.

A geometric measure of dark energy with pairs of galaxies.

PubMed

Marinoni, Christian; Buzzi, Adeline

2010-11-25

Observations indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance (Ω(X)) and equation of state (W(X)) of dark energy. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at Ω(k)≡0 and the dark energy equation-of-state parameter at W(X)≡-1, and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and -0.85>W(X)>-1.12 and 0.60<Ω(X)<0.80.

Generalized Ehrenfest Relations, Deformation Quantization, and the Geometry of Inter-model Reduction

NASA Astrophysics Data System (ADS)

Rosaler, Joshua

2018-03-01

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \\hbar → 0, and, on the other, a certain generalization of Ehrenfest's Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models.

Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors

NASA Astrophysics Data System (ADS)

Bärenz, Manuel; Barrett, John

2017-11-01

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed.

Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors

NASA Astrophysics Data System (ADS)

Bärenz, Manuel; Barrett, John

2018-06-01

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed.

Generalized Kähler geometry and current algebras in classical N=2 superconformal WZW model

NASA Astrophysics Data System (ADS)

Parkhomenko, S. E.

2018-04-01

I examine the Generalized Kähler (GK) geometry of classical N = (2, 2) superconformal WZW model on a compact group and relate the right-moving and left-moving Kac-Moody superalgebra currents to the GK geometry data using biholomorphic gerbe formulation and Hamiltonian formalism. It is shown that the canonical Poisson homogeneous space structure induced by the GK geometry of the group manifold is crucial to provide N = (2, 2) superconformal σ-model with the Kac-Moody superalgebra symmetries. Then, the biholomorphic gerbe geometry is used to prove that Kac-Moody superalgebra currents are globally defined.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Livine, Etera R.

We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)).more » We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in a similar fashion trading the unitary group for the orthogonal group. We conclude with a discussion of the possible (deformation) dynamics that one can define on the space of polygons or polyhedra. This work is a priori useful in the context of discrete geometry but it should hopefully also be relevant to (loop) quantum gravity in 2+1 and 3+1 dimensions when the quantum geometry is defined in terms of gluing of (quantized) polygons and polyhedra.« less

Electronic excitations in long polyenes revisited

NASA Astrophysics Data System (ADS)

Schmidt, Maximilian; Tavan, Paul

2012-03-01

We apply the valence shell model OM2 [W. Weber and W. Thiel, Theor. Chem. Acc. 103, 495, (2000), 10.1007/s002149900083] combined with multireference configuration interaction (MRCI) to compute the vertical excitation energies and transition dipole moments of the low-energy singlet excitations in the polyenes with 4 ⩽ N ⩽ 22π-electrons. We find that the OM2/MRCI descriptions closely resemble those of Pariser-Parr-Pople (PPP) π-electron models [P. Tavan and K. Schulten, Phys. Rev. B 36, 4337, (1987)], if equivalent MRCI procedures and regularly alternating model geometries are used. OM2/MRCI optimized geometries are shown to entail improved descriptions particularly for smaller polyenes (N ⩽ 12), for which sizeable deviations from the regular model geometries are found. With configuration interaction active spaces covering also the σ- in addition to the π-electrons, OM2/MRCI excitation energies turn out to become smaller by at most 0.35 eV for the ionic and 0.15 eV for the covalent excitations. The particle-hole (ph) symmetry, which in Pariser-Parr-Pople models arises from the zero-differential overlap approximation, is demonstrated to be only weakly broken in OM2 such that the oscillator strengths of the covalent 1B_u^- states, which artificially vanish in ph-symmetric models, are predicted to be very small. According to OM2/MRCI and experimental data the 1B_u^- state is the third excited singlet state for N < 12 and becomes the second for N ⩾ 14. By comparisons with results of other theoretical approaches and experimental evidence we argue that deficiencies of the particular MRCI method employed by us, which show up in a poor size consistency of the covalent excitations for N > 12, are caused by its restriction to at most doubly excited references.

Intersecting solitons, amoeba, and tropical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujimori, Toshiaki; Nitta, Muneto; Ohta, Kazutoshi

2008-11-15

We study the generic intersection (or web) of vortices with instantons inside, which is a 1/4 Bogomol'nyi-Prasad-Sommerfield state in the Higgs phase of five-dimensional N=1 supersymmetric U(N{sub C}) gauge theory on R{sub t}x(C*){sup 2}{approx_equal}R{sup 2,1}xT{sup 2} with N{sub F}=N{sub C} Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (N{sub F}=N{sub C}=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortexmore » charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C*){sup 2}. The Wilson loops in T{sup 2} are related with derivatives of the Ronkin function. The general form of the Kaehler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.« less

Vertex Space Analysis for Model-Based Target Recognition.

DTIC Science & Technology

1996-08-01

performed in our unique invariant representation, Vertex Space, that reduces both the dimensionality and size of the required search space. Vertex Space ... mapping results in a reduced representation that serves as a characteristic target signature which is invariant to four of the six viewing geometry

Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.

A structurally adaptive space crane concept for assembling space systems on orbit

NASA Technical Reports Server (NTRS)

Dorsey, John T.; Sutter, Thomas R.; Wu, K. C.

1992-01-01

A space crane concept is presented which is based on erectable truss hardware to achieve high stiffness and low mass booms and articulating-truss joints which can be assembled on orbit. The hardware is characterized by linear load-deflection response and is structurally predictable. The crane can be reconfigured into different geometries to meet future assembly requirements. Articulating-truss joint concepts with significantly different geometries are analyzed and found to have similar static and dynamic performance, which indicates that criteria other than structural and kinematic performance can be used to select a joint. Passive damping and an open-loop preshaped command input technique greatly enhance the structural damping in the space crane and may preclude the need for an active vibrations suppression system.

Effects of Using Dynamic Mathematics Software on Preservice Mathematics Teachers' Spatial Visualization Skills: The Case of Spatial Analytic Geometry

ERIC Educational Resources Information Center

Kösa, Temel

2016-01-01

The purpose of this study was to investigate the effects of using dynamic geometry software on preservice mathematics teachers' spatial visualization skills and to determine whether spatial visualization skills can be a predictor of success in learning analytic geometry of space. The study used a quasi-experimental design with a control group.…

A low-order model of the equatorial ocean-atmosphere system

NASA Astrophysics Data System (ADS)

Legnani, Roberto

A low order model of the equatorial ocean-atmosphere coupled system is presented. The model atmosphere includes a hydrological cycle with cloud-radiation interaction. The model ocean is based on mixed layer dynamics with a parameterization of entrainment processes. The coupling takes place via transfer to momentum, sensible heat, latent heat and short wave and long wave radiation through the ocean surface. The dynamical formulation is that of the primitive equations of an equatorial beta-plane, with zonally periodic and meridionally infinite geometry. The system is expanded into the set of normal modes pertinent to the linear problem and severly truncated to a few modes; 54 degrees of freedom are retained. Some nonlinear terms of the equations are evaluated in physical space and then projected onto the functional space; other terms are evaluated directly in the functional space. Sensitivity tests to variations of the parameters are performed, and some results from 10-year initial value simulations are presented. The model is capable of supporting oscillations of different time scales, ranging from a few days to a few years; it prefers a particular zonally asymmetric state, but temporarily switches to a different (opposite) zonally asymmetric state in an event-like fashion.

a Low-Order Model of the Equatorial Ocean-Atmosphere System.

NASA Astrophysics Data System (ADS)

Legnani, Roberto

A low order model of the equatorial ocean-atmosphere coupled system is presented. The model atmosphere includes a hydrological cycle with cloud-radiation interaction. The model ocean is based on mixed layer dynamics with a parameterization of entrainment processes. The coupling takes place via transfer to momentum, sensible heat, latent heat and short -wave and long-wave radiation through the ocean surface. The dynamical formulation is that of the primitive equations of an equatorial beta-plane, with zonally periodic and meridionally infinite geometry. The system is expanded into the set of normal modes pertinent to the linear problem and severely truncated to a few modes; 54 degrees of freedom are retained. Some nonlinear terms of the equations are evaluated in physical space and then projected onto the functional space; other terms are evaluated directly in the functional space. Sensitivity tests to variations of the parameters are performed, and some results from 10-year initial value simulations are presented. The model is capable of supporting oscillations of different time scales, ranging from a few days to a few years; it prefers a particular zonally asymmetric state, but temporarily switches to a different (opposite) zonally asymmetric state in an event-like fashion.

Non-minimally coupled condensate cosmologies: a phase space analysis

NASA Astrophysics Data System (ADS)

Carloni, Sante; Vignolo, Stefano; Cianci, Roberto

2014-09-01

We present an analysis of the phase space of cosmological models based on a non-minimal coupling between the geometry and a fermionic condensate. We observe that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models, and at the same time guarantees an evolution towards a state indistinguishable from general relativistic cosmological models. In this light, we show in detail how the use of some specific potentials can naturally reproduce a phase of accelerated expansion. In particular, we find for the first time that an exponential potential is able to induce two de Sitter phases separated by a power law expansion, which could be an interesting model for the unification of an inflationary phase and a dark energy era.

Simplified analysis and optimization of space base and space shuttle heat rejection systems

NASA Technical Reports Server (NTRS)

Wulff, W.

1972-01-01

A simplified radiator system analysis was performed to predict steady state radiator system performance. The system performance was found to be describable in terms of five non-dimensional system parameters. The governing differential equations are integrated numerically to yield the enthalpy rejection for the coolant fluid. The simplified analysis was extended to produce the derivatives of the coolant exit temperature with respect to the governing system parameters. A procedure was developed to find the optimum set of system parameters which yields the lowest possible coolant exit temperature for either a given projected area or a given total mass. The process can be inverted to yield either the minimum area or the minimum mass, together with the optimum geometry, for a specified heat rejection rate.

The Use of Geometry Learning Media Based on Augmented Reality for Junior High School Students

NASA Astrophysics Data System (ADS)

Rohendi, D.; Septian, S.; Sutarno, H.

2018-02-01

Understanding the geometry especially of three-dimensional space is still considered difficult by some students. Therefore, a learning innovation is required to overcome students’ difficulties in learning geometry. In this research, we developed geometry learning media based on augmented reality in android flatform’s then it was implemented in teaching three-dimensional objects for some junior high school students to find out: how is the students response in using this new media in geometry and is this media can solve the student’s difficulties in understanding geometry concept. The results showed that the use of geometry learning media based on augmented reality in android flatform is able to get positive responses from the students in learning geometry concepts especially three-dimensional objects and students more easy to understand concept of diagonal in geometry than before using this media.

Asymmetry between absorption and photoluminescence line shapes of TPD: spectroscopic fingerprint of the twisted biphenyl core.

PubMed

Scholz, Reinhard; Gisslén, Linus; Himcinschi, Cameliu; Vragović, Igor; Calzado, Eva M; Louis, Enrique; San Fabián Maroto, Emilio; Díaz-García, María A

2009-01-08

We analyze absorption, photoluminescence (PL), and resonant Raman spectra of N,N'-diphenyl-N,N'-bis(3-methylphenyl)-(1,1'-biphenyl)-4,4'-diamine (TPD), with the aim of providing a microscopic interpretation of a significant Stokes shift of about 0.5 eV that makes this material suitable for stimulated emission. The optical spectra were measured for TPD dissolved in toluene and chloroform, as well as for polystyrene films doped with varying amounts of TPD. In addition, we measured preresonant and resonant Raman spectra, giving direct access to the vibrational modes elongated in the relaxed excited geometry of the molecule. The experimental data are interpreted with calculations of the molecular geometry in the electronic ground state and the optically excited state using density functional theory. Several strongly elongated high-frequency modes within the carbon rings results in a vibronic progression with a calculated spacing of 158 meV, corroborated by the observation of vibrational sidebands in the PL spectra. The peculiarities of the potential energy surfaces related to a twisting around the central bond in the biphenyl core of TPD allow to quantify the asymmetry between the line shapes observed in absorption and emission.

Black Holes as Brains: Neural Networks with Area Law Entropy

NASA Astrophysics Data System (ADS)

Dvali, Gia

2018-04-01

Motivated by the potential similarities between the underlying mechanisms of the enhanced memory storage capacity in black holes and in brain networks, we construct an artificial quantum neural network based on gravity-like synaptic connections and a symmetry structure that allows to describe the network in terms of geometry of a d-dimensional space. We show that the network possesses a critical state in which the gapless neurons emerge that appear to inhabit a (d-1)-dimensional surface, with their number given by the surface area. In the excitations of these neurons, the network can store and retrieve an exponentially large number of patterns within an arbitrarily narrow energy gap. The corresponding micro-state entropy of the brain network exhibits an area law. The neural network can be described in terms of a quantum field, via identifying the different neurons with the different momentum modes of the field, while identifying the synaptic connections among the neurons with the interactions among the corresponding momentum modes. Such a mapping allows to attribute a well-defined sense of geometry to an intrinsically non-local system, such as the neural network, and vice versa, it allows to represent the quantum field model as a neural network.

Studies on N-picolinoyl-N‧-benzothioylhydrazide and its Zn(II) complex: Synthesis, structure, antibacterial activity, thermal analysis and DFT calculation

NASA Astrophysics Data System (ADS)

Kushawaha, S. K.; Dani, R. K.; Bharty, M. K.; Chaudhari, U. K.; Sharma, V. K.; Kharwar, R. N.; Singh, N. K.

2014-04-01

A new Zn(II) complex [Zn(pbth)2] (where Hpbth = N-picolinoyl-N‧-benzothioylhydrazide) has been synthesized and characterized by elemental analyses, IR, UV-Visible and single crystal X-ray data. The distorted octahedral complex [Zn(pbth)2] crystallizes in monoclinic system with space group C2/c and is stabilized by various types of inter and intramolecular extended hydrogen bonding providing supramolecular framework. The optimized molecular geometry of N-picolinoyl-N‧-benzothioylhydrazide (Hpbth) and the zinc complex in the ground state have been calculated by using the DFT method using B3LYP functional with 6-311 G(d,p){C,H,N,O,S}/Lanl2DZ basis set. The results of the optimized molecular geometry are presented and compared with the experimental X-ray diffraction data. In addition, quantum chemical calculations of Hpbth and the complex, molecular electrostatic potential (MEP), contour map and frontier molecular orbital analysis were performed. The solid state electrical conductivity and thermal behaviour (TGA) of the complex were investigated. The bioefficacy of the complex has been examined against the growth of bacteria in vitro to evaluate its anti-microbial potential.

Finsler-type modification of the Coulomb law

NASA Astrophysics Data System (ADS)

Itin, Yakov; Lämmerzahl, Claus; Perlick, Volker

2014-12-01

Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest a modified dispersion relation which could be phrased in terms of Finsler geometry. On a Finslerian space-time, the universality of free fall is still satisfied but local Lorentz invariance is violated in a way not covered by standard Lorentz invariance violation schemes. In this paper we consider a Finslerian modification of Maxwell's equations. The corrections to the Coulomb potential and to the hydrogen energy levels are computed. We find that the Finsler metric corrections yield a splitting of the energy levels. Experimental data provide bounds for the Finsler parameters.

Impingement Flow Heat Transfer Measurements of Turbine Blades Using a Jet Array

DTIC Science & Technology

1994-08-01

jet spacing of Sd and a plate thickness to jet diameter of 1.2. ExP were acoplished for a range of impingemet plate to target surface spacings z ( 1...Performance Improvements 1.2.1 Materials Monolithic ceramics have a good high temperature strength in the 1900 K range and a resistance to oxidation in the...with z in this range . Thes correlations do not apply to the inlet geometry and jet confinement of the current experiments. Their experimental geometry

SPICE: A Geometry Information System Supporting Planetary Mapping, Remote Sensing and Data Mining

NASA Technical Reports Server (NTRS)

Acton, C.; Bachman, N.; Semenov, B.; Wright, E.

2013-01-01

SPICE is an information system providing space scientists ready access to a wide assortment of space geometry useful in planning science observations and analyzing the instrument data returned therefrom. The system includes software used to compute many derived parameters such as altitude, LAT/LON and lighting angles, and software able to find when user-specified geometric conditions are obtained. While not a formal standard, it has achieved widespread use in the worldwide planetary science community

Birational geometry of Fano double spaces of index two

NASA Astrophysics Data System (ADS)

Pukhlikov, Aleksandr V.

2010-10-01

We study birational geometry of Fano varieties realized as double covers \\sigma\\colon V\\to{\\ P}^M, M\\ge5, branched over generic smooth hypersurfaces W=W_{2(M-1)} of degree 2(M-1). We prove that the only structures of a rationally connected fibre space on V are pencil-subsystems of the free linear system \\vert{-\\frac12K_V}\\vert. The groups of birational and biregular self-maps of V coincide: \\operatorname{Bir}V=\\operatorname{Aut}V.

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Three-dimensional magnetic engineering: The programs magnus and epilog

NASA Astrophysics Data System (ADS)

Fan, Mingwu; Pissanetzky, Sergio

1988-10-01

We present the post-processor EPILOG for the well established finite element program MAGNUS for three-dimensional magnetic engineering. MAGNUS solves problems of magnetostatics with nonlinear magnetic materials, permanent magnets and electric currents, for any 3-D geometry. The two-scalar-potentials formulation of magnetostatics used by MAGNUS combines numerical accuracy and computational efficiency, and is considered state of the art. The well known program KUBIK is used as a pre-processor to describe the geometry and finite element mesh. KUBIK is highly interactive and allows the user to effectively control all geometric details. The needs of magnetic engineers, however, go far beyond the simple availability of a mathematical solution. Once the solution has been obtained by MAGNUS in the form of a continuous magnetic scalar potential function defined at every point in the solution domain, those needs are met by EPILOG. EPILOG is command operated. Commands are independent of each other and can be used in any order, or not used at all. The purpose of each command is to use the solution for the calculation of a derived quantity or the production of a plot or table. The following derived quantities can be obtained: the magnetic energy in specific regions, the magnetic force on specified conductors in space, the magnetic torque on specified conductors, the magnetic flux across a given surface in space, the inductance of a circuit, and a variety of line integrals for specified lines in space. A useful facility is the automatic calculation of harmonic multipoles averaged along the beam direction for accelerator magnets, essential for end analysis and the integral effect of the magnetic field on the beam. Graphical facilities include color plots of the shapes of the conductors, the geometry, field lines and surfaces of constant magnetic scalar potential in specified regions of space. EPILOG produces a device independent graphical metafile, which can be seen on any device by running the Graphical Kernel System GKS or some other graphics package. Another important feature of EPILOG is its ability to produce tables of quantities such as the scalar potential, the total field, the field of conductors alone, the magnetic permeability, etc. Editing options allow the user to specify where the quantities are to be tabulated, such as on equispaced points on a line or arc in space. One useful application is the evaluation of the maximum field inside conductors for superconducting magnets. The ability of EPILOG to accurately provide the magnetic field components at any given point in space is convenient for its use as input to particle tracking programs. EPILOG can easily be interfaced to such a program. EPILOG is appropriate for complicated 3-D geometries, common in wigglers and undulators, or for the analysis of ends of bending magnets, as required in the design of synchrotron light sources.

On the geometry of mixed states and the Fisher information tensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Contreras, I., E-mail: icontrer@illinois.edu; Ercolessi, E., E-mail: ercolessi@bo.infn.it; Schiavina, M., E-mail: michele.schiavina@math.uzh.ch

2016-06-15

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjointmore » orbits, seen as spaces of mixed states, is also discussed.« less

Phenomenology of TeV little string theory from holography.

PubMed

Antoniadis, Ignatios; Arvanitaki, Asimina; Dimopoulos, Savas; Giveon, Amit

2012-02-24

We study the graviton phenomenology of TeV little string theory by exploiting its holographic gravity dual five-dimensional theory. This dual corresponds to a linear dilaton background with a large bulk that constrains the standard model fields on the boundary of space. The linear dilaton geometry produces a unique Kaluza-Klein graviton spectrum that exhibits a ~TeV mass gap followed by a near continuum of narrow resonances that are separated from each other by only ~30 GeV. Resonant production of these particles at the LHC is the signature of this framework that distinguishes it from large extra dimensions, where the Kaluza-Klein states are almost a continuum with no mass gap, and warped models, where the states are separated by a TeV.

Peak Pc Prediction in Conjunction Analysis: Conjunction Assessment Risk Analysis. Pc Behavior Prediction Models

NASA Technical Reports Server (NTRS)

Vallejo, J.J.; Hejduk, M.D.; Stamey, J. D.

2015-01-01

Satellite conjunction risk typically evaluated through the probability of collision (Pc). Considers both conjunction geometry and uncertainties in both state estimates. Conjunction events initially discovered through Joint Space Operations Center (JSpOC) screenings, usually seven days before Time of Closest Approach (TCA). However, JSpOC continues to track objects and issue conjunction updates. Changes in state estimate and reduced propagation time cause Pc to change as event develops. These changes a combination of potentially predictable development and unpredictable changes in state estimate covariance. Operationally useful datum: the peak Pc. If it can reasonably be inferred that the peak Pc value has passed, then risk assessment can be conducted against this peak value. If this value is below remediation level, then event intensity can be relaxed. Can the peak Pc location be reasonably predicted?

Results from an experiment that collected visible-light polarization data using unresolved imagery for classification of geosynchronous satellites

NASA Astrophysics Data System (ADS)

Speicher, Andy; Matin, Mohammad; Tippets, Roger; Chun, Francis; Strong, David

2015-05-01

In order to protect critical military and commercial space assets, the United States Space Surveillance Network must have the ability to positively identify and characterize all space objects. Unfortunately, positive identification and characterization of space objects is a manual and labor intensive process today since even large telescopes cannot provide resolved images of most space objects. The objective of this study was to collect and analyze visible-spectrum polarization data from unresolved images of geosynchronous satellites taken over various solar phase angles. Different collection geometries were used to evaluate the polarization contribution of solar arrays, thermal control materials, antennas, and the satellite bus as the solar phase angle changed. Since materials on space objects age due to the space environment, their polarization signature may change enough to allow discrimination of identical satellites launched at different times. Preliminary data suggests this optical signature may lead to positive identification or classification of each satellite by an automated process on a shorter timeline. The instrumentation used in this experiment was a United States Air Force Academy (USAFA) Department of Physics system that consists of a 20-inch Ritchey-Chrétien telescope and a dual focal plane optical train fed with a polarizing beam splitter. Following a rigorous calibration, polarization data was collected during two nights on eight geosynchronous satellites built by various manufacturers and launched several years apart. When Stokes parameters were plotted against time and solar phase angle, the data indicates that a polarization signature from unresolved images may have promise in classifying specific satellites.

Energy Landscapes for the Self-Assembly of Supramolecular Polyhedra

NASA Astrophysics Data System (ADS)

Russell, Emily R.; Menon, Govind

2016-06-01

We develop a mathematical model for the energy landscape of polyhedral supramolecular cages recently synthesized by self-assembly (Sun et al. in Science 328:1144-1147, 2010). Our model includes two essential features of the experiment: (1) geometry of the organic ligands and metallic ions; and (2) combinatorics. The molecular geometry is used to introduce an energy that favors square-planar vertices (modeling {Pd}^{2+} ions) and bent edges with one of two preferred opening angles (modeling boomerang-shaped ligands of two types). The combinatorics of the model involve two-colorings of edges of polyhedra with four-valent vertices. The set of such two-colorings, quotiented by the octahedral symmetry group, has a natural graph structure and is called the combinatorial configuration space. The energy landscape of our model is the energy of each state in the combinatorial configuration space. The challenge in the computation of the energy landscape is a combinatorial explosion in the number of two-colorings of edges. We describe sampling methods based on the symmetries of the configurations and connectivity of the configuration graph. When the two preferred opening angles encompass the geometrically ideal angle, the energy landscape exhibits a very low-energy minimum for the most symmetric configuration at equal mixing of the two angles, even when the average opening angle does not match the ideal angle.

Combustion of metal agglomerates in a solid rocket core flow

NASA Astrophysics Data System (ADS)

Maggi, Filippo; Dossi, Stefano; DeLuca, Luigi T.

2013-12-01

The need for access to space may require the use of solid propellants. High thrust and density are appealing features for different applications, spanning from boosting phase to other service applications (separation, de-orbiting, orbit insertion). Aluminum is widely used as a fuel in composite solid rocket motors because metal oxidation increases enthalpy release in combustion chamber and grants higher specific impulse. Combustion process of metal particles is complex and involves aggregation, agglomeration and evolution of reacting particulate inside the core flow of the rocket. It is always stated that residence time should be enough in order to grant complete metal oxidation but agglomerate initial size, rocket grain geometry, burning rate, and other factors have to be reconsidered. New space missions may not require large rocket systems and metal combustion efficiency becomes potentially a key issue to understand whether solid propulsion embodies a viable solution or liquid/hybrid systems are better. A simple model for metal combustion is set up in this paper. Metal particles are represented as single drops trailed by the core flow and reacted according to Beckstead's model. The fluid dynamics is inviscid, incompressible, 1D. The paper presents parametric computations on ideal single-size particles as well as on experimental agglomerate populations as a function of operating rocket conditions and geometries.

On Variability in Satellite Terrestrial Chlorophyll Fluorescence Measurements: Relationships with Phenology and Ecosystem-Atmosphere Carbon Exchange, Vegetation Structure, Clouds, and Sun-Satellite Geometry

NASA Astrophysics Data System (ADS)

Joiner, J.; Yoshida, Y.; Guanter, L.; Zhang, Y.; Vasilkov, A. P.; Schaefer, K. M.; Huemmrich, K. F.; Middleton, E.; Koehler, P.; Jung, M.; Tucker, C. J.; Lyapustin, A.; Wang, Y.; Frankenberg, C.; Berry, J. A.; Koster, R. D.; Reichle, R. H.; Lee, J. E.; Kawa, S. R.; Collatz, G. J.; Walker, G. K.; Van der Tol, C.

2014-12-01

Over the past several years, there have been several breakthroughs in our ability to detect the very small fluorescence emitted by chlorophyll in vegetation globally from space. There are now multiple instruments in space capable of measuring this signal at varying temporal and spatial resolutions. We will review the state-of-the-art with respect to these relatively new satellite measurements and ongoing studies that examine the relationships with photosynthesis. Now that we have a data record spanning more than seven years, we can examine variations due to seasonal carbon uptake, interannual variability, land-use changes, and water and temperature stress. In addition, we examine how clouds and satellite viewing geometry impact the signal. We compare and contrast these variations with those from popular vegetation indices, such as the Normalized Difference Vegetation Index (NDVI), related to the potential photosynthesis as well as with measurements from flux tower gas exchange measurements and other model-based estimates of Global Primary Productivity (GPP). Vegetation fluorescence can be simulated in global vegetation models as well as with 1D canopy radiative transport models. We will describe how the satellite fluorescence data are being used to evaluate and potentially improve these models.

Nano-optical scan probes: Opening doors to previously-inaccessible parameter spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schuck, James

2014-06-08

I will discuss recent progress on new near-field probe geometries, including the “campanile” geometry, which has been used in recent hyperspectral imaging experiments, providing nanoscale spectral information distinct from what is obtained with other methods. Article not available.

Magnetic resonance spectra and statistical geometry

USDA-ARS?s Scientific Manuscript database

Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints that introduce curvature into parameter space and discuss the appropriate...

Thermal Protection System Cavity Heating for Simplified and Actual Geometries Using Computational Fluid Dynamics Simulations with Unstructured Grids

NASA Technical Reports Server (NTRS)

McCloud, Peter L.

2010-01-01

Thermal Protection System (TPS) Cavity Heating is predicted using Computational Fluid Dynamics (CFD) on unstructured grids for both simplified cavities and actual cavity geometries. Validation was performed using comparisons to wind tunnel experimental results and CFD predictions using structured grids. Full-scale predictions were made for simplified and actual geometry configurations on the Space Shuttle Orbiter in a mission support timeframe.

Implementation Plan for Flexible Automation in U.S. Shipyards

DTIC Science & Technology

1985-01-01

process steps, cramped work sites, interrupted geometries , irregular or novel shapes, and other factors that affect automatability. We also try to...held by 2 hands in awkward places. Interrupt geometry of plates and beams. Cannot predict outcome. Creates need to measure and recut. Automation, if...of standard. enough over time I every job. I Rearrange work.Redefine work units. Too many interruptions Time, space, geometry only a little work gets

Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow.

PubMed

Holter, Karl Erik; Kehlet, Benjamin; Devor, Anna; Sejnowski, Terrence J; Dale, Anders M; Omholt, Stig W; Ottersen, Ole Petter; Nagelhus, Erlend Arnulf; Mardal, Kent-André; Pettersen, Klas H

2017-09-12

The brain lacks lymph vessels and must rely on other mechanisms for clearance of waste products, including amyloid [Formula: see text] that may form pathological aggregates if not effectively cleared. It has been proposed that flow of interstitial fluid through the brain's interstitial space provides a mechanism for waste clearance. Here we compute the permeability and simulate pressure-mediated bulk flow through 3D electron microscope (EM) reconstructions of interstitial space. The space was divided into sheets (i.e., space between two parallel membranes) and tunnels (where three or more membranes meet). Simulation results indicate that even for larger extracellular volume fractions than what is reported for sleep and for geometries with a high tunnel volume fraction, the permeability was too low to allow for any substantial bulk flow at physiological hydrostatic pressure gradients. For two different geometries with the same extracellular volume fraction the geometry with the most tunnel volume had [Formula: see text] higher permeability, but the bulk flow was still insignificant. These simulation results suggest that even large molecule solutes would be more easily cleared from the brain interstitium by diffusion than by bulk flow. Thus, diffusion within the interstitial space combined with advection along vessels is likely to substitute for the lymphatic drainage system in other organs.

Binary space partitioning trees and their uses

NASA Technical Reports Server (NTRS)

Bell, Bradley N.

1989-01-01

Binary Space Partitioning (BSP) trees have some qualities that make them useful in solving many graphics related problems. The purpose is to describe what a BSP tree is, and how it can be used to solve the problem of hidden surface removal, and constructive solid geometry. The BSP tree is based on the idea that a plane acting as a divider subdivides space into two parts with one being on the positive side and the other on the negative. A polygonal solid is then represented as the volume defined by the collective interior half spaces of the solid's bounding surfaces. The nature of how the tree is organized lends itself well for sorting polygons relative to an arbitrary point in 3 space. The speed at which the tree can be traversed for depth sorting is fast enough to provide hidden surface removal at interactive speeds. The fact that a BSP tree actually represents a polygonal solid as a bounded volume also makes it quite useful in performing the boolean operations used in constructive solid geometry. Due to the nature of the BSP tree, polygons can be classified as they are subdivided. The ability to classify polygons as they are subdivided can enhance the simplicity of implementing constructive solid geometry.

Real-Time Utilization of STSS for Improved Collision Risk Management

NASA Astrophysics Data System (ADS)

Duncan, M.; Fero, R.; Smith, T.; Southworth, J.; Wysack, J.

2012-09-01

Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. The increased dependence on our space assets has in turn led to a greater need for accurate, near real-time knowledge of all space activities. Key areas of SSA include improved tracking of smaller objects more frequently, determining the intent of non- corporative maneuvering spacecraft, identifying all potential high risk conjunction events, and leveraging non-traditional sensors in support of the SSA mission. As the size of the space object catalog grows, the demand for more tracking capacity increases. One solution is to exploit existing sensors that are primarily dedicated to other mission areas. This paper presents details regarding the utilization of the Missile Defense Agency's (MDA) space-based asset Space Tracking Surveillance System (STSS) for operational SSA. Shown are the steps and analysis items that were performed to prepare STSS for real-time utilization during high interest conjunction events. Included in our work is: 1. STSS debris tracking capability, 2. Orbit estimation/data fusion between STSS raw observations and JSpOC state data, and finally 3. Orbit geometry for MDA assets 4. Development of the STSS tasking ConOps Several operational examples are included.

Casimir energy in Kerr space-time

NASA Astrophysics Data System (ADS)

Sorge, F.

2014-10-01

We investigate the vacuum energy of a scalar massless field confined in a Casimir cavity moving in a circular equatorial orbit in the exact Kerr space-time geometry. We find that both the orbital motion of the cavity and the underlying space-time geometry conspire in lowering the absolute value of the (renormalized) Casimir energy ⟨ɛvac⟩ren , as measured by a comoving observer, with respect to whom the cavity is at rest. This, in turn, causes a weakening in the attractive force between the Casimir plates. In particular, we show that the vacuum energy density ⟨ɛvac⟩ren→0 when the orbital path of the Casimir cavity comes close to the corotating or counter-rotating circular null orbits (possibly geodesic) allowed by the Kerr geometry. Such an effect could be of some astrophysical interest on relevant orbits, such as the Kerr innermost stable circular orbits, being potentially related to particle confinement (as in some interquark models). The present work generalizes previous results obtained by several authors in the weak field approximation.

Unsteady characteristics of low-Re flow past two tandem cylinders

NASA Astrophysics Data System (ADS)

Zhang, Wei; Dou, Hua-Shu; Zhu, Zuchao; Li, Yi

2018-06-01

This study investigated the two-dimensional flow past two tandem circular or square cylinders at Re = 100 and D / d = 4-10, where D is the center-to-center distance and d is the cylinder diameter. Numerical simulation was performed to comparably study the effect of cylinder geometry and spacing on the aerodynamic characteristics, unsteady flow patterns, time-averaged flow characteristics and flow unsteadiness. We also provided the first global linear stability analysis and sensitivity analysis on the physical problem for the potential application of flow control. The objective of this work is to quantitatively identify the effect of the cylinder geometry and spacing on the characteristic quantities. Numerical results reveal that there is wake flow transition for both geometries depending on the spacing. The characteristic quantities, including the time-averaged and fluctuating streamwise velocity and pressure coefficient, are quite similar to that of the single cylinder case for the upstream cylinder, while an entirely different variation pattern is observed for the downstream cylinder. The global linear stability analysis shows that the spatial structure of perturbation is mainly observed in the wake of the downstream cylinder for small spacing, while moves upstream with reduced size and is also observed after the upstream cylinder for large spacing. The sensitivity analysis reflects that the temporal growth rate of perturbation is the most sensitive to the near-wake flow of downstream cylinder for small spacing and upstream cylinder for large spacing.

Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak

2014-05-01

We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law [1+t/tc]-2, where tc diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries.

Quantum correlations are weaved by the spinors of the Euclidean primitives

PubMed Central

2018-01-01

The exceptional Lie group E8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which—thanks to their non-associativity—form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S3, with S7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S7, computed using manifestly local spinors within S3, thereby extending the stringent bounds of ±2 set by Bell inequalities to the bounds of ±22 on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell’s theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S3 and S7. PMID:29893385

Interplay of Zero-Field Splitting and Excited State Geometry Relaxation in fac-Ir(ppy)3.

PubMed

Gonzalez-Vazquez, José P; Burn, Paul L; Powell, Benjamin J

2015-11-02

The lowest energy triplet state, T1, of organometallic complexes based on iridium(III) is of fundamental interest, as the behavior of molecules in this state determines the suitability of the complex for use in many applications, e.g., organic light-emitting diodes. Previous characterization of T1 in fac-Ir(ppy)3 suggests that the trigonal symmetry of the complex is weakly broken in the excited state. Here we report relativistic time dependent density functional calculations of the zero-field splitting (ZFS) of fac-Ir(ppy)3 in the ground state (S0) and lowest energy triplet (T1) geometries and at intermediate geometries. We show that the energy scale of the geometry relaxation in the T1 state is large compared to the ZFS. Thus, the natural analysis of the ZFS and the radiative decay rates, based on the assumption that the structural distortion is a small perturbation, fails dramatically. In contrast, our calculations of these quantities are in good agreement with experiment.

Physical and geometrical aspects of de sitter interior of a gravastar

NASA Astrophysics Data System (ADS)

Morawiec, Pawel Jan

The principal motivation for the investigations reported in this thesis is the gravastar model for physical black holes. According to this model the final state of the gravitational collapse of cold super-dense stars with the mass greater than some critical value is a non-singular object called a gravastar. This thesis presents results related to the various aspects of the de Sitter interior of a gravastar. The main object of the research was a generalized rotating interior of a gravastar. It was shown that the rotation, characterized by the vorticity, is localized on the vortex line. The metric under considerations is the de Sitter metric, however in some variant of the oblate spheroidal coordinates. Additionally a cosmic string on the rotation axis is present. This new result is the de Sitter version of the Mazur string, which was obtained from the four dimensional Levi-Civita metric as the generalization of the three-dimensional cosmic string by Adler and Jackiw. Also, using analogy between rotation in the superfluid and the magnetic field we gave another example of the Cosmic No Hair Theorem, this time "no magnetic fields in de Sitter space". But we also have shown that when the de Sitter event horizon is replaced by a thin shell (with a finite thickness), as it is in the gravastar model, the non-vanishing magnetic field could be present. To our knowledge these are new results. In this thesis we have studied behavior of the massless Dirac field as an example of a matter field in the de Sitter spacetime in the vicinity of an event horizon. We found convenient to work in the frame of the optical geometry of the de Sitter space as it is related to the metric in the static coordinates through a conformal Weyl rescaling and the dynamics of the massless Dirac fields is conformally invariant. The fact that the spatial part of the metric in the optical geometry of de Sitter space is the constant negative curvature Lobachevski space (the Euclidean ant-de Sitter space) suggested the existenc of the emerging de Sitter quantum field theory and conformal field theory correspondence on the de Sitter event horizon. We have studied implications of this conjecture. According to the AdS/CFT correspondence prescription the functional integral over the matter fields described by the action with the properly chosen boundary terms defining the so called partition function as the functional of the boundary values of the matter fields is also the generating functional for the correlation functions in the conformal field theory on the boundary of AdS space. In the case of the optical geometry of the de Sitter space the boundary is the event horizon that is the boundary of its Lobachevski spatial part times time. We have chosen the action for the massless Dirac fields in the optical de Sitter geometry with appropriate surface term and subsequently we have evaluated the real time partition function as the functional of the carefully defined boundary values of the Dirac field. It turns out that this partition functional can be, indeed, interpreted as the generating functional of the real time conformal field theory correlation functions of the fermionic operators, dual to the fermionic fields on the boundary. This means that the conformal field theory correlation functions are evaluated as the vacuum expectation values of the chronologically ordered fermionic operator. This result demonstrates the emergence of the de Sitter/Conformal field theory correspondence on the de Sitter horizon. The presence of the negative curvature Lobachevski geometry in the spatial part of the optical geometry of the de Sitter space, is responsible for the effective one-dimensional behavior of the matter degrees of freedom and of the emergence of the de Sitter/Conformal field theory correspondence on the event horizon. Although we have demonstrated the existence of this correspondence for the fermionic fields only, we anticipate this result to be valid generally.

General Relativity: Geometry Meets Physics

ERIC Educational Resources Information Center

Thomsen, Dietrick E.

1975-01-01

Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

Lattice gas simulations of dynamical geometry in two dimensions.

PubMed

Klales, Anna; Cianci, Donato; Needell, Zachary; Meyer, David A; Love, Peter J

2010-10-01

We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.

A linear shock cell model for jets of arbitrary exit geometry

NASA Technical Reports Server (NTRS)

Morris, P. J.; Bhat, T. R. S.; Chen, G.

1989-01-01

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

Quantum entanglement in inhomogeneous 1D systems

NASA Astrophysics Data System (ADS)

Ramírez, Giovanni

2018-04-01

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, h, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = h2, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics "Marcos Moshinsky" 2017.

GVVPT2 energy gradient using a Lagrangian formulation.

PubMed

Theis, Daniel; Khait, Yuriy G; Hoffmann, Mark R

2011-07-28

A Lagrangian based approach was used to obtain analytic formulas for GVVPT2 energy nuclear gradients. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. An efficient means of evaluating the gradient equations is described. Demonstrative calculations were performed and compared with finite difference calculations on several molecules and show that the GVVPT2 gradients are accurate. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited singlet states of LiH, including calculations near an avoided crossing. The accuracy and usefulness of the GVVPT2 method and its gradient are highlighted by comparing the geometry of the near-C(2v) minimum on the conical intersection seam between the 1 (1)A(1) and 2 (1)A(1) surfaces of O(3) with values that were calculated at the multireference configuration interaction, including single and double excitations (MRCISD), level of theory. © 2011 American Institute of Physics

Mobile robot motion estimation using Hough transform

NASA Astrophysics Data System (ADS)

Aldoshkin, D. N.; Yamskikh, T. N.; Tsarev, R. Yu

2018-05-01

This paper proposes an algorithm for estimation of mobile robot motion. The geometry of surrounding space is described with range scans (samples of distance measurements) taken by the mobile robot’s range sensors. A similar sample of space geometry in any arbitrary preceding moment of time or the environment map can be used as a reference. The suggested algorithm is invariant to isotropic scaling of samples or map that allows using samples measured in different units and maps made at different scales. The algorithm is based on Hough transform: it maps from measurement space to a straight-line parameters space. In the straight-line parameters, space the problems of estimating rotation, scaling and translation are solved separately breaking down a problem of estimating mobile robot localization into three smaller independent problems. The specific feature of the algorithm presented is its robustness to noise and outliers inherited from Hough transform. The prototype of the system of mobile robot orientation is described.

Mass effects and internal space geometry in triatomic reaction dynamics

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang S.; Marsden, Jerrold E.

2006-05-01

The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing.

PubMed

Hou, Tingbo; Qin, Hong

2013-01-01

As signal processing tools, diffusion wavelets and biorthogonal diffusion wavelets have been propelled by recent research in mathematics. They employ diffusion as a smoothing and scaling process to empower multiscale analysis. However, their applications in graphics and visualization are overshadowed by nonadmissible wavelets and their expensive computation. In this paper, our motivation is to broaden the application scope to space-frequency processing of shape geometry and scalar fields. We propose the admissible diffusion wavelets (ADW) on meshed surfaces and point clouds. The ADW are constructed in a bottom-up manner that starts from a local operator in a high frequency, and dilates by its dyadic powers to low frequencies. By relieving the orthogonality and enforcing normalization, the wavelets are locally supported and admissible, hence facilitating data analysis and geometry processing. We define the novel rapid reconstruction, which recovers the signal from multiple bands of high frequencies and a low-frequency base in full resolution. It enables operations localized in both space and frequency by manipulating wavelet coefficients through space-frequency filters. This paper aims to build a common theoretic foundation for a host of applications, including saliency visualization, multiscale feature extraction, spectral geometry processing, etc.

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia

2018-02-01

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nivarti, Girish V., E-mail: g.nivarti@alumni.ubc.ca; Salehi, M. Mahdi; Bushe, W. Kendal

2015-01-15

Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton ordermore » curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.« less

Why there is something rather than nothing: cosmological constant from summing over everything in lorentzian quantum gravity.

PubMed

Barvinsky, A O

2007-08-17

The density matrix of the Universe for the microcanonical ensemble in quantum cosmology describes an equipartition in the physical phase space of the theory (sum over everything), but in terms of the observable spacetime geometry this ensemble is peaked about the set of recently obtained cosmological instantons limited to a bounded range of the cosmological constant. This suggests the mechanism of constraining the landscape of string vacua and a possible solution to the dark energy problem in the form of the quasiequilibrium decay of the microcanonical state of the Universe.

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

NASA Astrophysics Data System (ADS)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

Inversion Of Jacobian Matrix For Robot Manipulators

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1989-01-01

Report discusses inversion of Jacobian matrix for class of six-degree-of-freedom arms with spherical wrist, i.e., with last three joints intersecting. Shows by taking advantage of simple geometry of such arms, closed-form solution of Q=J-1X, which represents linear transformation from task space to joint space, obtained efficiently. Presents solutions for PUMA arm, JPL/Stanford arm, and six-revolute-joint coplanar arm along with all singular points. Main contribution of paper shows simple geometry of this type of arms exploited in performing inverse transformation without any need to compute Jacobian or its inverse explicitly. Implication of this computational efficiency advanced task-space control schemes for spherical-wrist arms implemented more efficiently.

Efficient geometry optimization by Hellmann-Feynman forces with the anti-Hermitian contracted Schrödinger equation

NASA Astrophysics Data System (ADS)

Foley, Jonathan J.; Mazziotti, David A.

2010-10-01

An efficient method for geometry optimization based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) is presented. We formulate a reduced version of the Hellmann-Feynman theorem (HFT) in terms of the two-electron reduced Hamiltonian operator and the two-electron reduced density matrix (2-RDM). The HFT offers a considerable reduction in computational cost over methods which rely on numerical derivatives. While previous geometry optimizations with numerical gradients required 2M evaluations of the ACSE where M is the number of nuclear degrees of freedom, the HFT requires only a single ACSE calculation of the 2-RDM per gradient. Synthesizing geometry optimization techniques with recent extensions of the ACSE theory to arbitrary electronic and spin states provides an important suite of tools for accurately determining equilibrium and transition-state structures of ground- and excited-state molecules in closed- and open-shell configurations. The ability of the ACSE to balance single- and multi-reference correlation is particularly advantageous in the determination of excited-state geometries where the electronic configurations differ greatly from the ground-state reference. Applications are made to closed-shell molecules N2, CO, H2O, the open-shell molecules B2 and CH, and the excited state molecules N2, B2, and BH. We also study the HCN ↔ HNC isomerization and the geometry optimization of hydroxyurea, a molecule which has a significant role in the treatment of sickle-cell anaemia.

Mental Rotation, Pictured Rotation, and Tandem Rotation in Depth

DTIC Science & Technology

1997-01-01

field. Such an explanation by natural geometry conflates visual comparison with physical measurement. This application of geometry is called natural in...the theory of vision parasitic on geometry: it is unclear what could be meant by a ’mental operation of rotation’, except by reference to physical ...operation, a mental analogue of the physical operation of rotation in space. Since then the story of mental rotation has become far more complicated

The effect of pore-scale geometry and wettability on two-phase relative permeabilities within elementary cells

NASA Astrophysics Data System (ADS)

Bianchi Janetti, Emanuela; Riva, Monica; Guadagnini, Alberto

2017-04-01

We study the relative role of the complex pore space geometry and wettability of the solid matrix on the quantification of relative permeabilities characterizing steady state immiscible two-phase flow in porous media. We do so by considering elementary cells, which are typically employed in upscaling frameworks based on, e.g., homogenization or volume averaging. In this context one typically relies on the solution of pore-scale physics at a scale which is much smaller than that of an investigated porous system. Pressure-driven two-phase flow following simultaneous co-current injection of water and oil is numerically solved for a suite of regular and stochastically generated two-dimensional explicit elementary cells with fixed porosity and sharing main topological/morphological features. We show that relative permeabilities of the randomly generated elementary cells are significantly influenced by the formation of preferential percolation paths (principal pathways), giving rise to a strongly nonuniform distribution of fluid fluxes. These pathways are a result of the spatially variable resistance that the random pore structures exert on the fluid. The overall effect on relative permeabilities of the diverse organization of principal pathways, as driven by a given random realization at the scale of the unit cell, is significantly larger than that of the wettability of the host rock. In contrast to what can be observed for the random cells analyzed, relative permeabilities of regular cells display a clear trend with contact angle at the investigated scale. Our findings suggest the need to perform systematic upscaling studies in a stochastic context, to propagate the effects of uncertain pore space geometries to a probabilistic description of relative permeability curves at the continuum scale.

Scattering forms and the positive geometry of kinematics, color and the worldsheet

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Bai, Yuntao; He, Song; Yan, Gongwang

2018-05-01

The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint ϕ 3 scalar theory, we establish a direct connection between its "scattering form" and a classic polytope — the associahedron — known to mathematicians since the 1960's. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the "canonical form" associated with this "positive geometry". Fundamental physical properties such as locality and unitarity, as well as novel "soft" limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old "worldsheet associahedron" and the new "kinematic associahedron", providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find "scattering forms" on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—"Color is Kinematics"— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, all our scattering forms are well-defined on the projectivized kinematic space, a property which can be seen to provide a geometric origin for color-kinematics duality.

Five-Segment Solid Rocket Motor Development Status

NASA Technical Reports Server (NTRS)

Priskos, Alex S.

2012-01-01

In support of the National Aeronautics and Space Administration (NASA), Marshall Space Flight Center (MSFC) is developing a new, more powerful solid rocket motor for space launch applications. To minimize technical risks and development costs, NASA chose to use the Space Shuttle s solid rocket boosters as a starting point in the design and development. The new, five segment motor provides a greater total impulse with improved, more environmentally friendly materials. To meet the mass and trajectory requirements, the motor incorporates substantial design and system upgrades, including new propellant grain geometry with an additional segment, new internal insulation system, and a state-of-the art avionics system. Significant progress has been made in the design, development and testing of the propulsion, and avionics systems. To date, three development motors (one each in 2009, 2010, and 2011) have been successfully static tested by NASA and ATK s Launch Systems Group in Promontory, UT. These development motor tests have validated much of the engineering with substantial data collected, analyzed, and utilized to improve the design. This paper provides an overview of the development progress on the first stage propulsion system.

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

NASA Astrophysics Data System (ADS)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent as fine mesh DSA in slab geometry. For x-y geometry our coarse mesh DSA is very effective for thin and intermediate mesh spacings independent of the scattering ratio, but is not effective for purely scattering problems and high aspect ratio zoning. However, if the scattering ratio is less than about 0.95, this procedure is very effective for all mesh spacing.

Interplay between gravity and quintessence: a set of new GR solutions

NASA Astrophysics Data System (ADS)

Chernin, Arthur D.; Santiago, David I.; Silbergleit, Alexander S.

2002-02-01

A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space-time with a horizon-type singular surface; (2) time-dependent spatially homogeneous `spheres' which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a `true' singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme `density-free' form of energy that can generate regular space-time geometries.

Quanta of Geometry and Unification

NASA Astrophysics Data System (ADS)

Chamseddine, Ali H.

This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

A differential geometry model for the perceived colors space

NASA Astrophysics Data System (ADS)

Provenzi, Edoardo

2016-06-01

The space of perceived colors, before acquiring an industrial interest, has received a systematic theoretical attention from philosophers, physicists and mathematicians. The research about this topic is still active nowadays. In this paper, it will be presented a critical overview of a model based on differential geometry proposed by H. L. Resnikoff in 1974. It will be shown that, while some fundamental and elegant ideas behind this model can be still used as a guiding principle, some other parts of the model must be updated to comply with the modern findings about color perception.

The Geometry of Generations

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Jejjala, Vishnu; Matti, Cyril; Nelson, Brent D.; Stillman, Michael

2015-10-01

We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic variety for multiple generations of Standard Model matter and Higgs doublets. The space is shown to have Calabi-Yau, Grassmannian, and toric signatures, which sensitively depend on the number of generations of leptons, as well as inclusion of Majorana mass terms for right-handed neutrinos. We speculate as to why three generations is special.

Infrared realization of dS2 in AdS2

NASA Astrophysics Data System (ADS)

Anninos, Dionysios; Hofman, Diego M.

2018-04-01

We describe a two-dimensional geometry that smoothly interpolates between an asymptotically AdS2 geometry and the static patch of dS2. We find this ‘centaur’ geometry to be a solution of dilaton gravity with a specific class of potentials for the dilaton. We interpret the centaur geometry as a thermal state in the putative quantum mechanics dual to the AdS2 evolved with the global Hamiltonian. We compute the thermodynamic properties and observe that the centaur state has finite entropy and positive specific heat. The static patch is the infrared part of the centaur geometry. We discuss boundary observables sensitive to the static patch region.

NASA Has Joined America True's Design Mission for 2000

NASA Technical Reports Server (NTRS)

Steele, Gynelle C.

1999-01-01

Engineers at the NASA Lewis Research Center will support the America True design team led by America s Cup innovator Phil Kaiko. The joint effort between NASA and America True is encouraged by Mission HOME, the official public awareness campaign of the U.S. space community. NASA Lewis and America True have entered into a Space Act Agreement to focus on the interaction between the airfoil and the large deformation of the pretensioned sails and rigs along with the dynamic motions related to the boat motions. This work will require a coupled fluid and structural simulation. Included in the simulation will be both a steadystate capability, to capture the quasi-state interactions between the air loads and sail geometry and the lift and drag on the boat, and a transient capability, to capture the sail/mast pumping effects resulting from hull motions.

Work/control stations in Space Station weightlessness

NASA Technical Reports Server (NTRS)

Willits, Charles

1990-01-01

An ergonomic integration of controls, displays, and associated interfaces with an operator, whose body geometry and dynamics may be altered by the state of weightlessness, is noted to rank in importance with the optimal positioning of controls relative to the layout and architecture of 'body-ported' work/control stations applicable to the NASA Space Station Freedom. A long-term solution to this complex design problem is envisioned to encompass the following features: multiple imaging, virtual optics, screen displays controlled by a keyboard ergonomically designed for weightlessness, cursor control, a CCTV camera, and a hand-controller featuring 'no-grip' vernier/tactile positioning. This controller frees all fingers for multiple-switch actuations, while retaining index/register determination with the hand controller. A single architectural point attachment/restraint may be used which requires no residual muscle tension in either brief or prolonged operation.

Geometry of the generalized Bloch sphere for qutrits

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Neethi Simon, B.; Singh, Rajeev; Simon, Sudhavathani

2016-04-01

The geometry of the generalized Bloch sphere Ω3, the state space of a qutrit, is studied. Closed form expressions for Ω3, its boundary ∂Ω3, and the set of extremals {{{Ω }}}3{{ext}} are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU(3), the symmetry underlying Ω3, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .

Instantons, quivers and noncommutative Donaldson-Thomas theory

NASA Astrophysics Data System (ADS)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

Mechanism study on pressure fluctuation of pump-turbine runner with large blade lean angle

NASA Astrophysics Data System (ADS)

Yulin, Fan; Xuhe, Wang; Baoshan, Zhu; Dongyue, Zhou; Xijun, Zhou

2016-11-01

Excessive pressure fluctuations in the vaneless space can cause mechanical vibration and even mechanical failures in pump-turbine operation. Mechanism studies on the pressure fluctuations and optimization design of blade geometry to reduce the pressure fluctuations have important significance in industrial production. In the present paper, two pump-turbine runners with big positive and negative blade lean angle were designed by using a multiobjective design strategy. Model test showed that the runner with negative blade lean angle not only had better power performance, but also had lower pressure fluctuation than the runner with positive blade lean angle. In order to figure out the mechanism of pressure fluctuation reduction in the vaneless;jik8space, full passage model for both runners were built and transient CFD computations were conducted to simulate the flow states inside the channel. Detailed flow field analyses indicated that the difference of low-pressure area in the trailing edge of blade pressure side were the main causes of pressure fluctuation reduction in the vaneless space.

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

NASA Astrophysics Data System (ADS)

Mohanta, Narayan; Kampf, Arno P.; Kopp, Thilo

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like ``spin'' texture in momentum space. Here, we apply the previously formulated low-energy model for Bi2Se3, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to e2 / 2 h . The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator. The work was supported by the Deutsche Forschungsgemeinschaft through TRR 80.

Graph-drawing algorithms geometries versus molecular mechanics in fullereness

NASA Astrophysics Data System (ADS)

Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

1996-09-01

The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.

A computational study of the TiO2 molecule

NASA Technical Reports Server (NTRS)

Ramana, M. V.; Phillips, D. H.

1988-01-01

A computational investigation of the ground 1A1 and lowest energy B2 states of the titanium dioxide molecule has been carried out. The treatment utilized SCF calculations in an extended basis followed by a CI treatment for each geometry. The ground state geometry agrees well with experiment, while the agreement between the computed vibrational frequency nu1 and the experimental value for a matrix isolated TiO2 is less satisfactory. Population analysis for the ground state indicates less than one excess electron on each oxygen atom. The first excited state has a linear geometry and the singlet and triplet are essentially degenerate.

Geometric Model of Topological Insulators from the Maxwell Algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).

Charge state distribution and emission characteristics in a table top reflex discharge - Effect of ion confinement and electrons accelerated across the sheath

DOE PAGES

Kumar, Deepak; Englesbe, Alexander; Parman, Matthew; ...

2015-11-05

Tabletop reflex discharges in a Penning geometry have many applications including ion sources and eXtreme Ultra-Violet (XUV) sources. The presence of primary electrons accelerated across the cathode sheaths is responsible for the distribution of ion charge states and of the unusually high XUV brightness of these plasmas. Absolutely calibrated space resolved XUV spectra from a table top reflex discharge operating with Al cathodes and Ne gas are presented. The spectra are analyzed with a new and complete model for ion charge distribution in similar reflex discharges. The plasma in the discharge was found to have a density of ~10 18mmore » –3 with a significant fraction >0.01 of fast primary electrons. As a result, the implications of the new model on the ion states achievable in a tabletop reflex plasma discharge are also discussed.« less

A look towards the future in the handling of space science mission geometry

NASA Astrophysics Data System (ADS)

Acton, Charles; Bachman, Nathaniel; Semenov, Boris; Wright, Edward

2018-01-01

The "SPICE" system has been widely used since the days of the Magellan mission to Venus as the method for scientists and engineers to access a variety of space mission geometry such as positions, velocities, directions, orientations, sizes and shapes, and field-of-view projections (Acton, 1996). While originally focused on supporting NASA's planetary missions, the use of SPICE has slowly grown to include most worldwide planetary missions, and it has also been finding application in heliophysics and other space science disciplines. This paper peeks under the covers to see what new capabilities are being developed or planned at SPICE headquarters to better support the future of space science. The SPICE system is implemented and maintained by NASA's Navigation and Ancillary Information Facility (NAIF) located at the Jet Propulsion Laboratory in Pasadena, California (http://naif.jpl.nasa.gov).

Dynamic Hyperbolic Geometry: Building Intuition and Understanding Mediated by a Euclidean Model

ERIC Educational Resources Information Center

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-01-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

Self-organized topology of recurrence-based complex networks

NASA Astrophysics Data System (ADS)

Yang, Hui; Liu, Gang

2013-12-01

With the rapid technological advancement, network is almost everywhere in our daily life. Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods are proposed to construct a network from nonlinear time series, including the partition of state space, visibility graph, nearest neighbors, and recurrence approaches. However, most previous works focus on deriving the adjacency matrix to represent the complex network and extract new network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The research objective of this article is to develop a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. We simulate the recurrence network as a physical system by treating the edges as springs and the nodes as electrically charged particles. Then, force-directed algorithms are developed to automatically organize the network geometry by minimizing the system energy. Further, a set of experiments were designed to investigate important factors (i.e., dynamical systems, network construction methods, force-model parameter, nonhomogeneous distribution) affecting this self-organizing process. Interestingly, experimental results show that the self-organized geometry recovers the attractor of a dynamical system that produced the adjacency matrix. This research addresses a question, i.e., "what is the self-organizing geometry of a recurrence network?" and provides a new way to reproduce the attractor or time series from the recurrence plot. As a result, novel network-theoretic measures (e.g., average path length and proximity ratio) can be achieved based on actual node-to-node distances in the self-organized network topology. The paper brings the physical models into the recurrence analysis and discloses the spatial geometry of recurrence networks.

Self-organized topology of recurrence-based complex networks.

PubMed

Yang, Hui; Liu, Gang

2013-12-01

With the rapid technological advancement, network is almost everywhere in our daily life. Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods are proposed to construct a network from nonlinear time series, including the partition of state space, visibility graph, nearest neighbors, and recurrence approaches. However, most previous works focus on deriving the adjacency matrix to represent the complex network and extract new network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The research objective of this article is to develop a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. We simulate the recurrence network as a physical system by treating the edges as springs and the nodes as electrically charged particles. Then, force-directed algorithms are developed to automatically organize the network geometry by minimizing the system energy. Further, a set of experiments were designed to investigate important factors (i.e., dynamical systems, network construction methods, force-model parameter, nonhomogeneous distribution) affecting this self-organizing process. Interestingly, experimental results show that the self-organized geometry recovers the attractor of a dynamical system that produced the adjacency matrix. This research addresses a question, i.e., "what is the self-organizing geometry of a recurrence network?" and provides a new way to reproduce the attractor or time series from the recurrence plot. As a result, novel network-theoretic measures (e.g., average path length and proximity ratio) can be achieved based on actual node-to-node distances in the self-organized network topology. The paper brings the physical models into the recurrence analysis and discloses the spatial geometry of recurrence networks.

Self-organized topology of recurrence-based complex networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Hui, E-mail: huiyang@usf.edu; Liu, Gang

With the rapid technological advancement, network is almost everywhere in our daily life. Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods are proposed to construct a network from nonlinear time series, including the partition of state space, visibility graph, nearest neighbors, and recurrence approaches. However, most previous works focus on deriving the adjacency matrix to represent the complex network and extract new network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The research objective of this article ismore » to develop a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. We simulate the recurrence network as a physical system by treating the edges as springs and the nodes as electrically charged particles. Then, force-directed algorithms are developed to automatically organize the network geometry by minimizing the system energy. Further, a set of experiments were designed to investigate important factors (i.e., dynamical systems, network construction methods, force-model parameter, nonhomogeneous distribution) affecting this self-organizing process. Interestingly, experimental results show that the self-organized geometry recovers the attractor of a dynamical system that produced the adjacency matrix. This research addresses a question, i.e., “what is the self-organizing geometry of a recurrence network?” and provides a new way to reproduce the attractor or time series from the recurrence plot. As a result, novel network-theoretic measures (e.g., average path length and proximity ratio) can be achieved based on actual node-to-node distances in the self-organized network topology. The paper brings the physical models into the recurrence analysis and discloses the spatial geometry of recurrence networks.« less

Geometry, topology, and response in condensed matter systems

NASA Astrophysics Data System (ADS)

Varjas, Daniel

Topological order provides a new paradigm to view phases of matter. Unlike conventional symmetry breaking order, these states are not distinguished by different patterns of symmetry breaking, instead by their intricate mathematical structure, topology. By the bulk-boundary correspondence, the nontrivial topology of the bulk results in robust gapless excitations on symmetry preserving surfaces. We utilize both of these views to study topological phases together with the analysis of their quantized physical responses to perturbations. First we study the edge excitations of strongly interacting abelian fractional quantum Hall liquids on an infinite strip geometry. We use the infinite density matrix renormalization group method to numerically measure edge exponents in model systems, including subleading orders. Using analytic methods we derive a generalized Luttinger's theorem that relates momenta of edge excitations. Next we consider topological crystalline insulators protected by space group symmetry. After reviewing the general formalism, we present results about the quantization of the magnetoelectric response protected by orientation-reversing space group symmetries. We construct and analyze insulating and superconducting tight-binding models with glide symmetry in three dimensions to illustrate the general result. Following this, we derive constraints on weak indices of three dimensional topological insulators imposed by space group symmetries. We focus on spin-orbit coupled insulators with and without time reversal invariance and consider both symmorphic and nonsymmorphic symmetries. Finally, we calculate the response of metals and generalize the notion of the magnetoelectric effect to noninteracting gapless systems. We use semiclassical dynamics to study the magnetopiezoelectric effect, the current response to elastic strain in static external magnetic fields.

Observability and Estimation of Distributed Space Systems via Local Information-Exchange Networks

NASA Technical Reports Server (NTRS)

Fathpour, Nanaz; Hadaegh, Fred Y.; Mesbahi, Mehran; Rahmani, Amirreza

2011-01-01

Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation-flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are proposed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms rely on a local information exchange network, relaxing the assumptions on existing algorithms. Distributed space systems rely on a signal transmission network among multiple spacecraft for their operation. Control and coordination among multiple spacecraft in a formation is facilitated via a network of relative sensing and interspacecraft communications. Guidance, navigation, and control rely on the sensing network. This network becomes more complex the more spacecraft are added, or as mission requirements become more complex. The observability of a formation state was observed by a set of local observations from a particular node in the formation. Formation observability can be parameterized in terms of the matrices appearing in the formation dynamics and observation matrices. An agreement protocol was used as a mechanism for observing formation states from local measurements. An agreement protocol is essentially an unforced dynamic system whose trajectory is governed by the interconnection geometry and initial condition of each node, with a goal of reaching a common value of interest. The observability of the interconnected system depends on the geometry of the network, as well as the position of the observer relative to the topology. For the first time, critical GN&C (guidance, navigation, and control estimation) subsystems are synthesized by bringing the contribution of the spacecraft information-exchange network to the forefront of algorithmic analysis and design. The result is a formation estimation algorithm that is modular and robust to variations in the topology and link properties of the underlying formation network.

Development of the geometry database for the CBM experiment

NASA Astrophysics Data System (ADS)

Akishina, E. P.; Alexandrov, E. I.; Alexandrov, I. N.; Filozova, I. A.; Friese, V.; Ivanov, V. V.

2018-01-01

The paper describes the current state of the Geometry Database (Geometry DB) for the CBM experiment. The main purpose of this database is to provide convenient tools for: (1) managing the geometry modules; (2) assembling various versions of the CBM setup as a combination of geometry modules and additional files. The CBM users of the Geometry DB may use both GUI (Graphical User Interface) and API (Application Programming Interface) tools for working with it.

Interactive Design and Visualization of Branched Covering Spaces.

PubMed

Roy, Lawrence; Kumar, Prashant; Golbabaei, Sanaz; Zhang, Yue; Zhang, Eugene

2018-01-01

Branched covering spaces are a mathematical concept which originates from complex analysis and topology and has applications in tensor field topology and geometry remeshing. Given a manifold surface and an -way rotational symmetry field, a branched covering space is a manifold surface that has an -to-1 map to the original surface except at the ramification points, which correspond to the singularities in the rotational symmetry field. Understanding the notion and mathematical properties of branched covering spaces is important to researchers in tensor field visualization and geometry processing, and their application areas. In this paper, we provide a framework to interactively design and visualize the branched covering space (BCS) of an input mesh surface and a rotational symmetry field defined on it. In our framework, the user can visualize not only the BCSs but also their construction process. In addition, our system allows the user to design the geometric realization of the BCS using mesh deformation techniques as well as connecting tubes. This enables the user to verify important facts about BCSs such as that they are manifold surfaces around singularities, as well as the Riemann-Hurwitz formula which relates the Euler characteristic of the BCS to that of the original mesh. Our system is evaluated by student researchers in scientific visualization and geometry processing as well as faculty members in mathematics at our university who teach topology. We include their evaluations and feedback in the paper.

Inherent Structure versus Geometric Metric for State Space Discretization

PubMed Central

Liu, Hanzhong; Li, Minghai; Fan, Jue; Huo, Shuanghong

2016-01-01

Inherent structure (IS) and geometry-based clustering methods are commonly used for analyzing molecular dynamics trajectories. ISs are obtained by minimizing the sampled conformations into local minima on potential/effective energy surface. The conformations that are minimized into the same energy basin belong to one cluster. We investigate the influence of the applications of these two methods of trajectory decomposition on our understanding of the thermodynamics and kinetics of alanine tetrapeptide. We find that at the micro cluster level, the IS approach and root-mean-square deviation (RMSD) based clustering method give totally different results. Depending on the local features of energy landscape, the conformations with close RMSDs can be minimized into different minima, while the conformations with large RMSDs could be minimized into the same basin. However, the relaxation timescales calculated based on the transition matrices built from the micro clusters are similar. The discrepancy at the micro cluster level leads to different macro clusters. Although the dynamic models established through both clustering methods are validated approximately Markovian, the IS approach seems to give a meaningful state space discretization at the macro cluster level. PMID:26915811

Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically with Multi-Material 3D Printing.

PubMed

Chen, Tian; Mueller, Jochen; Shea, Kristina

2017-03-31

Multi-material 3D printing has created new opportunities for fabricating deployable structures. We design reversible, deployable structures that are fabricated flat, have defined load bearing capacity, and multiple, predictable activated geometries. These structures are designed with a hierarchical framework where the proposed bistable actuator serves as the base building block. The actuator is designed to maximise its stroke length, with the expansion ratio approaching one when serially connected. The activation force of the actuator is parameterised through its joint material and joint length. Simulation and experimental results show that the bistability triggering force can be tuned between 0.5 and 5.0 N. Incorporating this bistable actuator, the first group of hierarchical designs demonstrate the deployment of space frame structures with a tetrahedron module consisting of three active edges, each containing four serially connected actuators. The second group shows the design of flat structures that assume either positive or negative Gaussian curvature once activated. By flipping the initial configuration of the unit actuators, structures such as a dome and an enclosure are demonstrated. A modified Dynamic Relaxation method is used to simulate all possible geometries of the hierarchical structures. Measured geometries differ by less than 5% compared to simulation results.

Multimode Bose-Hubbard model for quantum dipolar gases in confined geometries

NASA Astrophysics Data System (ADS)

Cartarius, Florian; Minguzzi, Anna; Morigi, Giovanna

2017-06-01

We theoretically consider ultracold polar molecules in a wave guide. The particles are bosons: They experience a periodic potential due to an optical lattice oriented along the wave guide and are polarized by an electric field orthogonal to the guide axis. The array is mechanically unstable by opening the transverse confinement in the direction orthogonal to the polarizing electric field and can undergo a transition to a double-chain (zigzag) structure. For this geometry we derive a multimode generalized Bose-Hubbard model for determining the quantum phases of the gas at the mechanical instability, taking into account the quantum fluctuations in all directions of space. Our model limits the dimension of the numerically relevant Hilbert subspace by means of an appropriate decomposition of the field operator, which is obtained from a field theoretical model of the linear-zigzag instability. We determine the phase diagrams of small systems using exact diagonalization and find that, even for tight transverse confinement, the aspect ratio between the two transverse trap frequencies controls not only the classical but also the quantum properties of the ground state in a nontrivial way. Convergence tests at the linear-zigzag instability demonstrate that our multimode generalized Bose-Hubbard model can catch the essential features of the quantum phases of dipolar gases in confined geometries with a limited computational effort.

Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically with Multi-Material 3D Printing

PubMed Central

Chen, Tian; Mueller, Jochen; Shea, Kristina

2017-01-01

Multi-material 3D printing has created new opportunities for fabricating deployable structures. We design reversible, deployable structures that are fabricated flat, have defined load bearing capacity, and multiple, predictable activated geometries. These structures are designed with a hierarchical framework where the proposed bistable actuator serves as the base building block. The actuator is designed to maximise its stroke length, with the expansion ratio approaching one when serially connected. The activation force of the actuator is parameterised through its joint material and joint length. Simulation and experimental results show that the bistability triggering force can be tuned between 0.5 and 5.0 N. Incorporating this bistable actuator, the first group of hierarchical designs demonstrate the deployment of space frame structures with a tetrahedron module consisting of three active edges, each containing four serially connected actuators. The second group shows the design of flat structures that assume either positive or negative Gaussian curvature once activated. By flipping the initial configuration of the unit actuators, structures such as a dome and an enclosure are demonstrated. A modified Dynamic Relaxation method is used to simulate all possible geometries of the hierarchical structures. Measured geometries differ by less than 5% compared to simulation results. PMID:28361891

Is the choice of a standard zeroth-order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

PubMed

Wolański, Łukasz; Grabarek, Dawid; Andruniów, Tadeusz

2018-04-10

To account for systematic error of CASPT2 method empirical modification of the zeroth-order Hamiltonian with Ionization Potential-Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S-IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S-IPEA, is whether the introduction of the modified zeroth-order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0-0.35 a.u., on vertical excitation energies to low-lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S-IPEA significantly overestimates both S 0 →S 1 and S 0 →S 2 energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth-order Hamiltonian or small value of the IPEA shift in a range of 0.05-0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Dualities and Topological Field Theories from Twisted Geometries

NASA Astrophysics Data System (ADS)

Markov, Ruza

I will present three studies of string theory on twisted geometries. In the first calculation included in this dissertation we use gauge/gravity duality to study the Coulomb branch of an unusual type of nonlocal field theory, called Puff Field Theory. On the gravity side, this theory is given in terms of D3-branes in type IIB string theory with a geometric twist. While the field theory description, available in the IR limit, is a deformation of Yang-Mills gauge theory by an order seven operator which we here compute. In the rest of this dissertation we explore N = 4 super Yang-Mills (SYM) theory compactied on a circle with S-duality and R-symmetry twists that preserve N = 6 supersymmetry in 2 + 1D. It was shown that abelian theory on a flat manifold gives Chern-Simons theory in the low-energy limit and here we are interested in the non-abelian counterpart. To that end, we introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a two-torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory. The last result discussed in this dissertation demonstrates a connection between gravitational Chern-Simons theory and N = 4 four-dimensional SYM theory compactified on a circle twisted by S-duality where the remaining three-manifold is not flat starting with the explicit geometric realization of S-duality in terms of (2, 0) theory.

The use of virtual reality to reimagine two-dimensional representations of three-dimensional spaces

NASA Astrophysics Data System (ADS)

Fath, Elaine

2015-03-01

A familiar realm in the world of two-dimensional art is the craft of taking a flat canvas and creating, through color, size, and perspective, the illusion of a three-dimensional space. Using well-explored tricks of logic and sight, impossible landscapes such as those by surrealists de Chirico or Salvador Dalí seem to be windows into new and incredible spaces which appear to be simultaneously feasible and utterly nonsensical. As real-time 3D imaging becomes increasingly prevalent as an artistic medium, this process takes on an additional layer of depth: no longer is two-dimensional space restricted to strategies of light, color, line and geometry to create the impression of a three-dimensional space. A digital interactive environment is a space laid out in three dimensions, allowing the user to explore impossible environments in a way that feels very real. In this project, surrealist two-dimensional art was researched and reimagined: what would stepping into a de Chirico or a Magritte look and feel like, if the depth and distance created by light and geometry were not simply single-perspective illusions, but fully formed and explorable spaces? 3D environment-building software is allowing us to step into these impossible spaces in ways that 2D representations leave us yearning for. This art project explores what we gain--and what gets left behind--when these impossible spaces become doors, rather than windows. Using sketching, Maya 3D rendering software, and the Unity Engine, surrealist art was reimagined as a fully navigable real-time digital environment. The surrealist movement and its key artists were researched for their use of color, geometry, texture, and space and how these elements contributed to their work as a whole, which often conveys feelings of unexpectedness or uneasiness. The end goal was to preserve these feelings while allowing the viewer to actively engage with the space.

A linguistic geometry for space applications

NASA Technical Reports Server (NTRS)

Stilman, Boris

1994-01-01

We develop a formal theory, the so-called Linguistic Geometry, in order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, and apply them to different systems. This research relies on the formalization of search heuristics of high-skilled human experts which allow for the decomposition of complex system into the hierarchy of subsystems, and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This paper includes a formal survey of the Linguistic Geometry, and new example of a solution of optimization problem for the space robotic vehicles. This example includes actual generation of the hierarchy of languages, some details of trajectory generation and demonstrates the drastic reduction of search in comparison with conventional search algorithms.

Universal properties of the near-horizon optical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibbons, G. W.; Warnick, C. M.

2009-03-15

Making use of the fact that the optical geometry near a static nondegenerate Killing horizon is asymptotically hyperbolic, we investigate some universal features of black-hole horizons. Applying the Gauss-Bonnet theorem allows us to establish some general properties of gravitational lensing, valid for all black holes. Hyperbolic geometry allows us to find rates for the loss of scalar, vector, and fermionic ''hair'' as objects fall quasistatically towards the horizon, extending previous results for Schwarzschild to all static Killing horizons. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending themore » flat space result of Feinberg and Sucher. We further demonstrate how these techniques allow us to derive the exact Copson-Linet potential due to a point charge in a Schwarzschild background in a simple fashion.« less

Balancing Newtonian gravity and spin to create localized structures

NASA Astrophysics Data System (ADS)

Bush, Michael; Lindner, John

2015-03-01

Using geometry and Newtonian physics, we design localized structures that do not require electromagnetic or other forces to resist implosion or explosion. In two-dimensional Euclidean space, we find an equilibrium configuration of a rotating ring of massive dust whose inward gravity is the centripetal force that spins it. We find similar solutions in three-dimensional Euclidean and hyperbolic spaces, but only in the limit of vanishing mass. Finally, in three-dimensional Euclidean space, we generalize the two-dimensional result by finding an equilibrium configuration of a spherical shell of massive dust that supports itself against gravitational collapse by spinning isoclinically in four dimensions so its three-dimensional acceleration is everywhere inward. These Newtonian ``atoms'' illuminate classical physics and geometry.

SPOC Benchmark Case: SNRE Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vishal Patel; Michael Eades; Claude Russel Joyner II

The Small Nuclear Rocket Engine (SNRE) was modeled in the Center for Space Nuclear Research’s (CSNR) Space Propulsion Optimization Code (SPOC). SPOC aims to create nuclear thermal propulsion (NTP) geometries quickly to perform parametric studies on design spaces of historic and new NTP designs. The SNRE geometry was modeled in SPOC and a critical core with a reasonable amount of criticality margin was found. The fuel, tie-tubes, reflector, and control drum masses were predicted rather well. These are all very important for neutronics calculations so the active reactor geometries created with SPOC can continue to be trusted. Thermal calculations ofmore » the average and hot fuel channels agreed very well. The specific impulse calculations used historically and in SPOC disagree so mass flow rates and impulses differed. Modeling peripheral and power balance components that do not affect nuclear characteristics of the core is not a feature of SPOC and as such, these components should continue to be designed using other tools. A full paper detailing the available SNRE data and comparisons with SPOC outputs will be submitted as a follow-up to this abstract.« less

Performance Analysis of the Automotive TEG with Respect to the Geometry of the Modules

NASA Astrophysics Data System (ADS)

Yu, C. G.; Zheng, S. J.; Deng, Y. D.; Su, C. Q.; Wang, Y. P.

2017-05-01

Recently there has been increasing interest in applying thermoelectric technology to recover waste heat in automotive exhaust gas. Due to the limited space in the vehicle, it's meaningful to improve the TEG (thermoelectric generator) performance by optimizing the module geometry. This paper analyzes the performance of bismuth telluride modules for two criteria (power density and power output per area), and researches the relationship between the performance and the geometry of the modules. A geometry factor is defined for the thermoelectric element to describe the module geometry, and a mathematical model is set up to study the effects of the module geometry on its performance. It has been found out that the optimal geometry factors for maximum output power, power density and power output per unit area are different, and the value of the optimal geometry factors will be affected by the volume of the thermoelectric material and the thermal input. The results can be referred to as the basis for optimizing the performance of the thermoelectric modules.

Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients.

PubMed

Baier, Gerold; Taylor, Peter N; Wang, Yujiang

2017-01-01

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To investigate the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity. We compare our dynamic mechanism with other mechanisms (such as a slow parameter change) to generate excitable transients, and we discuss the proposed excitability mechanism in the context of stimulation responses in the epileptic cortex.

Sandia Corporation (Albuquerque, NM)

DOEpatents

Ewsuk, Kevin G [Albuquerque, NM; Arguello, Jr., Jose G.

2006-01-31

A method of designing a primary geometry, such as for a forming die, to be used in a powder pressing application by using a combination of axisymmetric geometric shapes, transition radii, and transition spaces to simulate the geometry where the shapes can be selected from a predetermined list or menu of axisymmetric shapes and then developing a finite element mesh to represent the geometry. This mesh, along with material properties of the component to be designed and powder, is input to a standard deformation finite element code to evaluate the deformation characteristics of the component being designed. The user can develop the geometry interactively with a computer interface in minutes and execute a complete analysis of the deformation characteristics of the simulated component geometry.

Towards timelike singularity via AdS dual

NASA Astrophysics Data System (ADS)

Bhowmick, Samrat; Chatterjee, Soumyabrata

2017-07-01

It is well known that Kasner geometry with spacelike singularity can be extended to bulk AdS-like geometry, furthermore, one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a Kasner-like geometry with timelike singularity for which one can construct a dual gravity description. We then study various extremal surfaces including spacelike geodesics in the dual gravity description. Finally, we compute correlators of highly massive operators in the boundary field theory with a geodesic approximation.

Shape and Space at Key Stage 2

ERIC Educational Resources Information Center

Back, Jenni; Brooksbank, Chris; Faux, Geoff

2007-01-01

In this article, framed as a conversation, the authors discuss the learning resulting from a variety of geometry tasks they have conducted with their students. None of them are convinced that all the geometry tasks within the numeracy strategy prescribed in English schools are necessarily good for children or aimed at the right age range. Using…

Early Sex Differences in Weighting Geometric Cues

ERIC Educational Resources Information Center

Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia

2011-01-01

When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…

Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.

PubMed

Leibon, Gregory; Rockmore, Daniel N

2013-01-01

In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store.

Koszul information geometry and Souriau Lie group thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant bymore » their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].« less

Pressure Gradient Effects on Hypersonic Cavity Flow Heating

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Alter, Stephen J.; Merski, N. Ronald; Wood, William A.; Prabhu, Ramadas K.

2006-01-01

The effect of a pressure gradient on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated in support of the Space Shuttle Return-To-Flight Program. Two blunted-nose test surface geometries were developed, including an expansion plate test surface with nearly constant negative pressure gradient and a flat plate surface with nearly zero pressure gradient. The test surface designs and flow characterizations were performed using two-dimensional laminar computational methods, while the experimental boundary layer state conditions were inferred using the measured heating distributions. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process. Both open-flow and closed-flow cavities were tested on each test surface. The cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary conclusions based on an analysis of only the cavity centerline data indicate that the presence of the pressure gradient did not alter the open cavity heating for laminar-entry/laminar-exit flows, but did raise the average floor heating for closed cavities. The results of these risk-reduction studies will be used to formulate a heating assessment of potential damage scenarios occurring during future Space Shuttle flights.

Pressure Gradient Effects on Hypersonic Cavity Flow Heating

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Alter, Stephen J.; Merski, N. Ronald; Wood, William A.; Prabhu, Ramdas K.

2007-01-01

The effect of a pressure gradient on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated in support of the Space Shuttle Return-To-Flight Program. Two blunted-nose test surface geometries were developed, including an expansion plate test surface with nearly constant negative pressure gradient and a flat plate surface with nearly zero pressure gradient. The test surface designs and flow characterizations were performed using two-dimensional laminar computational methods, while the experimental boundary layer state conditions were inferred using the measured heating distributions. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process. Both open-flow and closed-flow cavities were tested on each test surface. The cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary conclusions based on an analysis of only the cavity centerline data indicate that the presence of the pressure gradient did not alter the open cavity heating for laminar-entry/laminar-exit flows, but did raise the average floor heating for closed cavities. The results of these risk-reduction studies will be used to formulate a heating assessment of potential damage scenarios occurring during future Space Shuttle flights.

More Analytical Tools for Fluids Management in Space

NASA Astrophysics Data System (ADS)

Weislogel, Mark

Continued advances during the 2000-2010 decade in the analysis of a class of capillary-driven flows relevant to materials processing and fluids management aboard spacecraft have been made. The class of flows addressed concern combined forced and spontaneous capillary flows in complex containers with interior edges. Such flows are commonplace in space-based fluid systems and arise from the particular container geometry and wetting properties of the system. Important applications for this work include low-g liquid fill and/or purge operations and passive fluid phase separation operations, where the container (i.e. fuel tank, water processer, etc.) geometry possesses interior edges, and where quantitative information of fluid location, transients, flow rates, and stability is critical. Examples include the storage and handling of liquid propellants and cryogens, water conditioning for life support, fluid phase-change thermal systems, materials processing in the liquid state, on-orbit biofluids processing, among others. For a growing number of important problems, closed-form expressions to transient three-dimensional flows are possible that, as design tools, replace difficult, time-consuming, and rarely performed numerical calculations. An overview of a selection of solutions in-hand is presented with example problems solved. NASA drop tower, low-g aircraft, and ISS flight ex-periment results are employed where practical to buttress the theoretical findings. The current review builds on a similar review presented at COSPAR, 2002, for the approximate decade 1990-2000.

Machine learning spatial geometry from entanglement features

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang

2018-02-01

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).

Killing-Yano forms and Killing tensors on a warped space

NASA Astrophysics Data System (ADS)

Krtouš, Pavel; KubizÅák, David; Kolář, Ivan

2016-01-01

We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several examples, providing new prototypes of spacetimes admitting such tensors. In particular, we study a warped product of two Kerr-NUT-(A)dS spacetimes and show that it gives rise to a new class of highly symmetric vacuum (with a cosmological constant) black hole solutions that inherit many of the properties of the Kerr-NUT-(A)dS geometry.

General very special relativity in Finsler cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C.

2009-05-15

General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.

High-order continuum kinetic method for modeling plasma dynamics in phase space

DOE PAGES

Vogman, G. V.; Colella, P.; Shumlak, U.

2014-12-15

Continuum methods offer a high-fidelity means of simulating plasma kinetics. While computationally intensive, these methods are advantageous because they can be cast in conservation-law form, are not susceptible to noise, and can be implemented using high-order numerical methods. Advances in continuum method capabilities for modeling kinetic phenomena in plasmas require the development of validation tools in higher dimensional phase space and an ability to handle non-cartesian geometries. To that end, a new benchmark for validating Vlasov-Poisson simulations in 3D (x,v x,v y) is presented. The benchmark is based on the Dory-Guest-Harris instability and is successfully used to validate a continuummore » finite volume algorithm. To address challenges associated with non-cartesian geometries, unique features of cylindrical phase space coordinates are described. Preliminary results of continuum kinetic simulations in 4D (r,z,v r,v z) phase space are presented.« less

Blackfolds, plane waves and minimal surfaces

NASA Astrophysics Data System (ADS)

Armas, Jay; Blau, Matthias

2015-07-01

Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

DOE PAGES

Theis, Daniel; Ivanic, Joseph; Windus, Theresa L.; ...

2016-03-10

The metastable ring structure of the ozone 1 1A 1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two 1A 1 states. In the present work, valence correlated energies of the 1 1A 1 state and the 2 1A 1 state were calculated at the 1 1A 1 open minimum, the 1 1A 1 ring minimum, themore » transition state between these two minima, the minimum of the 2 1A 1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of CorrelationEnergy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 11A1 state, the present calculations yield the estimates of (ring minimum—open minimum) ~45–50 mh and (transition state—open minimum) ~85–90 mh. For the (2 1A 1– 1A 1) excitation energy, the estimate of ~130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (2 1A 1– 1A 1) is found to be between 1 and 10 mh. The geometry of the transition state on the 11A1 surface and that of the minimum on the 2 1A 1 surface nearly coincide. More accurate predictions of the energydifferences also require CI expansions to at least sextuple excitations with respect to the valence space. Furthermore, for every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.« less

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Theis, Daniel; Ivanic, Joseph; Windus, Theresa L.

The metastable ring structure of the ozone 1 1A 1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two 1A 1 states. In the present work, valence correlated energies of the 1 1A 1 state and the 2 1A 1 state were calculated at the 1 1A 1 open minimum, the 1 1A 1 ring minimum, themore » transition state between these two minima, the minimum of the 2 1A 1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of CorrelationEnergy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 11A1 state, the present calculations yield the estimates of (ring minimum—open minimum) ~45–50 mh and (transition state—open minimum) ~85–90 mh. For the (2 1A 1– 1A 1) excitation energy, the estimate of ~130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (2 1A 1– 1A 1) is found to be between 1 and 10 mh. The geometry of the transition state on the 11A1 surface and that of the minimum on the 2 1A 1 surface nearly coincide. More accurate predictions of the energydifferences also require CI expansions to at least sextuple excitations with respect to the valence space. Furthermore, for every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.« less

Three-dimensional and time-ordered surface-enhanced Raman scattering hotspot matrix.

PubMed

Liu, Honglin; Yang, Zhilin; Meng, Lingyan; Sun, Yudie; Wang, Jie; Yang, Liangbao; Liu, Jinhuai; Tian, Zhongqun

2014-04-09

The "fixed" or "flexible" design of plasmonic hotspots is a frontier area of research in the field of surface-enhanced Raman scattering (SERS). Most reported SERS hotspots have been shown to exist in zero-dimensional point-like, one-dimensional linear, or two-dimensional planar geometries. Here, we demonstrate a novel three-dimensional (3D) hotspot matrix that can hold hotspots between every two adjacent particles in 3D space, simply achieved by evaporating a droplet of citrate-Ag sols on a fluorosilylated silicon wafer. In situ synchrotron-radiation small-angle X-ray scattering (SR-SAXS), combined with dark-field microscopy and in situ micro-UV, was employed to explore the evolution of the 3D geometry and plasmonic properties of Ag nanoparticles in a single droplet. In such a droplet, there is a distinct 3D geometry with minimal polydispersity of particle size and maximal uniformity of interparticle distance, significantly different from the dry state. According to theoretical simulations, the liquid adhesive force promotes a closely packed assembly of particles, and the interparticle distance is not fixed but can be balanced in a small range by the interplay of the van der Waals attraction and electrostatic repulsion experienced by a particle. The "trapping well" for immobilizing particles in 3D space can result in a large number of hotspots in a 3D geometry. Both theoretical and experimental results demonstrate that the 3D hotspots are predictable and time-ordered in the absence of any sample manipulation. Use of the matrix not only produces giant Raman enhancement at least 2 orders of magnitude larger than that of dried substrates, but also provides the structural basis for trapping molecules. Even a single molecule of resonant dye can generate a large SERS signal. With a portable Raman spectrometer, the detection capability is also greatly improved for various analytes with different natures, including pesticides and drugs. This 3D hotspot matrix overcomes the long-standing limitations of SERS for the ultrasensitive characterization of various substrates and analytes and promises to transform SERS into a practical analytical technique.

Nonreciprocal lasing in topological cavities of arbitrary geometries

NASA Astrophysics Data System (ADS)

Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe; El Amili, Abdelkrim; Fainman, Yeshaiahu; Kanté, Boubacar

2017-11-01

Resonant cavities are essential building blocks governing many wave-based phenomena, but their geometry and reciprocity fundamentally limit the integration of optical devices. We report, at telecommunication wavelengths, geometry-independent and integrated nonreciprocal topological cavities that couple stimulated emission from one-way photonic edge states to a selected waveguide output with an isolation ratio in excess of 10 decibels. Nonreciprocity originates from unidirectional edge states at the boundary between photonic structures with distinct topological invariants. Our experimental demonstration of lasing from topological cavities provides the opportunity to develop complex topological circuitry of arbitrary geometries for the integrated and robust generation and transport of photons in classical and quantum regimes.

The Perspective Structure of Visual Space

PubMed Central

2015-01-01

Luneburg’s model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg’s model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg’s model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances. PMID:27648222

Earthquakes triggered by fluid extraction

USGS Publications Warehouse

Segall, P.

1989-01-01

Seismicity is correlated in space and time with production from some oil and gas fields where pore pressures have declined by several tens of megapascals. Reverse faulting has occurred both above and below petroleum reservoirs, and normal faulting has occurred on the flanks of at least one reservoir. The theory of poroelasticity requires that fluid extraction locally alter the state of stress. Calculations with simple geometries predict stress perturbations that are consistent with observed earthquake locations and focal mechanisms. Measurements of surface displacement and strain, pore pressure, stress, and poroelastic rock properties in such areas could be used to test theoretical predictions and improve our understanding of earthquake mechanics. -Author

Resistive-pulse and rectification sensing with glass and carbon nanopipettes

PubMed Central

Wang, Yixian; Wang, Dengchao

2017-01-01

Along with more prevalent solid-state nanopores, glass or quartz nanopipettes have found applications in resistive-pulse and rectification sensing. Their advantages include the ease of fabrication, small physical size and needle-like geometry, rendering them useful for local measurements in small spaces and delivery of nanoparticles/biomolecules. Carbon nanopipettes fabricated by depositing a thin carbon layer on the inner wall of a quartz pipette provide additional means for detecting electroactive species and fine-tuning the current rectification properties. In this paper, we discuss the fundamentals of resistive-pulse sensing with nanopipettes and our recent studies of current rectification in carbon pipettes. PMID:28413354

Resistive-pulse and rectification sensing with glass and carbon nanopipettes.

PubMed

Wang, Yixian; Wang, Dengchao; Mirkin, Michael V

2017-03-01

Along with more prevalent solid-state nanopores, glass or quartz nanopipettes have found applications in resistive-pulse and rectification sensing. Their advantages include the ease of fabrication, small physical size and needle-like geometry, rendering them useful for local measurements in small spaces and delivery of nanoparticles/biomolecules. Carbon nanopipettes fabricated by depositing a thin carbon layer on the inner wall of a quartz pipette provide additional means for detecting electroactive species and fine-tuning the current rectification properties. In this paper, we discuss the fundamentals of resistive-pulse sensing with nanopipettes and our recent studies of current rectification in carbon pipettes.

Toward quantum plasmonic networks

DOE PAGES

Holtfrerich, M. W.; Dowran, M.; Davidson, R.; ...

2016-08-30

Here, we demonstrate the transduction of macroscopic quantum entanglement by independent, distant plasmonic structures embedded in separate thin silver films. In particular, we show that the plasmon-mediated transmission through each film conserves spatially dependent, entangled quantum images, opening the door for the implementation of parallel quantum protocols, super-resolution imaging, and quantum plasmonic sensing geometries at the nanoscale level. The conservation of quantum information by the transduction process shows that continuous variable multi-mode entanglement is momentarily transferred from entangled beams of light to the space-like separated, completely independent plasmonic structures, thus providing a first important step toward establishing a multichannel quantummore » network across separate solid-state substrates.« less

Minimal scales from an extended Hilbert space

NASA Astrophysics Data System (ADS)

Kober, Martin; Nicolini, Piero

2010-12-01

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to noncommutative geometry. We explore, as a toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.

Microcomponent assembly for efficient contacting of fluid

DOEpatents

Drost, Monte K.; Wegeng, Robert S.; Friedrich, Michele; Hanna, William T.; Call, Charles J.; Kurath, Dean E.

2000-01-01

The present invention is a fundamental method and apparatus of a microcomponent assembly that overcomes the inherent limitations of state of the art chemical separations. The fundamental element enabling miniaturization is the porous contactor contained within a microcomponent assembly for mass transfer of a working compound from a first medium to a second medium. The porous contactor has a thickness, and a plurality of pores extending through the thickness. The pores are of a geometry cooperating with a boundary tension of one or the other or both of the media thereby preventing migration of one, other or both through the microporous contactor while permitting passage of the working compound. In the microcomponent assembly, the porous contactor is placed between a first laminate such that a first space or first microplenum is formed between the microporous contactor and the first laminate. Additionally, a cover sheet provides a second space or second plenum between the porous contactor and the cover sheet.

Competition between anisotropic viscous fingers

NASA Astrophysics Data System (ADS)

Pecelerowicz, M.; Budek, A.; Szymczak, P.

2014-09-01

We consider viscous fingers created by injection of low viscosity fluid into the network of capillaries initially filled with a more viscous fluid (motor oil). Due to the anisotropy of the system and its geometry, such a setup promotes the formation of long-and-thin fingers which then grow and compete for the available flow, interacting through the pressure field. The interaction between the fingers is analyzed using the branched growth formalism of Halsey and Leibig (Phys. Rev. A 46, 7723, 1992) using a number of simple, analytically tractable models. It is shown that as soon as the fingers are allowed to capture the flow from one another, the fixed point appears in the phase space, corresponding to the asymptotic state in which the growth of one of the fingers in hindered by the other. The properties of phase space flows in such systems are shown to be remarkably insensitive to the details of the dynamics.

The effect of helicopter main rotor blade phasing and spacing on performance, blade loads, and acoustics

NASA Technical Reports Server (NTRS)

Gangwani, S. T.

1976-01-01

The performance, blade loads, and acoustic characteristics of a variable geometry rotor (VGR) system in forward flight and in a pullup maneuver were determined by the use of existing analytical programs. The investigation considered the independent effects of vertical separation of two three-bladed rotor systems as well as the effects of azimuthal spacing between the blades of the two rotors. The computations were done to determine the effects of these parameters on the performance, blade loads, and acoustic characteristics at two advance ratios in steady-state level flight and for two different g pullups at one advance ratio. To evaluate the potential benefits of the VGR concept in forward flight and pullup maneuvers, the results were compared as to performance, oscillatory blade loadings, vibratory forces transmitted to the fixed fuselage, and the rotor noise characteristics of the various VGR configurations with those of the conventional six-bladed rotor system.

The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup

NASA Astrophysics Data System (ADS)

Lehrer, G. I.; Zhang, R. B.

2017-01-01

We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.

Comparison of Slab and Cylinder Expansion Test Geometries for PBX 9501

NASA Astrophysics Data System (ADS)

Jackson, Scott; Anderson, Eric; Aslam, Tariq; Whitley, Von

2017-06-01

The slab expansion test or ``sandwich test'' is the two-dimensional analog of the axisymmetric cylinder expansion test. The test consists of a high-aspect-ratio rectangular cuboid of high explosive with the two large sides confined by a thin metal confiner. Analysis of the confiner motion after the passage of the detonation yields the detonation product isentrope, which is a specialized form of the product equation of state. The slab expansion geometry inherently exhibits a lower product expansion rate and lower plastic work on the confiner than the cylinder expansion geometry. The slab geometry does, however, have a shorter test time. We review recent slab and cylinder expansion data with PBX 9501, the associated equation of state analysis, and the advantages of each geometry for different applications.

Shape-matching soft mechanical metamaterials.

PubMed

Mirzaali, M J; Janbaz, S; Strano, M; Vergani, L; Zadpoor, A A

2018-01-17

Architectured materials with rationally designed geometries could be used to create mechanical metamaterials with unprecedented or rare properties and functionalities. Here, we introduce "shape-matching" metamaterials where the geometry of cellular structures comprising auxetic and conventional unit cells is designed so as to achieve a pre-defined shape upon deformation. We used computational models to forward-map the space of planar shapes to the space of geometrical designs. The validity of the underlying computational models was first demonstrated by comparing their predictions with experimental observations on specimens fabricated with indirect additive manufacturing. The forward-maps were then used to devise the geometry of cellular structures that approximate the arbitrary shapes described by random Fourier's series. Finally, we show that the presented metamaterials could match the contours of three real objects including a scapula model, a pumpkin, and a Delft Blue pottery piece. Shape-matching materials have potential applications in soft robotics and wearable (medical) devices.

Holography for a De Sitter-Esque geometry

NASA Astrophysics Data System (ADS)

Anninos, Dionysios; de Buyl, Sophie; Detournay, Stéphane

2011-05-01

Warped dS3 arises as a solution to topologically massive gravity (TMG) with positive cosmological constant +1/ ℓ 2 and Chern-Simons coefficient 1/ μ in the region μ 2 ℓ 2 < 27. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS3 asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regular de Sitter space. The asymptotic symmetry group resides at future infinity and is given by a semi-direct product of a Virasoro algebra and a current algebra. The right moving central charge vanishes when μ 2 ℓ 2 = 27/5. We discuss the possible holographic interpretation of these de Sitter-esque spacetimes.

A Brief History of Non-Euclidean Geometry

ERIC Educational Resources Information Center

Marshall, Daniel; Scott, Paul

2004-01-01

Around 300 BC, Euclid wrote "The Elements", a major treatise on the geometry of the time, and what would be considered "geometry" for many years after. Arguably "The Elements" is the second most read book of the western world, falling short only to The Bible. In his book, Euclid states five postulates of geometry which he uses as the foundation…

Shield Optimization in Simple Geometry for the Gateway Concept

NASA Technical Reports Server (NTRS)

Tripathi, R. K.; Simonsen, L. C.; Nealy, J. E.; Troutman, P. A.; Wilson, J. W.

2002-01-01

The great cost of added radiation shielding is a potential limiting factor in many deep space missions. For this enabling technology, we are developing tools for optimized shield design over multi-segmented missions involving multiple work and living areas in the transport and duty phase of various space missions. The total shield mass over all pieces of equipment and habitats is optimized subject to career dose and dose rate constraints. Preliminary studies of deep space missions indicate that for long duration space missions, improved shield materials will be required. The details of this new method and its impact on space missions and other technologies will be discussed. This study will provide a vital tool for evaluating Gateway designs in their usage context. Providing protection against the hazards of space radiation is one of the challenges to the Gateway infrastructure designs. We will use the mission optimization software to scope the impact of Gateway operations on human exposures and the effectiveness of alternate shielding materials on Gateway infrastructure designs. This study will provide a guide to the effectiveness of multifunctional materials in preparation to more detailed geometry studies in progress.

Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems.

PubMed

Burton, Hugh G A; Gross, Mark; Thom, Alex J W

2018-02-13

We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 / 2 (3 n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

Development and Validation of a Hypersonic Vehicle Design Tool Based On Waverider Design Technique

NASA Astrophysics Data System (ADS)

Dasque, Nastassja

Methodologies for a tool capable of assisting design initiatives for practical waverider based hypersonic vehicles were developed and validated. The design space for vehicle surfaces was formed using an algorithm that coupled directional derivatives with the conservation laws to determine a flow field defined by a set of post-shock streamlines. The design space is used to construct an ideal waverider with a sharp leading edge. A blunting method was developed to modify the ideal shapes to a more practical geometry for real-world application. Empirical and analytical relations were then systematically applied to the resulting geometries to determine local pressure, skin-friction and heat flux. For the ideal portion of the geometry, flat plate relations for compressible flow were applied. For the blunted portion of the geometry modified Newtonian theory, Fay-Riddell theory and Modified Reynolds analogy were applied. The design and analysis methods were validated using analytical solutions as well as empirical and numerical data. The streamline solution for the flow field generation technique was compared with a Taylor-Maccoll solution and showed very good agreement. The relationship between the local Stanton number and skin friction coefficient with local Reynolds number along the ideal portion of the body showed good agreement with experimental data. In addition, an automated grid generation routine was formulated to construct a structured mesh around resulting geometries in preparation for Computational Fluid Dynamics analysis. The overall analysis of the waverider body using the tool was then compared to CFD studies. The CFD flow field showed very good agreement with the design space. However, the distribution of the surface properties was near CFD results but did not have great agreement.

Phenylazopyridine as Switch in Photochemical Reactions. A Detailed Computational Description of the Mechanism of Its Photoisomerization

PubMed Central

Casellas, Josep; Alcover-Fortuny, Gerard; de Graaf, Coen

2017-01-01

Azo compounds are organic photochromic systems that have the possibility of switching between cis and trans isomers under irradiation. The different photochemical properties of these isomers make azo compounds into good light-triggered switches, and their significantly different geometries make them very interesting as components in molecular engines or mechanical switches. For instance, azo ligands are used in coordination complexes to trigger photoresponsive properties. The light-induced trans-to-cis isomerization of phenylazopyridine (PAPy) plays a fundamental role in the room-temperature switchable spin crossover of Ni-porphyrin derivatives. In this work, we present a computational study developed at the SA-CASSCF/CASPT2 level (State Averaged Complete Active Space Self Consistent Field/CAS second order Perturbation Theory) to elucidate the mechanism, up to now unknown, of the cis–trans photoisomerization of 3-PAPy. We have analyzed the possible reaction pathways along its lowest excited states, generated by excitation of one or two electrons from the lone pairs of the N atoms of the azo group (nazoπ*2 and nazo2π*2 states), from a π delocalized molecular orbital (ππ* state), or from the lone pair of the N atom of the pyridine moiety (npyπ* state). Our results show that the mechanism proceeds mainly along the rotation coordinate in both the nazoπ* and ππ* excited states, although the nazo2π*2 state can also be populated temporarily, while the npyπ* does not intervene in the reaction. For rotationally constrained systems, accessible paths to reach the cis minimum along planar geometries have also been located, again on the nazoπ* and ππ* potential energy surfaces, while the nazo2π*2 and npyπ* states are not involved in the reaction. The relative energies of the different paths differ from those found for azobenzene in a previous work, so our results predict some differences between the reactivities of both compounds. PMID:29168765

Evaluation of the performance of single root multireference coupled cluster method for ground and excited states, and its application to geometry optimization.

PubMed

Mahapatra, Uttam Sinha; Chattopadhyay, Sudip

2011-01-28

The complete model space (CAS) based "genuine" single root multireference (MR) coupled cluster (sr-MRCC) method [Mahapatra and Chattopadhyay, J. Chem. Phys. 133, 074102 (2010)] has been extended to enable geometry optimizations by adopting the numerical gradient scheme. The sr-MRCC theory is designed to treat quasidegeneracies of varying degrees through the computation of essential static and dynamic correlation effects in a balanced way while bypassing the intruder states problem in a size-extensive manner. The efficacy of our sr-MRCC gradient approach has been illustrated by the optimization of the geometries of N(2)H(2),CH(2),C(2)H(4),C(4)H(4),O(3) as well as trimethylenemethane (TMM) molecular systems, since such cases, by virtue of their complexity, warrant truly multireference description. We have explored the capability of the sr-MRCC approach to yield rotational energy surfaces for the ground and first singlet excited states of N(2)H(2). We also intend to explore the ground and the excited state energetics of some model systems (such as P4, H4, and H(8)) for the computation of excitation energies by relying on the sr-MRCC method. An analysis of the results and a comparison with previous pertinent theoretical works including state specific MRCC (SS-MRCC) theory of Mukherjee and co-workers have also been presented. Although in most of the cases, we observe a close behavior between the sr-MRCC and SS-MRCC method, the error in the sr-MRCC is lower than the overall error of the SS-MRCC calculations in the vicinity of the transition region (manifesting a significant quasidegenerate character). The present results show that the sr-MRCC method and its numerical gradient variant are generally applicable to very demanding model and realistic chemical problems at acceptable accuracy and affordable computational expense which together attests the efficacy and viability of the sr-MRCC formalism for handling of static and dynamic correlations simultaneously thereby ensuring a balanced description for bond-breaking and other quasidegenerate situations with a various degree of MR character. Our preliminary results illustrate that our sr-MRCC method is a potential competitor for other state specific MRCC theories.

Transition and mixing in axisymmetric jets and vortex rings

NASA Technical Reports Server (NTRS)

Allen, G. A., Jr.; Cantwell, B. J.

1986-01-01

A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.

On the bonding mechanism of CO to Pt(111) and its effect on the vibrational frequency of chemisorbed CO

NASA Astrophysics Data System (ADS)

Illas, F.; Zurita, S.; Márquez, A. M.; Rubio, J.

1997-04-01

The chemisorption of CO on the atop site of Pt(111) has been simulated by a Pt4 cluster model. Ab initio self consistent field (SCF) and complete active space self consistent field (CASSCF) cluster model wave functions have been obtained for the electronic ground state. Likewise, ab initio SCF wavefunctions have been obtained for two other electronic states. The optimum geometry and vibrational frequencies of chemisorbed CO are reported for the three states. The interaction energy and vibrational shift of chemisorbed CO, with respect to free gas phase CO, have been analyzed for the three electronic states. This analysis is carried out by means of the constrained space orbital variation (CSOV) method. In all cases the bond is found to be dominated by σ donation and π back-donation, known as Blyholder's mechanism. This mechanism is further supported by SCF calculations on a larger, Pt13, cluster model. For both clusters, the CSOV analysis of the vibrational frequency definitely shows that, contrary to previous recent studies, a major contribution to the experimentally observed vibrational shift comes from the π back-donation mechanism. However, we found that, contrary to common belief, σ donation also acts to lower the CO frequency and not to increase it. Physical reasons for such unexpected behaviour are given.

The Scintillation Prediction Observations Research Task (SPORT): A Multinational Science Mission using a CubeSat

NASA Astrophysics Data System (ADS)

Spann, J. F.; Habash Krause, L.; Swenson, C.; Heelis, R. A.; Bishop, R. L.; Le, G.; Abdu, M. A.; Durão, O.; Loures, L.; De Nardin, C. M.; Shibuya, L.; Casas, J.; Nash-STevenson, S.; Muralikrishana, P.; Costa, J. E. R.; Wrasse, C. M.; Fry, C. D.

2017-12-01

The Scintillation Prediction Observations Research Task (SPORT) is a 6U CubeSat pathfinder mission to address the very compelling but difficult problem of understanding the preconditions leading to equatorial plasma bubbles. The scientific literature describes the preconditions in both the plasma drifts and the density profiles related to bubble formations that occur several hours later in the evening. Most of the scientific discovery has resulted from observations at the Jicamarca Radio Observatory from Peru, a single site, within a single longitude sector. SPORT will provide a systematic study of the state of the pre-bubble conditions at all longitudes sectors to allow us to understand the differences between geography and magnetic geometry. This talk will present an overview of the mission and the anticipated data products. Products include global maps of scintillation occurrence as a function of local time, and magnetic conjugacy occurrence observations. SPORT is a multinational partnership between NASA, the Brazilian National Institute for Space Research (INPE), and the Technical Aeronautics Institute under the Brazilian Air Force Command Department (DCTA/ITA). It has been encouraged by U.S. Southern Command (SOUTHCOM) to foster increased cooperation and ties between academics, civilian space programs and the militaries. NASA Marshall Space Flight Center is coordinating this investigation by overseeing the launch to orbit and the flight instruments, which are being built by the Aerospace Corporation, University of Texas Dallas, Utah State University, and NASA Goddard Space Flight Center. The Brazilian partners are contributing the spacecraft, observatory integration and test, ground observation networks, and mission operations and data management. The science data will be distributed from and archived at the INPE/EMBRACE regional space-weather forecasting center in Brazil, and mirrored at the NASA GSFC Space Physics Data Facility (SPDF).

An application of geostatistics and fractal geometry for reservoir characterization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aasum, Y.; Kelkar, M.G.; Gupta, S.P.

1991-03-01

This paper presents an application of geostatistics and fractal geometry concepts for 2D characterization of rock properties (k and {phi}) in a dolomitic, layered-cake reservoir. The results indicate that lack of closely spaced data yield effectively random distributions of properties. Further, incorporation of geology reduces uncertainties in fractal interpolation of wellbore properties.

Fiatland: An Analogy between Mathematics and Physics

ERIC Educational Resources Information Center

Reich, Karin

2007-01-01

Before the 19th century the idea of more than three dimensions was exceptional. During the 19th century, however, geometry was revolutionized and new branches were developed. This revolution also created the idea of the possibility of a n-dimensional geometry or space; flatland, i.e. n = 2, was a consequence of this new thinking. In 1884 the…

The Effect of Dynamic Geometry Software on Student Mathematics Teachers' Spatial Visualization Skills

ERIC Educational Resources Information Center

Güven, Bülent; Kosa, Temel

2008-01-01

Geometry is the study of shape and space. Without spatial ability, students cannot fully appreciate the natural world. Spatial ability is also very important for work in various fields such as computer graphics, engineering, architecture, and cartography. A number of studies have demonstrated that technology has an important potential to develop…

A Simple, Powerful Method for Optimal Guidance of Spacecraft Formations

NASA Technical Reports Server (NTRS)

Hughes, Steven P.

2006-01-01

One of the most interesting and challenging aspects of formation guidance law design is the coupling of the orbit design and the science return. The analyst's role is more complicated than simply to design the formation geometry and evolution. He or she is also involved in designing a significant portion of the science instrument itself. The effectiveness of the formation as a science instrument is intimately coupled with the relative geometry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a simple method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to two missions: the Magnetospheric Multiscale mission (MMS) , and the Laser Interferometer Space Antenna (LISA).

On-chip non-reciprocal optical devices based on quantum inspired photonic lattices

NASA Astrophysics Data System (ADS)

El-Ganainy, R.; Eisfeld, A.; Levy, Miguel; Christodoulides, D. N.

2013-10-01

We propose integrated optical structures that can be used as isolators and polarization splitters based on engineered photonic lattices. Starting from optical waveguide arrays that mimic Fock space (quantum state with a well-defined particle number) representation of a non-interacting two-site Bose Hubbard Hamiltonian, we show that introducing magneto-optic nonreciprocity to these structures leads to a superior optical isolation performance. In the forward propagation direction, an input TM polarized beam experiences a perfect state transfer between the input and output waveguide channels while surface Bloch oscillations block the backward transmission between the same ports. Our analysis indicates a large isolation ratio of 75 dB after a propagation distance of 8 mm inside seven coupled waveguides. Moreover, we demonstrate that, a judicious choice of the nonreciprocity in this same geometry can lead to perfect polarization splitting.

Technical guidance for the development of a solid state image sensor for human low vision image warping

NASA Technical Reports Server (NTRS)

Vanderspiegel, Jan

1994-01-01

This report surveys different technologies and approaches to realize sensors for image warping. The goal is to study the feasibility, technical aspects, and limitations of making an electronic camera with special geometries which implements certain transformations for image warping. This work was inspired by the research done by Dr. Juday at NASA Johnson Space Center on image warping. The study has looked into different solid-state technologies to fabricate image sensors. It is found that among the available technologies, CMOS is preferred over CCD technology. CMOS provides more flexibility to design different functions into the sensor, is more widely available, and is a lower cost solution. By using an architecture with row and column decoders one has the added flexibility of addressing the pixels at random, or read out only part of the image.

Noncommutative complex structures on quantum homogeneous spaces

NASA Astrophysics Data System (ADS)

Ó Buachalla, Réamonn

2016-01-01

A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for quantum homogeneous spaces. A number of basic results are established, producing a simple set of necessary and sufficient conditions for noncommutative complex structures to exist. Throughout, the framework is applied to the quantum projective spaces endowed with the Heckenberger-Kolb calculus.

Theoretical study of singlet oxygen molecule generation via an exciplex with valence-excited thiophene.

PubMed

Sumita, Masato; Morihashi, Kenji

2015-02-05

Singlet-oxygen [O2((1)Δg)] generation by valence-excited thiophene (TPH) has been investigated using multireference Møller-Plesset second-order perturbation (MRMP2) theory of geometries optimized at the complete active space self-consistent field (CASSCF) theory level. Our results indicate that triplet TPH(1(3)B2) is produced via photoinduced singlet TPH(2(1)A1) because 2(1)A1 TPH shows a large spin-orbit coupling constant with the first triplet excited state (1(3)B2). The relaxed TPH in the 1(3)B2 state can form an exciplex with O2((3)Σg(-)) because this exciplex is energetically more stable than the relaxed TPH. The formation of the TPH(1(3)B2) exciplex with O2((3)Σg(-)) whose total spin multiplicity is triplet (T1 state) increases the likelihood of transition from the T1 state to the singlet ground or first excited singlet state. After the transition, O2((1)Δg) is emitted easily although the favorable product is that from a 2 + 4 cycloaddition reaction.

Numerical study of the effects of surface topography and chemistry on the wetting transition using the string method.

PubMed

Zhang, Yanan; Ren, Weiqing

2014-12-28

Droplets on a solid surface patterned with microstructures can exhibit the composite Cassie-Baxter (CB) state or the wetted Wenzel state. The stability of the CB state is determined by the energy barrier separating it from the wetted state. In this work, we study the CB to Wenzel transition using the string method [E et al., J. Chem. Phys. 126, 164103 (2007); W. Ren and E. Vanden-Eijnden, J. Chem. Phys. 138, 134105 (2013)]. We compute the transition states and energy barriers for a three-dimensional droplet on patterned surfaces. The liquid-vapor coexistence is modeled using the mean field theory. Numerical results are obtained for surfaces patterned with straight pillars and nails, respectively. It is found that on both type of surfaces, wetting occurs via infiltration of the liquid in a single groove. The reentrant geometry of nails creates large energy barrier for the wetting of the solid surface compared to straight pillars. We also study the effect of surface chemistry, pillar height, and inter-pillar spacing on the energy barrier and compare it with nails.

Numerical study of the effects of surface topography and chemistry on the wetting transition using the string method

NASA Astrophysics Data System (ADS)

Zhang, Yanan; Ren, Weiqing

2014-12-01

Droplets on a solid surface patterned with microstructures can exhibit the composite Cassie-Baxter (CB) state or the wetted Wenzel state. The stability of the CB state is determined by the energy barrier separating it from the wetted state. In this work, we study the CB to Wenzel transition using the string method [E et al., J. Chem. Phys. 126, 164103 (2007); W. Ren and E. Vanden-Eijnden, J. Chem. Phys. 138, 134105 (2013)]. We compute the transition states and energy barriers for a three-dimensional droplet on patterned surfaces. The liquid-vapor coexistence is modeled using the mean field theory. Numerical results are obtained for surfaces patterned with straight pillars and nails, respectively. It is found that on both type of surfaces, wetting occurs via infiltration of the liquid in a single groove. The reentrant geometry of nails creates large energy barrier for the wetting of the solid surface compared to straight pillars. We also study the effect of surface chemistry, pillar height, and inter-pillar spacing on the energy barrier and compare it with nails.

Image-based 3D reconstruction and virtual environmental walk-through

NASA Astrophysics Data System (ADS)

Sun, Jifeng; Fang, Lixiong; Luo, Ying

2001-09-01

We present a 3D reconstruction method, which combines geometry-based modeling, image-based modeling and rendering techniques. The first component is an interactive geometry modeling method which recovery of the basic geometry of the photographed scene. The second component is model-based stereo algorithm. We discus the image processing problems and algorithms of walking through in virtual space, then designs and implement a high performance multi-thread wandering algorithm. The applications range from architectural planning and archaeological reconstruction to virtual environments and cinematic special effects.

Walking through Architectural Spaces: The Impact of Interior Forms on Human Brain Dynamics

PubMed Central

Banaei, Maryam; Hatami, Javad; Yazdanfar, Abbas; Gramann, Klaus

2017-01-01

Neuroarchitecture uses neuroscientific tools to better understand architectural design and its impact on human perception and subjective experience. The form or shape of the built environment is fundamental to architectural design, but not many studies have shown the impact of different forms on the inhabitants’ emotions. This study investigated the neurophysiological correlates of different interior forms on the perceivers’ affective state and the accompanying brain activity. To understand the impact of naturalistic three-dimensional (3D) architectural forms, it is essential to perceive forms from different perspectives. We computed clusters of form features extracted from pictures of residential interiors and constructed exemplary 3D room models based on and representing different formal clusters. To investigate human brain activity during 3D perception of architectural spaces, we used a mobile brain/body imaging (MoBI) approach recording the electroencephalogram (EEG) of participants while they naturally walk through different interior forms in virtual reality (VR). The results revealed a strong impact of curvature geometries on activity in the anterior cingulate cortex (ACC). Theta band activity in ACC correlated with specific feature types (rs (14) = 0.525, p = 0.037) and geometry (rs (14) = −0.579, p = 0.019), providing evidence for a role of this structure in processing architectural features beyond their emotional impact. The posterior cingulate cortex and the occipital lobe were involved in the perception of different room perspectives during the stroll through the rooms. This study sheds new light on the use of mobile EEG and VR in architectural studies and provides the opportunity to study human brain dynamics in participants that actively explore and realistically experience architectural spaces. PMID:29033807

Walking through Architectural Spaces: The Impact of Interior Forms on Human Brain Dynamics.

PubMed

Banaei, Maryam; Hatami, Javad; Yazdanfar, Abbas; Gramann, Klaus

2017-01-01

Neuroarchitecture uses neuroscientific tools to better understand architectural design and its impact on human perception and subjective experience. The form or shape of the built environment is fundamental to architectural design, but not many studies have shown the impact of different forms on the inhabitants' emotions. This study investigated the neurophysiological correlates of different interior forms on the perceivers' affective state and the accompanying brain activity. To understand the impact of naturalistic three-dimensional (3D) architectural forms, it is essential to perceive forms from different perspectives. We computed clusters of form features extracted from pictures of residential interiors and constructed exemplary 3D room models based on and representing different formal clusters. To investigate human brain activity during 3D perception of architectural spaces, we used a mobile brain/body imaging (MoBI) approach recording the electroencephalogram (EEG) of participants while they naturally walk through different interior forms in virtual reality (VR). The results revealed a strong impact of curvature geometries on activity in the anterior cingulate cortex (ACC). Theta band activity in ACC correlated with specific feature types ( r s (14) = 0.525, p = 0.037) and geometry ( r s (14) = -0.579, p = 0.019), providing evidence for a role of this structure in processing architectural features beyond their emotional impact. The posterior cingulate cortex and the occipital lobe were involved in the perception of different room perspectives during the stroll through the rooms. This study sheds new light on the use of mobile EEG and VR in architectural studies and provides the opportunity to study human brain dynamics in participants that actively explore and realistically experience architectural spaces.

Quantum mechanics of conformally and minimally coupled Friedmann-Robertson-Walker cosmology

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

1992-10-01

The expansion method by a time-dependent basis of the eigenfunctions for the space-coordinate-dependent sub-Hamiltonian is one of the most natural frameworks for quantum systems, relativistic as well as nonrelativistic. The complete set of wave functions is found in the product integral formulation, whose constants of integration are fixed by Cauchy initial data. The wave functions for the Friedmann-Robertson-Walker (FRW) cosmology conformally and minimally coupled to a scalar field with a power-law potential or a polynomial potential are expanded in terms of the eigenfunctions of the scalar field sub-Hamiltonian part. The resultant gravitational field part which is an ``intrinsic'' timelike variable-dependent matrix-valued differential equation is solved again in the product integral formulation. There are classically allowed regions for the ``intrinsic'' timelike variable depending on the scalar field quantum numbers and these regions increase accordingly as the quantum numbers increase. For a fixed large three-geometry the wave functions corresponding to the low excited (small quantum number) states of the scalar field are exponentially damped or diverging and the wave functions corresponding to the high excited (large quantum number) states are still oscillatory but become eventually exponential as the three-geometry becomes larger. Furthermore, a proposal is advanced that the wave functions exponentially damped for a large three-geometry may be interpreted as ``tunneling out'' wave functions into, and the wave functions exponentially diverging as ``tunneling in'' from, different universes with the same or different topologies, the former being interpreted as the recently proposed Hawking-Page wormhole wave functions. It is observed that there are complex as well as Euclidean actions depending on the quantum numbers of the scalar field part outside the classically allowed region both of the gravitational and scalar fields, suggesting the usefulness of complex geometry and complex trajectories. From the most general wave functions for the FRW cosmology conformally coupled to scalar field, the boundary conditions for the wormhole wave functions are modified so that the modulus of wave functions, instead of the wave functions themselves, should be exponentially damped for a large three-geometry and be regular up to some negative power of the three-geometry as the three-geometry collapses. The wave functions for the FRW cosmology minimally coupled to an inhomogeneous scalar field are similarly found in the product integral formulation. The role of a large number of the inhomogeneous modes of the scalar field is not only to increase the classically allowed regions for the gravitational part but also to provide a mechanism of the decoherence of quantum interferences between the different sizes of the universe.

Embedding of the brane into six dimensions

NASA Astrophysics Data System (ADS)

Gogberashvili, Merab

2002-10-01

Embedding of the brane metric into Euclidean (2+4)-space is found. Brane geometry can be visualized as the surface of the hypersphere in six dimensions which ``radius'' is governed by the cosmological constant. Minkowski space in this picture is placed on the intersection of this surface with the plane formed by the extra space-like and time-like coordinates.

Pore space analysis of NAPL distribution in sand-clay media

USGS Publications Warehouse

Matmon, D.; Hayden, N.J.

2003-01-01

This paper introduces a conceptual model of clays and non-aqueous phase liquids (NAPLs) at the pore scale that has been developed from a mathematical unit cell model, and direct micromodel observation and measurement of clay-containing porous media. The mathematical model uses a unit cell concept with uniform spherical grains for simulating the sand in the sand-clay matrix (???10% clay). Micromodels made with glass slides and including different clay-containing porous media were used to investigate the two clays (kaolinite and montmorillonite) and NAPL distribution within the pore space. The results were used to understand the distribution of NAPL advancing into initially saturated sand and sand-clay media, and provided a detailed analysis of the pore-scale geometry, pore size distribution, NAPL entry pressures, and the effect of clay on this geometry. Interesting NAPL saturation profiles were observed as a result of the complexity of the pore space geometry with the different packing angles and the presence of clays. The unit cell approach has applications for enhancing the mechanistic understanding and conceptualization, both visually and mathematically, of pore-scale processes such as NAPL and clay distribution. ?? 2003 Elsevier Science Ltd. All rights reserved.

Gradient Space under Orthography and Perspective

DTIC Science & Technology

1982-05-24

surfaceorientation to image geometry [8, 9, 10, 13, 15]. The descriptions of important gradient space properties, however, have been scattered throughout...Kanade, T. A Theory of Origami World. Artificial Intelligence 13:279-311, 1980. *[8] Kanade, T. and Kender, J. Mapping Image Properies into Shape

Cosmological evolution as squeezing: a toy model for group field cosmology

NASA Astrophysics Data System (ADS)

Adjei, Eugene; Gielen, Steffen; Wieland, Wolfgang

2018-05-01

We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat Friedmann–Lemaître–Robertson–Walker universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton’s constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve as an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application.

[Geometry Through Symmetry, Cambridge Conference on School Mathematics Feasibility Study No. 32.

ERIC Educational Resources Information Center

Friedman, Bernard

These materials were written for the use of a class of eighth grade high ability students in a four week course sponsored by Educational Services Incorporated on the Stanford campus. They represent a practical response to the proposal by the Cambridge Conference of 1963 that geometry be taught by vector space methods. Instead of using vector…

Automated Welding System

NASA Technical Reports Server (NTRS)

Bayless, E. O.; Lawless, K. G.; Kurgan, C.; Nunes, A. C.; Graham, B. F.; Hoffman, D.; Jones, C. S.; Shepard, R.

1993-01-01

Fully automated variable-polarity plasma arc VPPA welding system developed at Marshall Space Flight Center. System eliminates defects caused by human error. Integrates many sensors with mathematical model of the weld and computer-controlled welding equipment. Sensors provide real-time information on geometry of weld bead, location of weld joint, and wire-feed entry. Mathematical model relates geometry of weld to critical parameters of welding process.

"There is One Geometry and in Each Case There is a Different Formula"

ERIC Educational Resources Information Center

Rizos, Ioannis; Patronis, Anastasios; Lappas, Dionyssios

2017-01-01

In this paper, we analyze two episodes from an inquiry-based didactical research; the complete analysis of our research data is still ongoing. By taking into consideration various developments from the history of the geometry of space-time, our general aim is to explore high school students' conceptions about measurement of length and time in…

A Study of Multi-Representation of Geometry Problem Solving with Virtual Manipulatives and Whiteboard System

ERIC Educational Resources Information Center

Hwang, Wu-Yuin; Su, Jia-Han; Huang, Yueh-Min; Dong, Jian-Jie

2009-01-01

In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…

Foam structure :from soap froth to solid foams.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kraynik, Andrew Michael

2003-01-01

The properties of solid foams depend on their structure, which usually evolves in the fluid state as gas bubbles expand to form polyhedral cells. The characteristic feature of foam structure-randomly packed cells of different sizes and shapes-is examined in this article by considering soap froth. This material can be modeled as a network of minimal surfaces that divide space into polyhedral cells. The cell-level geometry of random soap froth is calculated with Brakke's Surface Evolver software. The distribution of cell volumes ranges from monodisperse to highly polydisperse. Topological and geometric properties, such as surface area and edge length, of themore » entire foam and individual cells, are discussed. The shape of struts in solid foams is related to Plateau borders in liquid foams and calculated for different volume fractions of material. The models of soap froth are used as templates to produce finite element models of open-cell foams. Three-dimensional images of open-cell foams obtained with x-ray microtomography allow virtual reconstruction of skeletal structures that compare well with the Surface Evolver simulations of soap-froth geometry.« less

Characterization of Swirl-Venturi Lean Direct Injection Designs for Aviation Gas-Turbine Combustion

NASA Technical Reports Server (NTRS)

Heath, Christopher M.

2013-01-01

Injector geometry, physical mixing, chemical processes, and engine cycle conditions together govern performance, operability and emission characteristics of aviation gas-turbine combustion systems. The present investigation explores swirl-venturi lean direct injection combustor fundamentals, characterizing the influence of key geometric injector parameters on reacting flow physics and emission production trends. In this computational study, a design space exploration was performed using a parameterized swirl-venturi lean direct injector model. From the parametric geometry, 20 three-element lean direct injection combustor sectors were produced and simulated using steady-state, Reynolds-averaged Navier-Stokes reacting computations. Species concentrations were solved directly using a reduced 18-step reaction mechanism for Jet-A. Turbulence closure was obtained using a nonlinear ?-e model. Results demonstrate sensitivities of the geometric perturbations on axially averaged flow field responses. Output variables include axial velocity, turbulent kinetic energy, static temperature, fuel patternation and minor species mass fractions. Significant trends have been reduced to surrogate model approximations, intended to guide future injector design trade studies and advance aviation gas-turbine combustion research.

Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian geometry

NASA Astrophysics Data System (ADS)

Zanardi, Paolo; Campos Venuti, Lorenzo

2018-01-01

We establish a direct connection between the power of a unitary map in d-dimensions (d < ∞) to generate quantum coherence and the geometry of the set Md of maximally abelian subalgebras (of the quantum system full operator algebra). This set can be seen as a topologically non-trivial subset of the Grassmannian over linear operators. The natural distance over the Grassmannian induces a metric structure on Md, which quantifies the lack of commutativity between the pairs of subalgebras. Given a maximally abelian subalgebra, one can define, on physical grounds, an associated measure of quantum coherence. We show that the average quantum coherence generated by a unitary map acting on a uniform ensemble of quantum states in the algebra (the so-called coherence generating power of the map) is proportional to the distance between a pair of maximally abelian subalgebras in Md connected by the unitary transformation itself. By embedding the Grassmannian into a projective space, one can pull-back the standard Fubini-Study metric on Md and define in this way novel geometrical measures of quantum coherence generating power. We also briefly discuss the associated differential metric structures.

Simultaneous two-view epipolar geometry estimation and motion segmentation by 4D tensor voting.

PubMed

Tong, Wai-Shun; Tang, Chi-Keung; Medioni, Gérard

2004-09-01

We address the problem of simultaneous two-view epipolar geometry estimation and motion segmentation from nonstatic scenes. Given a set of noisy image pairs containing matches of n objects, we propose an unconventional, efficient, and robust method, 4D tensor voting, for estimating the unknown n epipolar geometries, and segmenting the static and motion matching pairs into n independent motions. By considering the 4D isotropic and orthogonal joint image space, only two tensor voting passes are needed, and a very high noise to signal ratio (up to five) can be tolerated. Epipolar geometries corresponding to multiple, rigid motions are extracted in succession. Only two uncalibrated frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) other than the pin-hole camera model is made. Our novel approach consists of propagating a local geometric smoothness constraint in the 4D joint image space, followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions. We have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved. Results on challenging data sets are presented.

Role of jet spacing and strut geometry on the formation of large scale structures and mixing characteristics

NASA Astrophysics Data System (ADS)

Soni, Rahul Kumar; De, Ashoke

2018-05-01

The present study primarily focuses on the effect of the jet spacing and strut geometry on the evolution and structure of the large-scale vortices which play a key role in mixing characteristics in turbulent supersonic flows. Numerically simulated results corresponding to varying parameters such as strut geometry and jet spacing (Xn = nDj such that n = 2, 3, and 5) for a square jet of height Dj = 0.6 mm are presented in the current study, while the work also investigates the presence of the local quasi-two-dimensionality for the X2(2Dj) jet spacing; however, the same is not true for higher jet spacing. Further, the tapered strut (TS) section is modified into the straight strut (SS) for investigation, where the remarkable difference in flow physics is unfolded between the two configurations for similar jet spacing (X2: 2Dj). The instantaneous density and vorticity contours reveal the structures of varying scales undergoing different evolution for the different configurations. The effect of local spanwise rollers is clearly manifested in the mixing efficiency and the jet spreading rate. The SS configuration exhibits excellent near field mixing behavior amongst all the arrangements. However, in the case of TS cases, only the X2(2Dj) configuration performs better due to the presence of local spanwise rollers. The qualitative and quantitative analysis reveals that near-field mixing is strongly affected by the two-dimensional rollers, while the early onset of the wake mode is another crucial parameter to have improved mixing. Modal decomposition performed for the SS arrangement sheds light onto the spatial and temporal coherence of the structures, where the most dominant structures are found to be the von Kármán street vortices in the wake region.

The Use of Pro/Engineer CAD Software and Fishbowl Tool Kit in Ray-tracing Analysis

NASA Technical Reports Server (NTRS)

Nounu, Hatem N.; Kim, Myung-Hee Y.; Ponomarev, Artem L.; Cucinotta, Francis A.

2009-01-01

This document is designed as a manual for a user who wants to operate the Pro/ENGINEER (ProE) Wildfire 3.0 with the NASA Space Radiation Program's (SRP) custom-designed Toolkit, called 'Fishbowl', for the ray tracing of complex spacecraft geometries given by a ProE CAD model. The analysis of spacecraft geometry through ray tracing is a vital part in the calculation of health risks from space radiation. Space radiation poses severe risks of cancer, degenerative diseases and acute radiation sickness during long-term exploration missions, and shielding optimization is an important component in the application of radiation risk models. Ray tracing is a technique in which 3-dimensional (3D) vehicle geometry can be represented as the input for the space radiation transport code and subsequent risk calculations. In ray tracing a certain number of rays (on the order of 1000) are used to calculate the equivalent thickness, say of aluminum, of the spacecraft geometry seen at a point of interest called the dose point. The rays originate at the dose point and terminate at a homogenously distributed set of points lying on a sphere that circumscribes the spacecraft and that has its center at the dose point. The distance a ray traverses in each material is converted to aluminum or other user-selected equivalent thickness. Then all equivalent thicknesses are summed up for each ray. Since each ray points to a direction, the aluminum equivalent of each ray represents the shielding that the geometry provides to the dose point from that particular direction. This manual will first list for the user the contact information for help in installing ProE and Fishbowl in addition to notes on the platform support and system requirements information. Second, the document will show the user how to use the software to ray trace a Pro/E-designed 3-D assembly and will serve later as a reference for troubleshooting. The user is assumed to have previous knowledge of ProE and CAD modeling.

Spectral geometry of {kappa}-Minkowski space

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Andrea, Francesco

After recalling Snyder's idea [Phys. Rev. 71, 38 (1947)] of using vector fields over a smooth manifold as 'coordinates on a noncommutative space', we discuss a two-dimensional toy-model whose 'dual' noncommutative coordinates form a Lie algebra: this is the well-known {kappa}-Minkowski space [Phys. Lett. B 334, 348 (1994)]. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of {kappa}-Minkowski as linear operators on an Hilbert space (a major problem in the construction of a physical theory), study its 'spectral properties', and discuss how tomore » obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of Dimitrijevic et al. [Eur. Phys. J. C 31, 129 (2003)] can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.« less

Ground-state geometries and stability of impurity doped clusters: LinBe and LinMg (n=1-12)

NASA Astrophysics Data System (ADS)

Deshpande, M.; Dhavale, A.; Zope, R. R.; Chacko, S.; Kanhere, D. G.

2000-12-01

We have investigated the ground-state geometries of LinBe and LinMg (n=1-12) clusters using ab initio molecular dynamics. These divalent impurities Be and Mg induce different geometries and follow a different growth path for n>5. LinMg clusters are significantly different from the host geometries while LinBe clusters can be approximately viewed as Be occupying an interstitial site in the host. Our results indicate that Be gets trapped inside the Li cage, while Mg remains on the surface of the cluster. Mg-induced geometries become three-dimensional earlier at n=4 as compared to the Be system. In spite of a distinct arrangement of atoms in both cases the character of the wave functions in the d manifold is remarkably similar. In both cases an eight valence electron system has been found to be the most stable, in conformity with the spherical jellium model.

Inherent structure versus geometric metric for state space discretization.

PubMed

Liu, Hanzhong; Li, Minghai; Fan, Jue; Huo, Shuanghong

2016-05-30

Inherent structure (IS) and geometry-based clustering methods are commonly used for analyzing molecular dynamics trajectories. ISs are obtained by minimizing the sampled conformations into local minima on potential/effective energy surface. The conformations that are minimized into the same energy basin belong to one cluster. We investigate the influence of the applications of these two methods of trajectory decomposition on our understanding of the thermodynamics and kinetics of alanine tetrapeptide. We find that at the microcluster level, the IS approach and root-mean-square deviation (RMSD)-based clustering method give totally different results. Depending on the local features of energy landscape, the conformations with close RMSDs can be minimized into different minima, while the conformations with large RMSDs could be minimized into the same basin. However, the relaxation timescales calculated based on the transition matrices built from the microclusters are similar. The discrepancy at the microcluster level leads to different macroclusters. Although the dynamic models established through both clustering methods are validated approximately Markovian, the IS approach seems to give a meaningful state space discretization at the macrocluster level in terms of conformational features and kinetics. © 2016 Wiley Periodicals, Inc.

A Comparison of Geometry Problems in Middle-Grade Mathematics Textbooks from Taiwan, Singapore, Finland, and the United States

ERIC Educational Resources Information Center

Yang, Der-Ching; Tseng, Yi-Kuan; Wang, Tzu-Ling

2017-01-01

This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students' learning experiences with these problems. An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation…

Overcoming turbulence-induced space-variant blur by using phase-diverse speckle.

PubMed

Thelen, Brian J; Paxman, Richard G; Carrara, David A; Seldin, John H

2009-01-01

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. Space-variant effects are particularly severe in horizontal-path imaging, slant-path (air-to-ground or ground-to-air) geometries, and ground-based imaging of low-elevation satellites or astronomical objects. In these geometries, the isoplanatic angle can be comparable to or even smaller than the diffraction-limited resolution angle. We report on a postdetection correction method that seeks to correct for the effects of space-variant aberrations, with the goal of reconstructing near-diffraction-limited imagery. Our approach has been to generalize the method of phase-diverse speckle (PDS) by using a physically motivated distributed-phase-screen model. Simulation results are presented that demonstrate the reconstruction of near-diffraction-limited imagery under both matched and mismatched model assumptions. In addition, we present evidence that PDS could be used as a beaconless wavefront sensor in a multiconjugate adaptive optics system when imaging extended scenes.

Dark State Optical Lattice with a Subwavelength Spatial Structure

NASA Astrophysics Data System (ADS)

Wang, Y.; Subhankar, S.; Bienias, P.; ŁÄ cki, M.; Tsui, T.-C.; Baranov, M. A.; Gorshkov, A. V.; Zoller, P.; Porto, J. V.; Rolston, S. L.

2018-02-01

We report on the experimental realization of a conservative optical lattice for cold atoms with a subwavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a one-dimensional array of ultranarrow barriers with widths less than 10 nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice and find good agreement with theoretical predictions. Even on resonance, the observed lifetimes of atoms trapped in the lattice are as long as 44 ms, nearly 1 05 times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimensions and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with subwavelength spacings.

Radio frequency measurements of tunnel couplings and singlet–triplet spin states in Si:P quantum dots

PubMed Central

House, M. G.; Kobayashi, T.; Weber, B.; Hile, S. J.; Watson, T. F.; van der Heijden, J.; Rogge, S.; Simmons, M. Y.

2015-01-01

Spin states of the electrons and nuclei of phosphorus donors in silicon are strong candidates for quantum information processing applications given their excellent coherence times. Designing a scalable donor-based quantum computer will require both knowledge of the relationship between device geometry and electron tunnel couplings, and a spin readout strategy that uses minimal physical space in the device. Here we use radio frequency reflectometry to measure singlet–triplet states of a few-donor Si:P double quantum dot and demonstrate that the exchange energy can be tuned by at least two orders of magnitude, from 20 μeV to 8 meV. We measure dot–lead tunnel rates by analysis of the reflected signal and show that they change from 100 MHz to 22 GHz as the number of electrons on a quantum dot is increased from 1 to 4. These techniques present an approach for characterizing, operating and engineering scalable qubit devices based on donors in silicon. PMID:26548556

Analysis of space radiation exposure levels at different shielding configurations by ray-tracing dose estimation method

NASA Astrophysics Data System (ADS)

Kartashov, Dmitry; Shurshakov, Vyacheslav

2018-03-01

A ray-tracing method to calculate radiation exposure levels of astronauts at different spacecraft shielding configurations has been developed. The method uses simplified shielding geometry models of the spacecraft compartments together with depth-dose curves. The depth-dose curves can be obtained with different space radiation environment models and radiation transport codes. The spacecraft shielding configurations are described by a set of geometry objects. To calculate the shielding probability functions for each object its surface is composed from a set of the disjoint adjacent triangles that fully cover the surface. Such description can be applied for any complex shape objects. The method is applied to the space experiment MATROSHKA-R modeling conditions. The experiment has been carried out onboard the ISS from 2004 to 2016. Dose measurements were realized in the ISS compartments with anthropomorphic and spherical phantoms, and the protective curtain facility that provides an additional shielding on the crew cabin wall. The space ionizing radiation dose distributions in tissue-equivalent spherical and anthropomorphic phantoms and for an additional shielding installed in the compartment are calculated. There is agreement within accuracy of about 15% between the data obtained in the experiment and calculated ones. Thus the calculation method used has been successfully verified with the MATROSHKA-R experiment data. The ray-tracing radiation dose calculation method can be recommended for estimation of dose distribution in astronaut body in different space station compartments and for estimation of the additional shielding efficiency, especially when exact compartment shielding geometry and the radiation environment for the planned mission are not known.

Teaching Geometry to Visually Impaired Students

ERIC Educational Resources Information Center

Pritchard, Christine K.; Lamb, John H.

2012-01-01

NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

Optimal shield mass distribution for space radiation protection

NASA Technical Reports Server (NTRS)

Billings, M. P.

1972-01-01

Computational methods have been developed and successfully used for determining the optimum distribution of space radiation shielding on geometrically complex space vehicles. These methods have been incorporated in computer program SWORD for dose evaluation in complex geometry, and iteratively calculating the optimum distribution for (minimum) shield mass satisfying multiple acute and protected dose constraints associated with each of several body organs.

A Continuum Mechanical Approach to Geodesics in Shape Space

DTIC Science & Technology

2010-01-01

the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a ...investigate the close link between abstract geometry on the infinite -dimen- sional space of shapes and the continuum mechanical view of shapes as boundary...are texture-coded in the bottom row. of multiple components of volumetric objects. The

The "normal" elongation of river basins

NASA Astrophysics Data System (ADS)

Castelltort, Sebastien

2013-04-01

The spacing between major transverse rivers at the front of Earth's linear mountain belts consistently scales with about half of the mountain half-width [1], despite strong differences in climate and rock uplift rates. Like other empirical measures describing drainage network geometry this result seems to indicate that the form of river basins, among other properties of landscapes, is invariant. Paradoxically, in many current landscape evolution models, the patterns of drainage network organization, as seen for example in drainage density and channel spacing, seem to depend on both climate [2-4] and tectonics [5]. Hovius' observation [1] is one of several unexplained "laws" in geomorphology that still sheds mystery on how water, and rivers in particular, shape the Earth's landscapes. This narrow range of drainage network shapes found in the Earth's orogens is classicaly regarded as an optimal catchment geometry that embodies a "most probable state" in the uplift-erosion system of a linear mountain belt. River basins currently having an aspect away from this geometry are usually considered unstable and expected to re-equilibrate over geological time-scales. Here I show that the Length/Width~2 aspect ratio of drainage basins in linear mountain belts is the natural expectation of sampling a uniform or normal distribution of basin shapes, and bears no information on the geomorphic processes responsible for landscape development. This finding also applies to Hack's [6] law of river basins areas and lengths, a close parent of Hovius' law. [1]Hovius, N. Basin Res. 8, 29-44 (1996) [2]Simpson, G. & Schlunegger, F. J. Geophys. Res. 108, 2300 (2003) [3]Tucker, G. & Bras, R. Water Resour. Res. 34, 2751-2764 (1998) [4]Tucker, G. & Slingerland, R. Water Resour. Res. 33, 2031-2047 (1997) [5]Tucker, G. E. & Whipple, K. X. J. Geophys. Res. 107, 1-1 (2002) [6]Hack, J. US Geol. Surv. Prof. Pap. 294-B (1957)

Geometry dependent suppression of collective quantum jumps in Rydberg atoms

NASA Astrophysics Data System (ADS)

Lees, Eitan; Clemens, James

2015-05-01

We consider N driven, damped Rydberg atoms in different spatial arrangements. Treating the atoms as two-level systems we model the coupling to the environment via the Lehmberg-Agarwal master equation which interpolates between fully independent and fully collective spontaneous emission depending on the specific locations of the atoms. We also include a collective dipole-dipole energy shift in the excited Rydberg state which leads to collective quantum jumps in the atomic excitation when the system is driven off resonance. We show that the quantum jumps are suppressed as the system makes a transition from independent to collective emission as the spacing of a linear array of atoms is decreased below the emission wavelength.

Discontinuity stresses in metallic pressure vessels

NASA Technical Reports Server (NTRS)

1971-01-01

The state of the art, criteria, and recommended practices for the theoretical and experimental analyses of discontinuity stresses and their distribution in metallic pressure vessels for space vehicles are outlined. The applicable types of pressure vessels include propellant tanks ranging from main load-carrying integral tank structure to small auxiliary tanks, storage tanks, solid propellant motor cases, high pressure gas bottles, and pressurized cabins. The major sources of discontinuity stresses are discussed, including deviations in geometry, material properties, loads, and temperature. The advantages, limitations, and disadvantages of various theoretical and experimental discontinuity analysis methods are summarized. Guides are presented for evaluating discontinuity stresses so that pressure vessel performance will not fall below acceptable levels.

A link between torse-forming vector fields and rotational hypersurfaces

NASA Astrophysics Data System (ADS)

Chen, Bang-Yen; Verstraelen, Leopold

Torse-forming vector fields introduced by Yano [On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo 20 (1944) 340-346] are natural extension of concurrent and concircular vector fields. Such vector fields have many nice applications to geometry and mathematical physics. In this paper, we establish a link between rotational hypersurfaces and torse-forming vector fields. More precisely, our main result states that, for a hypersurface M of 𝔼n+1 with n ≥ 3, the tangential component xT of the position vector field of M is a proper torse-forming vector field on M if and only if M is contained in a rotational hypersurface whose axis of rotation contains the origin.

Study of geometric phase using classical coupled oscillators

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sharba; Dey, Biprateep; Mohapatra, Ashok K.

2018-05-01

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

Contribution to the optimal shape design of two-dimensional internal flows with embedded shocks

NASA Technical Reports Server (NTRS)

Iollo, Angelo; Salas, Manuel D.

1995-01-01

We explore the practicability of optimal shape design for flows modeled by the Euler equations. We define a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solving a co-state equation. The optimization problem is then examined by comparing the performance of several gradient-based optimization algorithms. In this formulation, the flow field can be computed to an arbitrary order of accuracy. Finally, some results for internal flows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.

Phenotypic models of evolution and development: geometry as destiny.

PubMed

François, Paul; Siggia, Eric D

2012-12-01

Quantitative models of development that consider all relevant genes typically are difficult to fit to embryonic data alone and have many redundant parameters. Computational evolution supplies models of phenotype with relatively few variables and parameters that allows the patterning dynamics to be reduced to a geometrical picture for how the state of a cell moves. The clock and wavefront model, that defines the phenotype of somitogenesis, can be represented as a sequence of two discrete dynamical transitions (bifurcations). The expression-time to space map for Hox genes and the posterior dominance rule are phenotypes that naturally follow from computational evolution without considering the genetics of Hox regulation. Copyright © 2012 Elsevier Ltd. All rights reserved.

Ab initio study of the ground state surface of Cu3

NASA Technical Reports Server (NTRS)

Langhoff, Stephen R.; Bauschlicher, Charles W., Jr.; Walch, Stephen P.; Laskowski, Bernard C.

1986-01-01

The ground state surface of the metallic trimer Cu3 is investigated theoretically. Relativistic and correlation effects are taken into account in ab initio computations, which are calibrated against analogous computations for the 1Sigma(g)+ state of Cu2; the results are presented in tables and analyzed. The Cu3 ground state is found to have a 2B2 C(2v) structure with angle greater than 60 deg, lying 59/cm below a 2A1 C(2v) geometry and 280/cm below the D(3h) equilateral geometry. These findings are shown to be in good agreement with the experimental measurements of Rohlfing and Valentini (1986) and their analysis (in terms of a Jahn-Teller distortion of 2E-prime equilateral-triangle geometry) by Truhlar et al. (1986).

Quantum Entanglement of Matter and Geometry in Large Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogan, Craig J.

2014-12-04

Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard quantum field theory with general relativity on macroscopic scales can be reconciled by nonstandard, nonlocal entanglement of field states with quantum states of geometry. Wave functions of particle world lines are used to estimate scales of geometrical entanglement and emergent locality. Simple models of entanglement predict coherent fluctuations in position of massive bodies, of Planck scale origin, measurable on a laboratory scale, and may account formore » the fact that the information density of long lived position states in Standard Model fields, which is determined by the strong interactions, is the same as that determined holographically by the cosmological constant.« less

Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry

NASA Astrophysics Data System (ADS)

Gérard, Christian; Oulghazi, Omar; Wrochna, Michał

2017-06-01

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.

Laboratory research of fracture geometry in multistage HFF in triaxial state

NASA Astrophysics Data System (ADS)

Bondarenko, T. M.; Hou, B.; Chen, M.; Yan, L.

2017-05-01

Multistage hydraulic fracturing of formation (HFF) in wells with horizontal completion is an efficientmethod for intensifying oil extraction which, as a rule, is used to develop nontraditional collectors. It is assumed that the complicated character of HFF fractures significantly influences the fracture geometry in the rock matrix. Numerous theoretical models proposed to predict the fracture geometry and the character of interaction of mechanical stresses in the multistage HFF have not been proved experimentally. In this paper, we present the results of laboratory modeling of the multistage HFF performed on a contemporary laboratory-scale plant in the triaxial stress state by using a gel-solution as the HFF agent. As a result of the experiment, a fracturing pattern was formed in the cubic specimen of the model material. The laboratory results showed that a nearly plane fracture is formed at the firstHFF stage, while a concave fracture is formed at the second HFF stage. The interaction of the stress fields created by the two principal HFF fractures results in the growth of secondary fractures whose directions turned out to be parallel to the modeled well bore. But this stress interference leads to a decrease in the width of the second principal fracture. It is was discovered that the penny-shaped fracture model is more appropriate for predicting the geometry of HFF fractures in horizontal wells than the two-dimensional models of fracture propagation (PKN model, KGD model). A computational experiment based on the boundary element method was carried out to obtain the qualitative description of the multistage HFF processes. As a result, a mechanical model of fracture propagation was constructed,which was used to obtain the mechanical stress field (the stress contrast) and the fracture opening angle distribution over fracture length and fracture orientation direction. The conclusions made in the laboratory modeling of the multistage HFF technology agree well with the conclusions made in the computational experiment. Special attention must be paid to the design of the HFF stage spacing density in the implementation of the multistage HFF in wells with horizontal completion.

Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models

NASA Astrophysics Data System (ADS)

Soos, Z. G.; Ramasesha, S.

1984-05-01

The ground and low-lying states of finite quantum-cell models with one state per site are obtained exactly through a real-space basis of valence-bond (VB) diagrams that explicitly conserve the total spin. Regular and alternating Hubbard and Pariser-Parr-Pople (PPP) chains and rings with Ne electrons on N(<=12) sites are extrapolated to infinite arrays. The ground-state energy and optical gap of regular U=4|t| Hubbard chains agree with exact results, suggesting comparable accuracy for alternating Hubbard and PPP models, but differ from mean-field results. Molecular PPP parameters describe well the excitations of finite polyenes, odd polyene ions, linear cyanine dyes, and slightly overestimate the absorption peaks in polyacetylene (CH)x. Molecular correlations contrast sharply with uncorrelated descriptions of topological solitons, which are modeled by regular polyene radicals and their ions for both wide and narrow alternation crossovers. Neutral solitons have no midgap absorption and negative spin densities, while the intensity of the in-gap excitation of charged solitons is not enhanced. The properties of correlated states in quantum-cell models with one valence state per site are discussed in the adiabatic limit for excited-state geometries and instabilities to dimerization.

Space-charge-limited currents for cathodes with electric field enhanced geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Dingguo, E-mail: laidingguo@nint.ac.cn; Qiu, Mengtong; Xu, Qifu

This paper presents the approximate analytic solutions of current density for annulus and circle cathodes. The current densities of annulus and circle cathodes are derived approximately from first principles, which are in agreement with simulation results. The large scaling laws can predict current densities of high current vacuum diodes including annulus and circle cathodes in practical applications. In order to discuss the relationship between current density and electric field on cathode surface, the existing analytical solutions of currents for concentric cylinder and sphere diodes are fitted from existing solutions relating with electric field enhancement factors. It is found that themore » space-charge-limited current density for the cathode with electric-field enhanced geometry can be written in a general form of J = g(β{sub E}){sup 2}J{sub 0}, where J{sub 0} is the classical (1D) Child-Langmuir current density, β{sub E} is the electric field enhancement factor, and g is the geometrical correction factor depending on the cathode geometry.« less

Aspect Ratio of Receiver Node Geometry based Indoor WLAN Propagation Model

NASA Astrophysics Data System (ADS)

Naik, Udaykumar; Bapat, Vishram N.

2017-08-01

This paper presents validation of indoor wireless local area network (WLAN) propagation model for varying rectangular receiver node geometry. The rectangular client node configuration is a standard node arrangement in computer laboratories of academic institutes and research organizations. The model assists to install network nodes for the better signal coverage. The proposed model is backed by wide ranging real time received signal strength measurements at 2.4 GHz. The shadow fading component of signal propagation under realistic indoor environment is modelled with the dependency on varying aspect ratio of the client node geometry. The developed new model is useful in predicting indoor path loss for IEEE 802.11b/g WLAN. The new model provides better performance in comparison to well known International Telecommunication Union and free space propagation models. It is shown that the proposed model is simple and can be a useful tool for indoor WLAN node deployment planning and quick method for the best utilisation of the office space.

Space Radiation Transport Methods Development

NASA Technical Reports Server (NTRS)

Wilson, J. W.; Tripathi, R. K.; Qualls, G. D.; Cucinotta, F. A.; Prael, R. E.; Norbury, J. W.; Heinbockel, J. H.; Tweed, J.

2002-01-01

Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary design concepts to the final design. In particular, we will discuss the progress towards a full three-dimensional and computationally efficient deterministic code for which the current HZETRN evaluates the lowest order asymptotic term. HZETRN is the first deterministic solution to the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard Finite Element Method (FEM) geometry common to engineering design practice enabling development of integrated multidisciplinary design optimization methods. A single ray trace in ISS FEM geometry requires 14 milliseconds and severely limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given in terms of reconfigurable computing and could be utilized in the final design as verification of the deterministic method optimized design.

Geometry of Exploration: Water below the Surface of Mars? NASA Connect: Program 3 in the 1999-2000 Series.

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Hampton, VA. Langley Research Center.

This teaching unit is designed to help students in grades 4-8 explore the concepts of geometry in the context of space navigation. The units in this series have been developed to enhance and enrich mathematics, science, and technology education and to accommodate different teaching and learning styles. Each unit consists of a storyline presenting…

Algorithms for the Computation of Debris Risk

NASA Technical Reports Server (NTRS)

Matney, Mark J.

2017-01-01

Determining the risks from space debris involve a number of statistical calculations. These calculations inevitably involve assumptions about geometry - including the physical geometry of orbits and the geometry of satellites. A number of tools have been developed in NASA’s Orbital Debris Program Office to handle these calculations; many of which have never been published before. These include algorithms that are used in NASA’s Orbital Debris Engineering Model ORDEM 3.0, as well as other tools useful for computing orbital collision rates and ground casualty risks. This paper presents an introduction to these algorithms and the assumptions upon which they are based.

Algorithms for the Computation of Debris Risks

NASA Technical Reports Server (NTRS)

Matney, Mark

2017-01-01

Determining the risks from space debris involve a number of statistical calculations. These calculations inevitably involve assumptions about geometry - including the physical geometry of orbits and the geometry of non-spherical satellites. A number of tools have been developed in NASA's Orbital Debris Program Office to handle these calculations; many of which have never been published before. These include algorithms that are used in NASA's Orbital Debris Engineering Model ORDEM 3.0, as well as other tools useful for computing orbital collision rates and ground casualty risks. This paper will present an introduction to these algorithms and the assumptions upon which they are based.

Development of high-vacuum planar magnetron sputtering using an advanced magnetic field geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohno, Takahiro; Yagyu, Daisuke; Saito, Shigeru, E-mail: saito@ee.kagu.tus.ac.jp

2015-11-15

A permanent magnet in a new magnetic field geometry (namely, with the magnetization in the radial direction) was fabricated and used for high-vacuum planar magnetron sputtering using Penning discharge. Because of the development of this magnet, the discharge current and deposition rate were increased two to three times in comparison with the values attainable with a magnet in the conventional geometry. This improvement was because the available space for effective discharge of the energetic electrons for the ionization increased because the magnetic field distribution increased in both the axial and radial directions of discharge.

A stowing and deployment strategy for large membrane space systems on the example of Gossamer-1

NASA Astrophysics Data System (ADS)

Seefeldt, Patric

2017-09-01

Deployment systems for innovative space applications such as solar sails require a technique for a controlled and autonomous deployment in space. The deployment process has a strong impact on the mechanism and structural design and sizing. On the example of the design implemented in the Gossamer-1 project of the German Aerospace Center (DLR), such a stowing and deployment process is analyzed. It is based on a combination of zig-zag folding and coiling of triangular sail segments spanned between crossed booms. The deployment geometry and forces introduced by the mechanism considered are explored in order to reveal how the loads are transferred through the membranes to structural components such as the booms. The folding geometry and force progressions are described by function compositions of an inverse trigonometric function with the considered trigonometric function itself. If these functions are evaluated over several periods of the trigonometric function, a non-smooth oscillating curve occurs. Depending on the trigonometric function, these are often vividly described as zig-zag or sawtooth functions. The developed functions are applied to the Gossamer-1 design. The deployment geometry reveals a tendency that the loads are transferred along the catheti of the sail segments and therefore mainly along the boom axes. The load introduced by the spool deployment mechanism is described. By combining the deployment geometry with that load, a prediction of the deployment load progression is achieved. The mathematical description of the stowing and deployment geometry, as well as the forces inflicted by the mechanism provides an understanding of how exactly the membrane deploys and through which edges the deployment forces are transferred. The mathematical analysis also gives an impression of sensitive parameters that could be influenced by manufacturing tolerances or unsymmetrical deployment of the sail segments. While the mathematical model was applied on the design of the Gossamer-1 hardware, it allows an analysis of other geometries. This is of particular interest as Gossamer-1 investigated deployment technology on a relatively small scale of 5m × 5m , while the currently considered solar sail missions require sails that are about one order of magnitude bigger.

Light-emitting nanolattices with enhanced brightness

NASA Astrophysics Data System (ADS)

Ng, Ryan C.; Mandal, Rajib; Anthony, Rebecca J.; Greer, Julia R.

2017-02-01

Three-dimensional (3D) photonic crystals have potential in solid state lighting applications due to their advantages over conventional planar thin film devices. Periodicity in a photonic crystal structure enables engineering of the density of states to improve spontaneous light emission according to Fermi's golden rule. Unlike planar thin films, which suffer significantly from total internal reflection, a 3D architectured structure is distributed in space with many non-flat interfaces, which facilitates a substantial enhancement in light extraction. We demonstrate the fabrication of 3D nano-architectures with octahedron geometry that utilize luminescing silicon nanocrystals as active media with an aluminum cathode and indium tin oxide anode towards the realization of a 3D light emitting device. The developed fabrication procedure allows charge to pass through the nanolattice between two contacts for electroluminescence. These initial fabrication efforts suggest that 3D nano-architected devices are realizable and can reach greater efficiencies than planar devices.

Fine refinement of solid state structure of racemic form of phospho-tyrosine employing NMR Crystallography approach.

PubMed

Paluch, Piotr; Pawlak, Tomasz; Oszajca, Marcin; Lasocha, Wieslaw; Potrzebowski, Marek J

2015-02-01

We present step by step facets important in NMR Crystallography strategy employing O-phospho-dl-tyrosine as model sample. The significance of three major techniques being components of this approach: solid state NMR (SS NMR), X-ray diffraction of powdered sample (PXRD) and theoretical calculations (Gauge Invariant Projector Augmented Wave; GIPAW) is discussed. Each experimental technique provides different set of structural constraints. From the PXRD measurement the size of the unit cell, space group and roughly refined molecular structure are established. SS NMR provides information about content of crystallographic asymmetric unit, local geometry, molecular motion in the crystal lattice and hydrogen bonding pattern. GIPAW calculations are employed for validation of quality of elucidation and fine refinement of structure. Crystal and molecular structure of O-phospho-dl-tyrosine solved by NMR Crystallography is deposited at Cambridge Crystallographic Data Center under number CCDC 1005924. Copyright © 2014 Elsevier Inc. All rights reserved.

A Nonlinear Gyrokinetic Vlasov-Maxwell System for High-frequency Simulation in Toroidal Geometry

NASA Astrophysics Data System (ADS)

Liu, Pengfei; Zhang, Wenlu; Lin, Jingbo; Li, Ding; Dong, Chao

2016-10-01

A nonlinear gyrokinetic Vlasov equation is derived through the Lie-perturbation method to the Lagrangian and Hamiltonian systems in extanded phase space. The gyrokinetic Maxwell equations are derived in terms of the moments of gyrocenter phase-space distribution through the push-forward and pull-back representations, where the polarization and magnetization effects of gyrocenter are retained. The goal of this work is to construct a global nonlinear gyrokinetic vlasov-maxwell system for high-frequency simulation in toroidal geometry relevent for ion cyclotron range of frequencies (ICRF) waves heating and lower hybrid wave current driven (LHCD). Supported by National Special Research Program of China For ITER and National Natural Science Foundation of China.

Coulomb branches with complex singularities

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Martone, Mario

2018-06-01

We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.

Internal Stresses Lead to Net Forces and Torques on Extended Elastic Bodies

NASA Astrophysics Data System (ADS)

Aharoni, Hillel; Kolinski, John M.; Moshe, Michael; Meirzada, Idan; Sharon, Eran

2016-09-01

A geometrically frustrated elastic body will develop residual stresses arising from the mismatch between the intrinsic geometry of the body and the geometry of the ambient space. We analyze these stresses for an ambient space with gradients in its intrinsic curvature, and show that residual stresses generate effective forces and torques on the center of mass of the body. We analytically calculate these forces in two dimensions, and experimentally demonstrate their action by the migration of a non-Euclidean gel disc in a curved Hele-Shaw cell. An extension of our analysis to higher dimensions shows that these forces are also generated in three dimensions, but are negligible compared to gravity.

RFQ device for accelerating particles

DOEpatents

Shepard, Kenneth W.; Delayen, Jean R.

1995-01-01

A superconducting radio frequency quadrupole (RFQ) device includes four spaced elongated, linear, tubular rods disposed parallel to a charged particle beam axis, with each rod supported by two spaced tubular posts oriented radially with respect to the beam axis. The rod and post geometry of the device has four-fold rotation symmetry, lowers the frequency of the quadrupole mode below that of the dipole mode, and provides large dipole-quadrupole mode isolation to accommodate a range of mechanical tolerances. The simplicity of the geometry of the structure, which can be formed by joining eight simple T-sections, provides a high degree of mechanical stability, is insensitive to mechanical displacement, and is particularly adapted for fabrication with superconducting materials such as niobium.

Structural weights analysis of advanced aerospace vehicles using finite element analysis

NASA Technical Reports Server (NTRS)

Bush, Lance B.; Lentz, Christopher A.; Rehder, John J.; Naftel, J. Chris; Cerro, Jeffrey A.

1989-01-01

A conceptual/preliminary level structural design system has been developed for structural integrity analysis and weight estimation of advanced space transportation vehicles. The system includes a three-dimensional interactive geometry modeler, a finite element pre- and post-processor, a finite element analyzer, and a structural sizing program. Inputs to the system include the geometry, surface temperature, material constants, construction methods, and aerodynamic and inertial loads. The results are a sized vehicle structure capable of withstanding the static loads incurred during assembly, transportation, operations, and missions, and a corresponding structural weight. An analysis of the Space Shuttle external tank is included in this paper as a validation and benchmark case of the system.

Control of the permeability loss-peak frequency of Ni81Fe19 thin films through laser ablation of triangular and square cluster geometries

NASA Technical Reports Server (NTRS)

Grimes, C. A.; Lumpp, J. K.

2000-01-01

Laser ablation arrays of triangular and square shaped clusters, comprised of 23 micrometers diam circular holes, are defined upon 100 nm thick Ni81Fe19 films used to control the rf permeability spectra. Cluster-to-cluster spacing is varied from 200 to 600 micrometers. For each geometry it is found that the loss peak frequency and permeability magnitude shift lower, in a step-wise fashion, at a cluster-to-cluster spacing between 275 and 300 micrometers. The nonlinear shift in the behavior of the permeability spectra correlates with a dramatic increase in domain wall density. c2000 American Institute of Physics.

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Theis, Daniel; Windus, Theresa L.; Ruedenberg, Klaus

The metastable ring structure of the ozone 1{sup 1}A{sub 1} ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two {sup 1}A{sub 1} states. In the present work, valence correlated energies of the 1{sup 1}A{sub 1} state and the 2{sup 1}A{sub 1} state were calculated at the 1{sup 1}A{sub 1} open minimum, the 1{sup 1}A{sub 1} ring minimum,more » the transition state between these two minima, the minimum of the 2{sup 1}A{sub 1} state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 1{sup 1}A{sub 1} state, the present calculations yield the estimates of (ring minimum—open minimum) ∼45–50 mh and (transition state—open minimum) ∼85–90 mh. For the (2{sup 1}A{sub 1}–{sup 1}A{sub 1}) excitation energy, the estimate of ∼130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (2{sup 1}A{sub 1}–{sup 1}A{sub 1}) is found to be between 1 and 10 mh. The geometry of the transition state on the 1{sup 1}A{sub 1} surface and that of the minimum on the 2{sup 1}A{sub 1} surface nearly coincide. More accurate predictions of the energy differences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.« less

Nucleation and arrest of slow slip earthquakes: mechanisms and nonlinear simulations using realistic fault geometries and heterogeneous medium properties

NASA Astrophysics Data System (ADS)

Alves da Silva Junior, J.; Frank, W.; Campillo, M.; Juanes, R.

2017-12-01

Current models for slow slip earthquakes (SSE) assume a simplified fault embedded on a homogeneous half-space. In these models SSE events nucleate on the transition from velocity strengthening (VS) to velocity weakening (VW) down dip from the trench and propagate towards the base of the seismogenic zone, where high normal effective stress is assumed to arrest slip. Here, we investigate SSE nucleation and arrest using quasi-static finite element simulations, with rate and state friction, on a domain with heterogeneous properties and realistic fault geometry. We use the fault geometry of the Guerrero Gap in the Cocos subduction zone, where SSE events occurs every 4 years, as a proxy for subduction zone. Our model is calibrated using surface displacements from GPS observations. We apply boundary conditions according to the plate convergence rate and impose a depth-dependent pore pressure on the fault. Our simulations indicate that the fault geometry and elastic properties of the medium play a key role in the arrest of SSE events at the base of the seismogenic zone. SSE arrest occurs due to aseismic deformations of the domain that result in areas with elevated effective stress. SSE nucleation occurs in the transition from VS to VW and propagates as a crack-like expansion with increased nucleation length prior to dynamic instability. Our simulations encompassing multiple seismic cycles indicate SSE interval times between 1 and 10 years and, importantly, a systematic increase of rupture area prior to dynamic instability, followed by a hiatus in the SSE occurrence. We hypothesize that these SSE characteristics, if confirmed by GPS observations in different subduction zones, can add to the understanding of nucleation of large earthquakes in the seismogenic zone.

A wave superposition method formulated in digital acoustic space

NASA Astrophysics Data System (ADS)

Hwang, Yong-Sin

In this thesis, a new formulation of the Wave Superposition method is proposed wherein the conventional mesh approach is replaced by a simple 3-D digital work space that easily accommodates shape optimization for minimizing or maximizing radiation efficiency. As sound quality is in demand in almost all product designs and also because of fierce competition between product manufacturers, faster and accurate computational method for shape optimization is always desired. Because the conventional Wave Superposition method relies solely on mesh geometry, it cannot accommodate fast shape changes in the design stage of a consumer product or machinery, where many iterations of shape changes are required. Since the use of a mesh hinders easy shape changes, a new approach for representing geometry is introduced by constructing a uniform lattice in a 3-D digital work space. A voxel (a portmanteau, a new word made from combining the sound and meaning, of the words, volumetric and pixel) is essentially a volume element defined by the uniform lattice, and does not require separate connectivity information as a mesh element does. In the presented method, geometry is represented with voxels that can easily adapt to shape changes, therefore it is more suitable for shape optimization. The new method was validated by computing radiated sound power of structures of simple and complex geometries and complex mode shapes. It was shown that matching volume velocity is a key component to an accurate analysis. A sensitivity study showed that it required at least 6 elements per acoustic wavelength, and a complexity study showed a minimal reduction in computational time.

Stress state in turbopump bearing induced by shrink fitting

NASA Technical Reports Server (NTRS)

Sims, P.; Zee, R.

1991-01-01

The stress generated by shrink fitting in bearing-like geometries is studied. The feasibility of using strain gages to determine the strain induced by shrink fitting process is demonstrated. Results from a ring with a uniform cross section reveal the validity of simple stress mechanics calculations for determining the stress state induced in this geometry by shrink fitting.

Time-dependent radiation dose estimations during interplanetary space flights

NASA Astrophysics Data System (ADS)

Dobynde, M. I.; Shprits, Y.; Drozdov, A.

2015-12-01

Time-dependent radiation dose estimations during interplanetary space flights 1,2Dobynde M.I., 2,3Drozdov A.Y., 2,4Shprits Y.Y.1Skolkovo institute of science and technology, Moscow, Russia 2University of California Los Angeles, Los Angeles, USA 3Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics, Moscow, Russia4Massachusetts Institute of Technology, Cambridge, USASpace radiation is the main restriction for long-term interplanetary space missions. It induces degradation of external components and propagates inside providing damage to internal environment. Space radiation particles and induced secondary particle showers can lead to variety of damage to astronauts in short- and long- term perspective. Contribution of two main sources of space radiation- Sun and out-of-heliosphere space varies in time in opposite phase due to the solar activity state. Currently the only habituated mission is the international interplanetary station that flights on the low Earth orbit. Besides station shell astronauts are protected with the Earth magnetosphere- a natural shield that prevents significant damage for all humanity. Current progress in space exploration tends to lead humanity out of magnetosphere bounds. With the current study we make estimations of spacecraft parameters and astronauts damage for long-term interplanetary flights. Applying time dependent model of GCR spectra and data on SEP spectra we show the time dependence of the radiation in a human phantom inside the shielding capsule. We pay attention to the shielding capsule design, looking for an optimal geometry parameters and materials. Different types of particles affect differently on the human providing more or less harm to the tissues. Incident particles provide a large amount of secondary particles while propagating through the shielding capsule. We make an attempt to find an optimal combination of shielding capsule parameters, namely material and thickness, that will effectively decrease the incident particle energy, at the same time minimizing flow of secondary induced particles and minimizing most harmful particle types flows.

Geometry, structure, and concealed lithology of the San Rafael Basin, southeastern Arizona

USGS Publications Warehouse

Bultman, Mark W.

1999-01-01

The contiguous United States has been well explored for exposed conventional mineral deposits. Therefore, it is likely that many economically viable and strategically significant conventional undiscovered mineral deposits will be found in bedrock concealed beneath basin sediments. Mineral resource assessments must incorporate an understanding of the geometry, structure, and concealed lithology of basins in order to be accurate. This report presents an analysis of the basin geometry and structure of the San Rafael basin in southeastern Arizona. In addition, a new methodology for inferring concealed lithology is presented and applied in the San Rafael basin. Gravity data is used to model the geometry of the basin using recent models of sediment density vs. depth developed in the region. This modeling indicates that the basin has a maximum depth of approximately 1.05 km plus or minus 0.10 km. In the southern portion, the basin can be modeled as an asymmetric graben faulted on the western margin. The northern portion of the basin is structurally more complex and may have high angle faults on the western, northern, and eastern margin. Near-ground closely spaced Earth’s total intensity magnetic field data is used to locate concealed faults within the basin. This data is also used to infer lithology concealed by shallow basin sediments. Airborne Earth’s total intensity magnetic field data is used to help infer concealed lithology in deep portions of the basin. The product of integrating all data and interpretations is a map which presents the geometry of the basin, faults and contacts concealed by basin sediments, and an estimate of the bedrock lithology concealed by basin sediment. Based on basin geometry and concealed lithology, the San Rafael basin has a high potential for concealed mineral deposits on its western and northern margin. In particular, a newly discovered magnetic anomaly in the northern portion of the basin can be modeled as a granitic intrusion with highly altered margins and may represent a potential mineral resource target. Based on the permeability and porosity of upper basin fill found in nearby basins, the San Rafael basin may contain an aquifer up to 300 meters thick over a substantial area of the basin.

Coupling MAST-1D, a sediment routing model for channel-floodplain complexes, with channel migration relationships to predict reach-averaged river morphodynamics. Preliminary results

NASA Astrophysics Data System (ADS)

Viparelli, E.; Eke, E. C.; Lauer, J. W.

2017-12-01

Sediment exchange between the channel and floodplain can occur via meander migration, overbank deposition or erosion, and changes in channel geometry. Depending on channel and floodplain history, floodplains can act either as sources or sinks of bed material and/or wash load. Here we present preliminary modeling results that explicitly account for the feedbacks between the changes in floodplain geometry and sediment size distribution and the changes in channel geometry and migration. These results are obtained by coupling the Morphodynamics And Sediment Tracers in 1D (MAST-1D) program with the results of meander migration studies linking the bankfull flow depth and mean velocity to channel migration, sinuosity and channel geometry. MAST-1D is a numerical model built to describe grain size specific transport of sediment and tracers and the long-term - i.e. decadal and longer - evolution of channel floodplain complexes. MAST-1D differs from other 1D numerical models because it allows for 1) uneven exchange of sediment and tracers between the river channel and the floodplain, 2) temporal changes in channel geometry, bed elevation and floodplain thickness, which result in changes in the channel hydraulic capacity, and 3) temporal changes of size distribution and tracer content in the floodplain, in the load and in the underlying substrate. Under conditions of constant base level, water and sediment supply, the system evolves toward a steady state wherein the amount of sediment deposited through point bar deposition and overbank sedimentation is balanced by the erosion of sediment from the floodplain through lateral migration. The current formulation couples MAST-1D with empirical channel migration relationships that link bankfull flow depth and mean velocity to channel migration, sinuosity and channel geometry. Future development of this preliminary work will involve a fully coupled MAST-1D model with a standard meander migration model that will allow for the building of floodplain stratigraphy and tracking of the position of the meandering channel in space and time.

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

Serious Play with Dynamic Plane Transformations

ERIC Educational Resources Information Center

King, James

2011-01-01

Transformations are a central organizing idea in geometry. They are included in most geometry curricula and are likely to appear with even greater emphasis in the future, given the central role they play in the "Common Core State Standards" for K-12 mathematics. One of the attractions of geometry is the ability to draw and construct the…

The slab geometry laser. I - Theory

NASA Technical Reports Server (NTRS)

Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.

1984-01-01

Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.

Development of bankfull hydraulic geometry relationships for the physiographic divisions of the United States

USDA-ARS?s Scientific Manuscript database

Bankfull hydraulic geometry relationships are used to estimate channel dimensions for stream flow simulation models, which require channel geometry data as input parameters. Often, one nationwide curve is used across the entire U.S. (e.g. in SWAT), even though studies have shown that the use of reg...

Heating of foods in space-vehicle environments. [by conductive heat transfer

NASA Technical Reports Server (NTRS)

Bannerot, R. B.; Cox, J. E.; Chen, C. K.; Heidelbaugh, N. D.

1973-01-01

In extended space missions, foods will be heated to enhance the psychological as well as the physiological well-being of the crew. In the low-gravity space environment natural convection is essentially absent so that the heat transfer within the food is by conduction alone. To prevent boiling in reduced pressure environments the maximum temperature of the heating system is severely limited. The Skylab food-heating system utilizes a tray with receptables for the food containers. The walls of the receptacles are lined with thermally controlled, electrical-resistance, blanket-type heating elements. A finite difference model is employed to perform parametric studies on the food-heating system. The effects on heating time of the (1) thermophysical properties of the food, (2) heater power level, (3) initial food temperatures, (4) container geometry, and (5) heater control temperature are presented graphically. The optimal heater power level and container geometry are determined.

Angular relation of axes in perceptual space

NASA Technical Reports Server (NTRS)

Bucher, Urs

1992-01-01

The geometry of perceptual space needs to be known to model spatial orientation constancy or to create virtual environments. To examine one main aspect of this geometry, the angular relation between the three spatial axes was measured. Experiments were performed consisting of a perceptual task in which subjects were asked to set independently their apparent vertical and horizontal plane. The visual background provided no other stimuli to serve as optical direction cues. The task was performed in a number of different body tilt positions with pitches and rolls varied in steps of 30 degs. The results clearly show the distortion of orthogonality of the perceptual space for nonupright body positions. Large interindividual differences were found. Deviations from orthogonality up to 25 deg were detected in the pitch as well as in the roll direction. Implications of this nonorthogonality on further studies of spatial perception and on the construction of virtual environments for human interaction is also discussed.

"There is One Geometry and in Each Case There is a Different Formula". Students' Conceptions and Strategies in an Attempt of Producing a Minkowskian Metric on Space-Time

NASA Astrophysics Data System (ADS)

Rizos, Ioannis; Patronis, Anastasios (Tasos); Lappas, Dionyssios

2017-08-01

In this paper, we analyze two episodes from an inquiry-based didactical research; the complete analysis of our research data is still ongoing. By taking into consideration various developments from the history of the geometry of space-time, our general aim is to explore high school students' conceptions about measurement of length and time in relatively moving systems, and lead the students to reconsider these conceptions in an attempt of constructing a new metric for space-time. The episodes are extracted from long (focused) interviews with two couples of students, based on a carefully designed fictional scenario. Two main strategies have been identified and are analyzed in the paper: one of them relies on imagination and intuition; the other one makes use of preexisting school mathematical knowledge, in arriving to a simplified formula of a Minkowskian metric.

Precise relative navigation using augmented CDGPS

NASA Astrophysics Data System (ADS)

Park, Chan-Woo

2001-10-01

Autonomous formation flying of multiple vehicles is a revolutionary enabling technology for many future space and earth science missions that require distributed measurements, such as sparse aperture radars and stellar interferometry. The techniques developed for the space applications will also have a significant impact on many terrestrial formation flying missions. One of the key requirements of formation flying is accurate knowledge of the relative positions and velocities between the vehicles. Several researchers have shown that the GPS is a viable sensor to perform this relative navigation. However, there are several limitations in the use of GPS because it requires adequate visibility to the NAVSTAR constellation. For some mission scenarios, such as MEO, GEO and tight formation missions, the visibility/geometry of the constellation may not be sufficient to accurately estimate the relative states. One solution to these problems is to include an RF ranging device onboard the vehicles in the formation and form a local constellation that augments the existing NAVSTAR constellation. These local range measurements, combined with the GPS measurements, can provide a sufficient number of measurements and adequate geometry to solve for the relative states. Furthermore, these RF ranging devices can be designed to provide substantially more accurate measures of the vehicle relative states than the traditional GPS pseudolites. The local range measurements also allow relative vehicle motion to be used to efficiently solve for the cycle ambiguities in real-time. This dissertation presents the development of an onboard ranging sensor and the extension of several related algorithms for a formation of vehicles with both GPS and local transmitters. Key among these are a robust cycle ambiguity estimation method and a decentralized relative navigation filter. The efficient decentralized approach to the GPS-only relative navigation problem is extended to an iterative cascade extended Kalman filtering (ICEKF) algorithm when the vehicles have onboard transmitters. Several ground testbeds were developed to demonstrate the feasibility of the augmentation concept and the relative navigation algorithms. The testbed includes the Stanford Pseudolite Transceiver Crosslink (SPTC), which was developed and extensively tested with a formation of outdoor ground vehicles.

Stratification and energy fluxes in the anelastic convection model

NASA Astrophysics Data System (ADS)

Hejda, Pavel; Reshetnyak, Maxim

2013-04-01

Convection in the planetary cores is usually connected with the geostrophic state. At the onset of convection, the ratio of horizontal scale to the scale along the axis of rotation is proportional to the cube root of the Ekman number, which characterises the ratio of the viscous forces to the Coriolis force. The Ekman number is extremely small in the liquid cores, which is a source of strong anisotropy. Even if further increase of the heat sources leads to decrease of anisotropy, the final state is still highly anisotropic. The influence of the rapid rotation on the structure of the flows in the physical space is also manifested by a substantial change of the spectral properties of the turbulence in the core (Reshetnyak and Hejda, 2008; Hejda and Reshetnyak, 2009). If for the non-rotating flow the kinetic energy in the wave space propagates from the large scales to the small dissipative scales (the so-called direct Richardson-Kolmogorov cascade), then in presence of rotation the turbulence degenerates to the quasi two-dimensional state and the inverse cascade of the kinetic energy is observed. Having in mind that Cartesian and spherical geometries exhibit similar results and reproduce the inverse cascades of the kinetic energy (Reshetnyak and Hejda, 2012), there is an open question how this cascade contributes to the more general energy balance, which includes the heat flux equation. As the heat energy definition in the Boussinesq model is quite questionable, we consider the anelastic model, where the heat fluxes can be compared with the kinetic energy fluxes in the adequate way. Here we consider the spherical geometry model in the shell that limits our study to the cascades in the azimuthal wave-number. As the self-consistent anelastic model includes new term, the adiabatic cooling, which produces "stratification" in the outer part of the core, we consider its influence on convection in the physical and wave spaces. We show that even small cooling can change the convection substantially, shifting maximum of convection to the inner part of the liquid core. Similar to the Boussinesq model the both direct and inverse cascades of the kinetic energy as well as the direct cascade of the specific entropy in the wave space occur. Reshetnyak, M. and Hejda, P., 2008. Direct and inverse cascades in the geodynamo. Nonlin. Proc. Geophys. 15, 873-880. Hejda, P. and Reshetnyak, M., 2009. Effect of anisotropy in the geostrophic turbulence. Phys. Earth Planet. Inter. 177, 152-160, doi: 10.1016/j.pepi.2009.08.006. Reshetnyak, M. and Hejda, P., 2012. Kinetic energy cascades in quasi-geostrophic convection in a spherical shell. Physica Scripta 86, article No. 018408, doi: 10.1088/0031-8949/86/01/018408.

Vibrations and structureborne noise in space station

NASA Technical Reports Server (NTRS)

Vaicaitis, R.

1985-01-01

The related literature was reviewed and a preliminary analytical model was developed for simplified acoustic and structural geometries for pressurized and unpressurized space station modules. In addition to the analytical work, an experimental program on structureborne noise generation and transmission was started. A brief review of those accomplishments is given.

Use of libration-point orbits for space observatories

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.; Dunham, David W.

1990-01-01

The sun-earth libration points, L1 and L2, are located 1.5 million kilometers from the earth toward and away from the sun. Halo orbits about these points have significant advantages for space observatories in terms of viewing geometry, thermal and radiation environment, and delta-V expediture.

Life-space foam: A medium for motivational and cognitive dynamics

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir; Aidman, Eugene

2007-08-01

General stochastic dynamics, developed in a framework of Feynman path integrals, have been applied to Lewinian field-theoretic psychodynamics [K. Lewin, Field Theory in Social Science, University of Chicago Press, Chicago, 1951; K. Lewin, Resolving Social Conflicts, and, Field Theory in Social Science, American Psychological Association, Washington, 1997; M. Gold, A Kurt Lewin Reader, the Complete Social Scientist, American Psychological Association, Washington, 1999], resulting in the development of a new concept of life-space foam (LSF) as a natural medium for motivational and cognitive psychodynamics. According to LSF formalisms, the classic Lewinian life space can be macroscopically represented as a smooth manifold with steady force fields and behavioral paths, while at the microscopic level it is more realistically represented as a collection of wildly fluctuating force fields, (loco)motion paths and local geometries (and topologies with holes). A set of least-action principles is used to model the smoothness of global, macro-level LSF paths, fields and geometry. To model the corresponding local, micro-level LSF structures, an adaptive path integral is used, defining a multi-phase and multi-path (multi-field and multi-geometry) transition process from intention to goal-driven action. Application examples of this new approach include (but are not limited to) information processing, motivational fatigue, learning, memory and decision making.

What to expect from dynamical modelling of galactic haloes - II. The spherical Jeans equation

NASA Astrophysics Data System (ADS)

Wang, Wenting; Han, Jiaxin; Cole, Shaun; More, Surhud; Frenk, Carlos; Schaller, Matthieu

2018-06-01

The spherical Jeans equation (SJE) is widely used in dynamical modelling of the Milky Way (MW) halo potential. We use haloes and galaxies from the cosmological Millennium-II simulation and hydrodynamical APOSTLE (A Project of Simulations of The Local Environment) simulations to investigate the performance of the SJE in recovering the underlying mass profiles of MW mass haloes. The best-fitting halo mass and concentration parameters scatter by 25 per cent and 40 per cent around their input values, respectively, when dark matter particles are used as tracers. This scatter becomes as large as a factor of 3 when using star particles instead. This is significantly larger than the estimated statistical uncertainty associated with the use of the SJE. The existence of correlated phase-space structures that violate the steady-state assumption of the SJE as well as non-spherical geometries is the principal source of the scatter. Binary haloes show larger scatter because they are more aspherical in shape and have a more perturbed dynamical state. Our results confirm that the number of independent phase-space structures sets an intrinsic limiting precision on dynamical inferences based on the steady-state assumption. Modelling with a radius-independent velocity anisotropy, or using tracers within a limited outer radius, result in significantly larger scatter, but the ensemble-averaged measurement over the whole halo sample is approximately unbiased.

Creation of Woven Structures Impacting Self-cleaning Superoleophobicity

NASA Astrophysics Data System (ADS)

Lim, Jihye

For protection of human life from harmful or toxic liquids in working areas, solid surface resistance to liquid with low surface tension (e.g. oil) should be achieved in the outermost layer of protective clothing. Based on the literature review, multiscale structures were emphasized because they can increase roughness on a solid surface and create more void spaces of different sizes. The roughness and void spaces contribute to creating a liquid-vapor interface and reducing the liquid contact area to the solid surface. Woven fabric inherently consists of multiscale structures by its construction: microscale in a yarn structure and macroscale in a fabric structure. When the solid surface tension is low relative to oil, creating an appropriate structural geometry will become a critical way to obtain a superoleophobic surface for oil-resistance. Theoretical modeling and experiments with actual fabric samples were utilized to predict and prove the highest performing structural geometry in woven fabric, respectively. The theoretical geometric modeling accounted for the different weave structures, the yarn compression by the yarn flattening factor, e, and the void space by the void space ratio to the fiber or yarn diameter, T, impacting the liquid apparent contact angle on a fabric surface. The Cassie-Baxter equations were developed using Young's contact angle, thetae, thetae and e, or thetae, e, and T, to predict the liquid apparent contact angle for different geometries. In addition, to prevent a liquid's penetration into a solid structure, the ranges of the protuberance height (>> h2) and distance (< 4ℓ 2 cap) were predicted by the definition of the Laplace pressure, the capillary pressure, and the sagging phenomenon. Those predictions were in strong agreement with the results from the empirical experiment using the actual woven fabric samples. This study identified the impact of the geometries in yarn and woven fabric structures on the fabric resistance against oil through theoretical modeling and experiments. The results suggest particular weave structures, the range of the void space (or the protuberance distance) and the protuberance height in the yarn and fabric structures for the highest performing self-cleaning superoleophobic woven fabric surface.

On the Use of CAD-Native Predicates and Geometry in Surface Meshing

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.

1999-01-01

Several paradigms for accessing CAD geometry during surface meshing for CFD are discussed. File translation, inconsistent geometry engines and non-native point construction are all identified as sources of non-robustness. The paper argues in favor of accessing CAD parts and assemblies in their native format, without translation, and for the use of CAD-native predicates and constructors in surface mesh generation. The discussion also emphasizes the importance of examining the computational requirements for exact evaluation of triangulation predicates during surface meshing. The native approach is demonstrated through an algorithm for the generation of closed manifold surface triangulations from CAD geometry. CAD parts and assemblies are used in their native format, and a part's native geometry engine is accessed through a modeler-independent application programming interface (API). In seeking a robust and fully automated procedure, the algorithm is based on a new physical space manifold triangulation technique specially developed to avoid robustness issues associated with poorly conditioned mappings. In addition, this approach avoids the usual ambiguities associated with floating-point predicate evaluation on constructed coordinate geometry in a mapped space. The technique is incremental, so that each new site improves the triangulation by some well defined quality measure. The algorithm terminates after achieving a prespecified measure of mesh quality and produces a triangulation such that no angle is less than a given angle bound, a or greater than pi - 2alpha. This result also sets bounds on the maximum vertex degree, triangle aspect-ratio and maximum stretching rate for the triangulation. In addition to the output triangulations for a variety of CAD parts, the discussion presents related theoretical results which assert the existence of such an angle bound, and demonstrate that maximum bounds of between 25 deg and 30 deg may be achieved in practice.

Image-based computational fluid dynamics in blood vessel models: toward developing a prognostic tool to assess cardiovascular function changes in prolonged space flights

NASA Astrophysics Data System (ADS)

Chatzimavroudis, George P.; Spirka, Thomas A.; Setser, Randolph M.; Myers, Jerry G.

2005-04-01

One of NASA"s objectives is to be able to perform a complete pre-flight evaluation of possible cardiovascular changes in astronauts scheduled for prolonged space missions. Blood flow is an important component of cardiovascular function. Lately, attention has focused on using computational fluid dynamics (CFD) to analyze flow with realistic vessel geometries. MRI can provide detailed geometrical information and is the only clinical technique to measure all three spatial velocity components. The objective of this study was to investigate the reliability of MRI-based model reconstruction for CFD simulations. An aortic arch model and a carotid bifurcation model were scanned in a 1.5T MRI scanner. Axial MRI acquisitions provided images for geometry reconstruction using different resolution settings. The vessel walls were identified and the geometry was reconstructed using existing software. The geometry was then imported into a commercial CFD package for meshing and numerical solution. MRI velocity acquisitions provided true inlet boundary conditions for steady flow, as well as three-directional velocity data at several locations. In addition, an idealized version of each geometry was created from the model drawings. Contour and vector plots of the velocity showed identical features between the MRI velocity data, the MRI-based CFD data, and the idealized-geometry CFD data, with mean differences <10%. CFD results from different MRI resolution settings did not show significant differences (<5%). This study showed quantitatively that reliable CFD simulations can be performed in models reconstructed from MRI acquisitions and gives evidence that a future, subject-specific, computational evaluation of the cardiovascular system is possible.

Probability Forecasting Using Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Duncan, M.; Frisbee, J.; Wysack, J.

2014-09-01

Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. Increased dependence on our space assets has in turn lead to a greater need for accurate, near real-time knowledge of all space activities. With the growth of the orbital debris population, satellite operators are performing collision avoidance maneuvers more frequently. Frequent maneuver execution expends fuel and reduces the operational lifetime of the spacecraft. Thus the need for new, more sophisticated collision threat characterization methods must be implemented. The collision probability metric is used operationally to quantify the collision risk. The collision probability is typically calculated days into the future, so that high risk and potential high risk conjunction events are identified early enough to develop an appropriate course of action. As the time horizon to the conjunction event is reduced, the collision probability changes. A significant change in the collision probability will change the satellite mission stakeholder's course of action. So constructing a method for estimating how the collision probability will evolve improves operations by providing satellite operators with a new piece of information, namely an estimate or 'forecast' of how the risk will change as time to the event is reduced. Collision probability forecasting is a predictive process where the future risk of a conjunction event is estimated. The method utilizes a Monte Carlo simulation that produces a likelihood distribution for a given collision threshold. Using known state and state uncertainty information, the simulation generates a set possible trajectories for a given space object pair. Each new trajectory produces a unique event geometry at the time of close approach. Given state uncertainty information for both objects, a collision probability value can be computed for every trail. This yields a collision probability distribution given known, predicted uncertainty. This paper presents the details of the collision probability forecasting method. We examine various conjunction event scenarios and numerically demonstrate the utility of this approach in typical event scenarios. We explore the utility of a probability-based track scenario simulation that models expected tracking data frequency as the tasking levels are increased. The resulting orbital uncertainty is subsequently used in the forecasting algorithm.

Extraction electrode geometry for a calutron

DOEpatents

Veach, A.M.; Bell, W.A. Jr.

1975-09-23

This patent relates to an improved geometry for the extraction electrode and the ground electrode utilized in the operation of a calutron. The improved electrodes are constructed in a partial-picture-frame fashion with the slits of both electrodes formed by two tungsten elongated rods. Additional parallel spaced-apart rods in each electrode are used to establish equipotential surfaces over the rest of the front of the ion source. (auth)

User manual for BUNVIS-RG: An exact buckling and vibration program for lattice structures, with repetitive geometry and substructuring options

NASA Technical Reports Server (NTRS)

Anderson, M. S.; Warnaar, D. B.; Ling, B. J. AEHERSTROM, C. l. afkennedy, d

1986-01-01

A computer program is described which is especially suited for making vibration and buckling calculations for prestressed lattice structures that might be used for space application. Structures having repetitive geometry are treated in a very efficient manner. Detailed instructions for data input are given along with several example problems illustrating the use and capability of the program.

Low Noise Infrasonic Sensor System with High Reduction of Natural Background Noise

DTIC Science & Technology

2006-05-01

local processing allows a variety of options both in the array geometry and signal processing. A generic geometry is indicated in Figure 2. Geometric...higher frequency sound detected . Table 1 provides a comparison of piezocable and microbarograph based arrays . Piezocable Sensor Local Signal ...aliasing associated with the current infrasound sensors used at large spacing in the present designs of infrasound monitoring arrays , particularly in the

Chemical etching and organometallic chemical vapor deposition on varied geometries of GaAs

NASA Technical Reports Server (NTRS)

Bailey, Sheila G.; Landis, Geoffrey A.; Wilt, David M.

1989-01-01

Results of micron-spaced geometries produced by wet chemical etching and subsequent OMCVD growth on various GaAs surfaces are presented. The polar lattice increases the complexity of the process. The slow-etch planes defined by anisotropic etching are not always the same as the growth facets produced during MOCVD deposition, especially for deposition on higher-order planes produced by the hex groove etching.

Illumination in diverse codimensions

NASA Technical Reports Server (NTRS)

Banks, David C.

1994-01-01

This paper derives a model of diffuse and specular illumination in arbitrarily large dimensions, based on a few characteristics of material and light in three-space. It then describes how to adjust for the anomaly of excess brightness in large codimensions. If a surface is grooved or furry, it can be illuminated with a hybrid model that incorporates both the one dimensional geometry (the grooves or fur) and the two dimensional geometry (the surface).

Code subspaces for LLM geometries

NASA Astrophysics Data System (ADS)

Berenstein, David; Miller, Alexandra

2018-03-01

We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.

Verifying the prevalence, properties, and congruent hydraulics of at-many-stations hydraulic geometry (AMHG) for rivers in the continental United States

NASA Astrophysics Data System (ADS)

Barber, Caitline A.; Gleason, Colin J.

2018-01-01

Hydraulic geometry (HG) has long enabled daily discharge estimates, flood risk monitoring, and water resource and habitat assessments, among other applications. At-many-stations HG (AMHG) is a newly discovered form of HG with an evolving understanding. AMHG holds that there are temporally and spatially invariant ('congruent') depth, width, velocity, and discharge values that are shared by all stations of a river. Furthermore, these river-wide congruent hydraulics have been shown to link at-a-station HG (AHG) in space, contrary to previous expectation of AHG as spatially unpredictable. To date, AMHG has only been thoroughly examined on six rivers, and its congruent hydraulics are not well understood. To address the limited understanding of AMHG, we calculated AMHG for 191 rivers in the United States using USGS field-measured data from over 1900 gauging stations. These rivers represent nearly all geologic and climatic settings found in the continental U.S. and allow for a robust assessment of AMHG across scales. Over 60% of rivers were found to have AMHG with strong explanatory power to predict AHG across space (defined as r2 > 0.6, 118/191 rivers). We also found that derived congruent hydraulics bear little relation to their observed time-varying counterparts, and the strength of AMHG did not correlate with any available observed or congruent hydraulic parameters. We also found that AMHG is expressed at all fluvial scales in this study. Some statistically significant spatial clusters of rivers with strong and weak AMHG were identified, but further research is needed to identify why these clusters exist. Thus, this first widespread empirical investigation of AMHG leads us to conclude that AMHG is indeed a widely prevalent natural fluvial phenomenon, and we have identified linkages between known fluvial parameters and AMHG. Our work should give confidence to future researchers seeking to perform the necessary detailed hydraulic analysis of AMHG.

An interactive user-friendly approach to surface-fitting three-dimensional geometries

NASA Technical Reports Server (NTRS)

Cheatwood, F. Mcneil; Dejarnette, Fred R.

1988-01-01

A surface-fitting technique has been developed which addresses two problems with existing geometry packages: computer storage requirements and the time required of the user for the initial setup of the geometry model. Coordinates of cross sections are fit using segments of general conic sections. The next step is to blend the cross-sectional curve-fits in the longitudinal direction using general conics to fit specific meridional half-planes. Provisions are made to allow the fitting of fuselages and wings so that entire wing-body combinations may be modeled. This report includes the development of the technique along with a User's Guide for the various menus within the program. Results for the modeling of the Space Shuttle and a proposed Aeroassist Flight Experiment geometry are presented.

Theoretical modeling of cellular and dendritic solidification microstructures

NASA Astrophysics Data System (ADS)

Song, Younggil

In this dissertation, we use three-dimensional (3D) phase-field (PF) modeling to investigate (i) 3D solid-liquid interface dynamics observed in microgravity experiments, and (ii) array patterns in a thin-sample geometry. In addition, using the two-dimensional (2D) dendritic-needle-network (DNN) model, we explore (iii) secondary sidebranching dynamics. Recently, solidification experiments are carried out in the DSI (Directional Solidification Insert) of the DECLIC (Device for the study of Critical LIquids and Crystallization) facility aboard the International Space Station (ISS). Thus, the directional solidification experiments are achieved under limited convective currents, and the experimental observations reveal unique dynamics of 3D microstructure in a purely diffusive growth regime. In this directional solidification setup, a temperature field between heat sources could evolve due to two main factors: (i) heat transfer within an adiabatic zone and (ii) latent heat rejection at the interface. These two thermal effects are phenomenologically characterized using a time-dependent thermal shift. In addition, we could quantitatively account for these thermal factors using a numerical calculation of the evolution of temperature field. We introduce these phenomenological and quantitative thermal representations into the PF model. The performed simulations using different thermal descriptions are compared to the experimental measurements from the initial planar interface dynamics to the final spacing selection. The DECLIC-DSI experimental observations exhibit complex grain boundary (GB) dynamics between large grains with a small misorientation. In the observations, several large grains with a small misorientation with respect to the temperature gradient are formed during solidification. Specifically, at a convergent GB, a localized group of misoriented cells penetrates into a nearby grain, which yields the morphological instability of grain boundaries. Remarkably, while the invasion process starts with a group of cells, the leader cell can detach itself from the group and grow continuously as a misoriented solitary cell in the other grain with a different misorientation. We use PF simulations to investigate the GB morphology and dynamics of a solitary cell. Solidification experiments on earth are typically performed in a thin-sample geometry to avoid fluid convection. Thus, we consider various influences on cellular and dendritic array patterns in thin samples. First, we explore the influence of crystal orientation. When a grain in a thin-sample geometry is misoriented with respect to the temperature gradient, primary cells and dendrites drift laterally in both experiments and simulations. At the same time, grain boundaries are systematically formed at the edges of the misoriented grain. The misoriented primary branches move away from the divergent grain boundary. At this boundary, cells/dendrites are generated continuously, and their spacings are larger than the dynamically selected spacings. Primary branches run into the other convergent GB, which leads to their elimination. Thus, at a stationary state, a spacing distribution is uniform with the spacing selected at the divergent GB until it decreases near the convergent GB. We perform simulations to illustrate the global evolutions of a primary spacing. In addition, we suggest a simple geometrical model and a nonlinear advection equation for the dynamics of the primary spacing evolution, which can predict the slow evolution of a primary spacing in a quasi-2D array. Experimental observations point out that the primary spacing selection could be affected by the sample thickness; however, the detailed description for the link between the primary spacing selection and a sample thickness is still missing. Here, we use PF simulations to investigate the primary cellular and dendritic spacing selection mechanisms under the influence of a sample thickness. A thin-sample geometry can limit thermal and solutal convective currents effectively. However, as the sample thickness increases, the convective currents can influence the solid- liquid interface dynamics. Then, the microstructure selection mechanisms can be different from the classical theories that are valid in a diffusive regime. We propose a simple approach for the PF model to demonstrate the microstructure selection when liquid convection is present. These simulations are compared to experimental results. Columnar microstructures with cells and dendrites typically form polycrystalline materials during directional solidification. Then, convergent and divergent grain boundaries form systematically between grains, which are misoriented with respect to the temperature gradient. Moreover, the GB is dynamically selected during the competition between two nearby misoriented grains. In order to investigate the GB orientation selection, we carry out 3D PF simulations in a thin-sample geometry. These simulations reveal the influence of the 3D GB bi-crystallography on grain competition. The results highlight the importance of considering the orientation of the orthogonal planes containing secondary branches in addition to the growth direction of primary branches. Finally, we propose three growth steps to demonstrate the secondary sidebranching growth dynamics under isothermal dendritic growth condition. (Abstract shortened by ProQuest.).

Dynamics of the Rydberg state population of slow highly charged ions impinging a solid surface at arbitrary collision geometry

NASA Astrophysics Data System (ADS)

Nedeljković, N. N.; Majkić, M. D.; Božanić, D. K.; Dojčilović, R. J.

2016-06-01

We consider the population dynamics of the intermediate Rydberg states of highly charged ions (core charge Z\\gg 1, principal quantum number {n}{{A}}\\gg 1) interacting with solid surfaces at arbitrary collision geometry. The recently developed resonant two-state vector model for the grazing incidence (2012 J. Phys. B: At. Mol. Opt. Phys. 45 215202) is extended to the quasi-resonant case and arbitrary angle of incidence. According to the model, the population probabilities depend both on the projectile parallel and perpendicular velocity components, in a complementary way. A cascade neutralization process for {{{Xe}}}Z+ ions, for Z=15{--}45, interacting with a conductive-surface is considered by taking into account the population dynamics. For an arbitrary collision geometry and given range of ionic velocities, a micro-staircase model for the simultaneous calculation of the kinetic energy gain and the charge state of the ion in front of the surface is proposed. The relevance of the obtained results for the explanation of the formation of nanostructures on solid surfaces by slow highly charged ions for normal incidence geometry is briefly discussed.

Connecting Research to Teaching: Evaluating and Writing Dynamic Geometry Tasks

ERIC Educational Resources Information Center

Trocki, Aaron

2014-01-01

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI…

Performance evaluation of GPU parallelization, space-time adaptive algorithms, and their combination for simulating cardiac electrophysiology.

PubMed

Sachetto Oliveira, Rafael; Martins Rocha, Bernardo; Burgarelli, Denise; Meira, Wagner; Constantinides, Christakis; Weber Dos Santos, Rodrigo

2018-02-01

The use of computer models as a tool for the study and understanding of the complex phenomena of cardiac electrophysiology has attained increased importance nowadays. At the same time, the increased complexity of the biophysical processes translates into complex computational and mathematical models. To speed up cardiac simulations and to allow more precise and realistic uses, 2 different techniques have been traditionally exploited: parallel computing and sophisticated numerical methods. In this work, we combine a modern parallel computing technique based on multicore and graphics processing units (GPUs) and a sophisticated numerical method based on a new space-time adaptive algorithm. We evaluate each technique alone and in different combinations: multicore and GPU, multicore and GPU and space adaptivity, multicore and GPU and space adaptivity and time adaptivity. All the techniques and combinations were evaluated under different scenarios: 3D simulations on slabs, 3D simulations on a ventricular mouse mesh, ie, complex geometry, sinus-rhythm, and arrhythmic conditions. Our results suggest that multicore and GPU accelerate the simulations by an approximate factor of 33×, whereas the speedups attained by the space-time adaptive algorithms were approximately 48. Nevertheless, by combining all the techniques, we obtained speedups that ranged between 165 and 498. The tested methods were able to reduce the execution time of a simulation by more than 498× for a complex cellular model in a slab geometry and by 165× in a realistic heart geometry simulating spiral waves. The proposed methods will allow faster and more realistic simulations in a feasible time with no significant loss of accuracy. Copyright © 2017 John Wiley & Sons, Ltd.

Evidence for tectonic, lithologic, and thermal controls on fracture system geometries in an andesitic high-temperature geothermal field

NASA Astrophysics Data System (ADS)

Massiot, Cécile; Nicol, Andrew; McNamara, David D.; Townend, John

2017-08-01

Analysis of fracture orientation, spacing, and thickness from acoustic borehole televiewer (BHTV) logs and cores in the andesite-hosted Rotokawa geothermal reservoir (New Zealand) highlights potential controls on the geometry of the fracture system. Cluster analysis of fracture orientations indicates four fracture sets. Probability distributions of fracture spacing and thickness measured on BHTV logs are estimated for each fracture set, using maximum likelihood estimations applied to truncated size distributions to account for sampling bias. Fracture spacing is dominantly lognormal, though two subordinate fracture sets have a power law spacing. This difference in spacing distributions may reflect the influence of the andesitic sequence stratification (lognormal) and tectonic faults (power law). Fracture thicknesses of 9-30 mm observed in BHTV logs, and 1-3 mm in cores, are interpreted to follow a power law. Fractures in thin sections (˜5 μm thick) do not fit this power law distribution, which, together with their orientation, reflect a change of controls on fracture thickness from uniform (such as thermal) controls at thin section scale to anisotropic (tectonic) at core and BHTV scales of observation. However, the ˜5% volumetric percentage of fractures within the rock at all three scales suggests a self-similar behavior in 3-D. Power law thickness distributions potentially associated with power law fluid flow rates, and increased connectivity where fracture sets intersect, may cause the large permeability variations that occur at hundred meter scales in the reservoir. The described fracture geometries can be incorporated into fracture and flow models to explore the roles of fracture connectivity, stress, and mineral precipitation/dissolution on permeability in such andesite-hosted geothermal systems.

Track Geometry Measurement System Software Manual

DOT National Transportation Integrated Search

1978-04-01

The Track Geometry Measurement System (TGMS) was developed through the United States Department of Transportation's, Urban Mass Transportation Administration by the Transportation Systems Center in Cambridge, Massachusetts under its Test and Evaluati...

Two-phase reduced gravity experiments for a space reactor design

NASA Technical Reports Server (NTRS)

Antoniak, Zenen I.

1987-01-01

Future space missions researchers envision using large nuclear reactors with either a single or a two-phase alkali-metal working fluid. The design and analysis of such reactors require state-of-the-art computer codes that can properly treat alkali-metal flow and heat transfer in a reduced-gravity environment. New flow regime maps, models, and correlations are required if the codes are to be successfully applied to reduced-gravity flow and heat transfer. General plans are put forth for the reduced-gravity experiments which will have to be performed, at NASA facilities, with benign fluids. Data from the reduced-gravity experiments with innocuous fluids are to be combined with normal gravity data from two-phase alkali-metal experiments. Because these reduced-gravity experiments will be very basic, and will employ small test loops of simple geometry, a large measure of commonality exists between them and experiments planned by other organizations. It is recommended that a committee be formed to coordinate all ongoing and planned reduced gravity flow experiments.

Scalable real space pseudopotential density functional codes for materials in the exascale regime

NASA Astrophysics Data System (ADS)

Lena, Charles; Chelikowsky, James; Schofield, Grady; Biller, Ariel; Kronik, Leeor; Saad, Yousef; Deslippe, Jack

Real-space pseudopotential density functional theory has proven to be an efficient method for computing the properties of matter in many different states and geometries, including liquids, wires, slabs, and clusters with and without spin polarization. Fully self-consistent solutions using this approach have been routinely obtained for systems with thousands of atoms. Yet, there are many systems of notable larger sizes where quantum mechanical accuracy is desired, but scalability proves to be a hindrance. Such systems include large biological molecules, complex nanostructures, or mismatched interfaces. We will present an overview of our new massively parallel algorithms, which offer improved scalability in preparation for exascale supercomputing. We will illustrate these algorithms by considering the electronic structure of a Si nanocrystal exceeding 104 atoms. Support provided by the SciDAC program, Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. Grant Numbers DE-SC0008877 (Austin) and DE-FG02-12ER4 (Berkeley).

Potential benefits of magnetic suspension and balance systems

NASA Technical Reports Server (NTRS)

Lawing, Pierce L.; Dress, David A.; Kilgore, Robert A.

1987-01-01

The potential of Magnetic Suspension and Balance Systems (MSBS) to improve conventional wind tunnel testing techniques is discussed. Topics include: elimination of model geometry distortion and support interference to improve the measurement accuracy of aerodynamic coefficients; removal of testing restrictions due to supports; improved dynamic stability data; and stores separation testing. Substantial increases in wind tunnel productivity are anticipated due to the coalescence of these improvements. Specific improvements in testing methods for missiles, helicopters, fighter aircraft, twin fuselage transports and bombers, state separation, water tunnels, and automobiles are also forecast. In a more speculative vein, new wind tunnel test techniques are envisioned as a result of applying MSBS, including free-flight computer trajectories in the test section, pilot-in-the-loop and designer-in-the-loop testing, shipboard missile launch simulation, and optimization of hybrid hypersonic configurations. Also addressed are potential applications of MSBS to such diverse technologies as medical research and practice, industrial robotics, space weaponry, and ore processing in space.

Modeling the truebeam linac using a CAD to Geant4 geometry implementation: dose and IAEA-compliant phase space calculations.

PubMed

Constantin, Magdalena; Perl, Joseph; LoSasso, Tom; Salop, Arthur; Whittum, David; Narula, Anisha; Svatos, Michelle; Keall, Paul J

2011-07-01

To create an accurate 6 MV Monte Carlo simulation phase space for the Varian TrueBeam treatment head geometry imported from CAD (computer aided design) without adjusting the input electron phase space parameters. GEANT4 v4.9.2.p01 was employed to simulate the 6 MV beam treatment head geometry of the Varian TrueBeam linac. The electron tracks in the linear accelerator were simulated with Parmela, and the obtained electron phase space was used as an input to the Monte Carlo beam transport and dose calculations. The geometry components are tessellated solids included in GEANT4 as GDML (generalized dynamic markup language) files obtained via STEP (standard for the exchange of product) export from Pro/Engineering, followed by STEP import in Fastrad, a STEP-GDML converter. The linac has a compact treatment head and the small space between the shielding collimator and the divergent are of the upper jaws forbids the implementation of a plane for storing the phase space. Instead, an IAEA (International Atomic Energy Agency) compliant phase space writer was implemented on a cylindrical surface. The simulation was run in parallel on a 1200 node Linux cluster. The 6 MV dose calculations were performed for field sizes varying from 4 x 4 to 40 x 40 cm2. The voxel size for the 60 x 60 x 40 cm3 water phantom was 4 x 4 x 4 mm3. For the 10 x 10 cm2 field, surface buildup calculations were performed using 4 x 4 x 2 mm3 voxels within 20 mm of the surface. For the depth dose curves, 98% of the calculated data points agree within 2% with the experimental measurements for depths between 2 and 40 cm. For depths between 5 and 30 cm, agreement within 1% is obtained for 99% (4 x 4), 95% (10 x 10), 94% (20 x 20 and 30 x 30), and 89% (40 x 40) of the data points, respectively. In the buildup region, the agreement is within 2%, except at 1 mm depth where the deviation is 5% for the 10 x 10 cm2 open field. For the lateral dose profiles, within the field size for fields up to 30 x 30 cm2, the agreement is within 2% for depths up to 10 cm. At 20 cm depth, the in-field maximum dose difference for the 30 x 30 cm2 open field is within 4%, while the smaller field sizes agree within 2%. Outside the field size, agreement within 1% of the maximum dose difference is obtained for all fields. The calculated output factors varied from 0.938 +/- 0.015 for the 4 x 4 cm2 field to 1.088 +/- 0.024 for the 40 x 40 cm2 field. Their agreement with the experimental output factors is within 1%. The authors have validated a GEANT4 simulated IAEA-compliant phase space of the TrueBeam linac for the 6 MV beam obtained using a high accuracy geometry implementation from CAD. These files are publicly available and can be used for further research.

Numerical study of the effects of surface topography and chemistry on the wetting transition using the string method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Yanan, E-mail: ynzhang@suda.edu.cn; Ren, Weiqing, E-mail: matrw@nus.edu.sg; Institute of High Performance Computing, Singapore 138632

2014-12-28

Droplets on a solid surface patterned with microstructures can exhibit the composite Cassie-Baxter (CB) state or the wetted Wenzel state. The stability of the CB state is determined by the energy barrier separating it from the wetted state. In this work, we study the CB to Wenzel transition using the string method [E et al., J. Chem. Phys. 126, 164103 (2007); W. Ren and E. Vanden-Eijnden, J. Chem. Phys. 138, 134105 (2013)]. We compute the transition states and energy barriers for a three-dimensional droplet on patterned surfaces. The liquid-vapor coexistence is modeled using the mean field theory. Numerical results aremore » obtained for surfaces patterned with straight pillars and nails, respectively. It is found that on both type of surfaces, wetting occurs via infiltration of the liquid in a single groove. The reentrant geometry of nails creates large energy barrier for the wetting of the solid surface compared to straight pillars. We also study the effect of surface chemistry, pillar height, and inter-pillar spacing on the energy barrier and compare it with nails.« less

Latent resonance in tidal rivers, with applications to River Elbe

NASA Astrophysics Data System (ADS)

Backhaus, Jan O.

2015-11-01

We describe a systematic investigation of resonance in tidal rivers, and of river oscillations influenced by resonance. That is, we explore the grey-zone between absent and fully developed resonance. Data from this study are the results of a one-dimensional numerical channel model applied to a four-dimensional parameter space comprising geometry, i.e. length and depths of rivers, and varying dissipation and forcing. Similarity of real rivers and channels from parameter space is obtained with the help of a 'run-time depth'. We present a model-channel, which reproduces tidal oscillations of River Elbe in Hamburg, Germany with accuracy of a few centimetres. The parameter space contains resonant regions and regions with 'latent resonance'. The latter defines tidal oscillations that are elevated yet not in full but juvenile resonance. Dissipation reduces amplitudes of resonance while creating latent resonance. That is, energy of resonance radiates into areas in parameter space where periods of Eigen-oscillations are well separated from the period of the forcing tide. Increased forcing enhances the re-distribution of resonance in parameter space. The River Elbe is diagnosed as being in a state of anthropogenic latent resonance as a consequence of ongoing deepening by dredging. Deepening the river, in conjunction with the expected sea level rise, will inevitably cause increasing tidal ranges. As a rule of thumb, we found that 1 m deepening would cause 0.5 m increase in tidal range.

Emerging geometry from maximally super-symmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Vazquez, Samuel Enrique

In this thesis, we explore the emergence of space-time geometry, and string theory physics from N = 4 supersymmetric Yang-Mills (SYM) theory with gauge group U(N). This is done in the context of the anti-de-Sitter/conformal field theory correspondence (AdS/CFT). The main results of this thesis are the following. First, we study single trace perturbations around generic 1/2 BPS states of the theory. We do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show how these states can be mapped to dynamical lattices with boson statistics and periodic boundary conditions. By dynamical, we mean that the total boson occupation number is not conserved in general. Then, we show how to derive an effective sigma model for these systems which coincides with the Polyakov action of a probe string on a 1/2 BPS geometry (in the fast string limit). Secondly, we study non-supersymmetric perturbations of the vacuum which give rise to bosonic lattices with open boundary conditions. We also do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show that these states are dual to open strings on D3-branes known as "Giant Gravitons". These lattice systems are also dynamical, but in some special cases, we show that we get an integrable spin chain with open boundary conditions. Next, we study single trace perturbations at strong coupling. We do this by taking a "dilute gas" approximation. We derive an all-loop result for the dispersion relation of the "magnons" which coincides with previous conjectures in the literature. What is more, we derive the geometrical picture of the so-called "giant magnon" string solution of Hofman and Maldacena, directly from the field theory. Finally, we explore the question of classical integrability of open strings on D-branes. In particular, we study the case of the giant gravitons, and compare the integrable structures on both sides of the AdS/CFT correspondence.

Numerical algebraic geometry: a new perspective on gauge and string theories

NASA Astrophysics Data System (ADS)

Mehta, Dhagash; He, Yang-Hui; Hauensteine, Jonathan D.

2012-07-01

There is a rich interplay between algebraic geometry and string and gauge theories which has been recently aided immensely by advances in computational algebra. However, symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these shortcomings. The so-called `embarrassing parallelizability' allows us to solve many problems and extract physical information which elude symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.

Impact of gate geometry on ionic liquid gated ionotronic systems

DOE PAGES

Wong, Anthony T.; Noh, Joo Hyon; Pudasaini, Pushpa Raj; ...

2017-01-23

Ionic liquid electrolytes are gaining widespread application as a gate dielectric used to control ion transport in functional materials. This letter systematically examines the important influence that device geometry in standard “side gate” 3-terminal geometries plays in device performance of a well-known oxygen ion conductor. We show that the most influential component of device design is the ratio between the area of the gate electrode and the active channel, while the spacing between these components and their individual shapes has a negligible contribution. Finally, these findings provide much needed guidance in device design intended for ionotronic gating with ionic liquids.

Theoretical regime diagrams for thermally driven flows in a beta-plane channel. [in atmosphere

NASA Technical Reports Server (NTRS)

Geisler, J. E.; Fowlis, W. W.

1979-01-01

It is noted that thermally driven flows in rotating laboratory containers with cylindrical geometry can be axially symmetric or wavelike depending on the experimental parameters. In anticipation that rotating fluid experiments might soon be done in spherical shell geometry, Barcilon's model has been extended to a beta-plane channel in order to gain a rough understanding of the effects of rotating spherical geometry. An incompressible fluid version of the Charney (1947) model of baroclinic instability, modified to include Ekman pumping at rigid horizontal boundaries is used. With this model, stability boundaries are mapped out for individual zonal wavenumbers in the parameter space used by Barcilon.

Fractional vector calculus and fluid mechanics

NASA Astrophysics Data System (ADS)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

Space Debris Surfaces - Probability of no penetration versus impact velocity and obliquity

NASA Technical Reports Server (NTRS)

Elfer, N.; Meibaum, R.; Olsen, G.

1992-01-01

A collection of computer codes called Space Debris Surfaces (SD-SURF), have been developed to assist in the design and analysis of space debris protection systems. An SD-SURF analysis will show which obliquities and velocities are most likely to cause a penetration to help the analyst select a shield design best suited to the predominant penetration mechanism. Examples of the interaction between space vehicle geometry, the space debris environment, and the penetration and critical damage ballistic limit surfaces of the shield under consideration are presented.

Finite Geometries in Quantum Theory:. from Galois (fields) to Hjelmslev (rings)

NASA Astrophysics Data System (ADS)

Saniga, Metod; Planat, Michel

Geometries over Galois fields (and related finite combinatorial structures/algebras) have recently been recognized to play an ever-increasing role in quantum theory, especially when addressing properties of mutually unbiased bases (MUBs). The purpose of this contribution is to show that completely new vistas open up if we consider a generalized class of finite (projective) geometries, viz. those defined over Galois rings and/or other finite Hjelmslev rings. The case is illustrated by demonstrating that the basic combinatorial properties of a complete set of MUBs of a q-dimensional Hilbert space { H}q, q = pr with p being a prime and r a positive integer, are qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p2 and rank r. The q vectors of a basis of { H}q correspond to the q points of a (so-called) neighbour class and the q + 1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic. Although this remarkable analogy is still established at the level of cardinalities only, we currently work on constructing an explicit mapping by associating a MUB to each neighbour class of the points of the conic and a state vector of this MUB to a particular point of the class. Further research in this direction may prove to be of great relevance for many areas of quantum information theory, in particular for quantum information processing.

The effect of plasma density and emitter geometry on space charge limits for field emitter array electron charge emission into a space plasma

NASA Astrophysics Data System (ADS)

Morris, Dave; Gilchrist, Brian; Gallimore, Alec

2001-02-01

Field Emitter Array Cathodes (FEACs) are a new technology being developed for several potential spacecraft electron emission and charge control applications. Instead of a single hot (i.e., high powered) emitter, or a gas dependant plasma contactor, FEAC systems consist of many (hundreds or thousands) of small (micron level) cathode/gate pairs printed on a semiconductor wafer that effect cold field emission at relatively low voltages. Each individual cathode emits only micro-amp level currents, but a functional array is capable of amp/cm2 current densities. It is hoped that thus FEAC offers the possibility of a relatively low-power, simple to integrate, and inexpensive technique for the high level of current emissions that are required for an electrodynamic tether (EDT) propulsion mission. Space charge limits are a significant concern for the EDT application. Vacuum chamber tests and PIC simulations are being performed at the University of Michigan Plasmadynamics and Electric Propulsion Laboratory and Space Physics Research Laboratory to determine the effect of plasma density and emitter geometry on space charge limitations. The results of this work and conclusions to date of how to best mitigate space charge limits will be presented. .

Efficiency Enhancement of a Cantilever-Based Vibration Energy Harvester

PubMed Central

Kubba, Ali E.; Jiang, Kyle

2014-01-01

Extracting energy from ambient vibration to power wireless sensor nodes has been an attractive area of research, particularly in the automotive monitoring field. This article reports the design, analysis and testing of a vibration energy harvesting device based on a miniature asymmetric air-spaced cantilever. The developed design offers high power density, and delivers electric power that is sufficient to support most wireless sensor nodes for structural health monitoring (SHM) applications. The optimized design underwent three evolutionary steps, starting from a simple cantilever design, going through an air-spaced cantilever, and ending up with an optimized air-spaced geometry with boosted power density level. Finite Element Analysis (FEA) was used as an initial tool to compare the three geometries' stiffness (K), output open-circuit voltage (Vave), and average normal strain in the piezoelectric transducer (εave) that directly affect its output voltage. Experimental tests were also carried out in order to examine the energy harvesting level in each of the three designs. The experimental results show how to boost the power output level in a thin air-spaced cantilever beam for energy within the same space envelope. The developed thin air-spaced cantilever (8.37 cm3), has a maximum power output of 2.05 mW (H = 29.29 μJ/cycle). PMID:24366177

Efficiency enhancement of a cantilever-based vibration energy harvester.

PubMed

Kubba, Ali E; Jiang, Kyle

2013-12-23

Extracting energy from ambient vibration to power wireless sensor nodes has been an attractive area of research, particularly in the automotive monitoring field. This article reports the design, analysis and testing of a vibration energy harvesting device based on a miniature asymmetric air-spaced cantilever. The developed design offers high power density, and delivers electric power that is sufficient to support most wireless sensor nodes for structural health monitoring (SHM) applications. The optimized design underwent three evolutionary steps, starting from a simple cantilever design, going through an air-spaced cantilever, and ending up with an optimized air-spaced geometry with boosted power density level. Finite Element Analysis (FEA) was used as an initial tool to compare the three geometries' stiffness (K), output open-circuit voltage (V(ave)), and average normal strain in the piezoelectric transducer (ε(ave)) that directly affect its output voltage. Experimental tests were also carried out in order to examine the energy harvesting level in each of the three designs. The experimental results show how to boost the power output level in a thin air-spaced cantilever beam for energy within the same space envelope. The developed thin air-spaced cantilever (8.37 cm3), has a maximum power output of 2.05 mW (H = 29.29 μJ/cycle).

Non-Relativistic Twistor Theory and Newton-Cartan Geometry

NASA Astrophysics Data System (ADS)

Dunajski, Maciej; Gundry, James

2016-03-01

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O oplus O(2)}. We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.

Development of a large scale Chimera grid system for the Space Shuttle Launch Vehicle

NASA Technical Reports Server (NTRS)

Pearce, Daniel G.; Stanley, Scott A.; Martin, Fred W., Jr.; Gomez, Ray J.; Le Beau, Gerald J.; Buning, Pieter G.; Chan, William M.; Chiu, Ing-Tsau; Wulf, Armin; Akdag, Vedat

1993-01-01

The application of CFD techniques to large problems has dictated the need for large team efforts. This paper offers an opportunity to examine the motivations, goals, needs, problems, as well as the methods, tools, and constraints that defined NASA's development of a 111 grid/16 million point grid system model for the Space Shuttle Launch Vehicle. The Chimera approach used for domain decomposition encouraged separation of the complex geometry into several major components each of which was modeled by an autonomous team. ICEM-CFD, a CAD based grid generation package, simplified the geometry and grid topology definition by provoding mature CAD tools and patch independent meshing. The resulting grid system has, on average, a four inch resolution along the surface.

RFQ device for accelerating particles

DOEpatents

Shepard, K.W.; Delayen, J.R.

1995-06-06

A superconducting radio frequency quadrupole (RFQ) device includes four spaced elongated, linear, tubular rods disposed parallel to a charged particle beam axis, with each rod supported by two spaced tubular posts oriented radially with respect to the beam axis. The rod and post geometry of the device has four-fold rotation symmetry, lowers the frequency of the quadrupole mode below that of the dipole mode, and provides large dipole-quadrupole mode isolation to accommodate a range of mechanical tolerances. The simplicity of the geometry of the structure, which can be formed by joining eight simple T-sections, provides a high degree of mechanical stability, is insensitive to mechanical displacement, and is particularly adapted for fabrication with superconducting materials such as niobium. 5 figs.

Heat flow in variable polarity plasma arc welds

NASA Technical Reports Server (NTRS)

Abdelmessih, Amanie N.

1992-01-01

The space shuttle external tank and the space station Freedom are fabricated by the variable polarity plasma arc (VPPA) welding. Heat sink effects (taper) are observed when there are irregularities in the work-piece configuration especially if these irregularities are close to the weld bead. These heat sinks affect the geometry of the weld bead, and in extreme cases they could cause defects such as incomplete fusion. Also, different fixtures seem to have varying heat sink effects. The objective of the previous, present, and consecutive research studies is to investigate the effect of irregularities in the work-piece configuration and fixture differences on the weld bead geometry with the ultimate objective to compensate automatically for the heat sink effects and achieve a perfect weld.

Computing the scalar field couplings in 6D supergravity

NASA Astrophysics Data System (ADS)

Saidi, El Hassan

2008-11-01

Using non-chiral supersymmetry in 6D space-time, we compute the explicit expression of the metric the scalar manifold SO(1,1)×{SO(4,20)}/{SO(4)×SO(20)} of the ten-dimensional type IIA superstring on generic K3. We consider as well the scalar field self-couplings in the general case where the non-chiral 6D supergravity multiplet is coupled to generic n vector supermultiplets with moduli space SO(1,1)×{SO(4,n)}/{SO(4)×SO(n)}. We also work out a dictionary giving a correspondence between hyper-Kähler geometry and the Kähler geometry of the Coulomb branch of 10D type IIA on Calabi-Yau threefolds. Others features are also discussed.

Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states

NASA Astrophysics Data System (ADS)

Lapa, Matthew F.; Hughes, Taylor L.

2018-05-01

We study geometric aspects of the Laughlin fractional quantum Hall (FQH) states using a description of these states in terms of a matrix quantum mechanics model known as the Chern-Simons matrix model (CSMM). This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here, we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. For this model, we compute the Hall viscosity, Hall conductance in a nonuniform electric field, and the Hall viscosity in the presence of anisotropy (or intrinsic geometry). Our calculations show that the CSMM captures the guiding center contribution to the known values of these quantities in the Laughlin states, but lacks the Landau orbit contribution. The interesting correlations in a Laughlin state are contained entirely in the guiding center part of the state/wave function, and so we conclude that the CSMM accurately describes the most important aspects of the physics of the Laughlin FQH states, including the Hall viscosity and other geometric properties of these states, which are of current interest.

Hidden symmetries in Sasaki-Einstein geometries

NASA Astrophysics Data System (ADS)

Slesar, V.; Visinescu, M.; Vîlcu, G. E.

2017-07-01

We describe a method for constructing Killing-Yano tensors on Sasaki spaces using their geometrical properties, without the need of solving intricate generalized Killing equations. We obtain the Killing-Yano tensors on toric Sasaki-Einstein spaces using the fact that the metric cones of these spaces are Calabi-Yau manifolds which in turn are described in terms of toric data. We extend the search of Killing-Yano tensors on mixed 3-Sasakian manifolds. We illustrate the method by explicit construction of Killing forms on some spaces of current interest.

Performance measure that indicates geometry sufficiency of state highways : volume II -- clear zones and cross-section information extraction.

DOT National Transportation Integrated Search

2015-03-01

Evaluationmethod employedforthe proposed corridor projects by IndianaDepartment of Transportation(INDOT) considerroad : geometry improvements by a generalized categorization. A newmethod which consi...

Centrifuge in space fluid flow visualization experiment

NASA Technical Reports Server (NTRS)

Arnold, William A.; Wilcox, William R.; Regel, Liya L.; Dunbar, Bonnie J.

1993-01-01

A prototype flow visualization system is constructed to examine buoyancy driven flows during centrifugation in space. An axial density gradient is formed by imposing a thermal gradient between the two ends of the test cell. Numerical computations for this geometry showed that the Prandtl number plays a limited part in determining the flow.

Diversifying Our Perspectives on Mathematics about Space and Geometry: An Ecocultural Approach

ERIC Educational Resources Information Center

Owens, Kay

2014-01-01

School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and…

Length, Area, and Volume--or, Just Geometry Really

ERIC Educational Resources Information Center

Ball, Derek

2012-01-01

Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

Improving Problem-Solving Skills with the Help of Plane-Space Analogies

ERIC Educational Resources Information Center

Budai, László

2013-01-01

We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry…

Bootstrapping on Undirected Binary Networks Via Statistical Mechanics

NASA Astrophysics Data System (ADS)

Fushing, Hsieh; Chen, Chen; Liu, Shan-Yu; Koehl, Patrice

2014-09-01

We propose a new method inspired from statistical mechanics for extracting geometric information from undirected binary networks and generating random networks that conform to this geometry. In this method an undirected binary network is perceived as a thermodynamic system with a collection of permuted adjacency matrices as its states. The task of extracting information from the network is then reformulated as a discrete combinatorial optimization problem of searching for its ground state. To solve this problem, we apply multiple ensembles of temperature regulated Markov chains to establish an ultrametric geometry on the network. This geometry is equipped with a tree hierarchy that captures the multiscale community structure of the network. We translate this geometry into a Parisi adjacency matrix, which has a relative low energy level and is in the vicinity of the ground state. The Parisi adjacency matrix is then further optimized by making block permutations subject to the ultrametric geometry. The optimal matrix corresponds to the macrostate of the original network. An ensemble of random networks is then generated such that each of these networks conforms to this macrostate; the corresponding algorithm also provides an estimate of the size of this ensemble. By repeating this procedure at different scales of the ultrametric geometry of the network, it is possible to compute its evolution entropy, i.e. to estimate the evolution of its complexity as we move from a coarse to a fine description of its geometric structure. We demonstrate the performance of this method on simulated as well as real data networks.

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

PubMed Central

Piao, Daqing; Barbour, Randall L.; Graber, Harry L.; Lee, Daniel C.

2015-01-01

Abstract. This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01  mm−1 and μs′=1.0  mm−1 are on average less than 5% different. The approximation for sphere, generally valid for a diameter ≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation. PMID:26465613

Development of the 3DHZETRN code for space radiation protection

NASA Astrophysics Data System (ADS)

Wilson, John; Badavi, Francis; Slaba, Tony; Reddell, Brandon; Bahadori, Amir; Singleterry, Robert

Space radiation protection requires computationally efficient shield assessment methods that have been verified and validated. The HZETRN code is the engineering design code used for low Earth orbit dosimetric analysis and astronaut record keeping with end-to-end validation to twenty percent in Space Shuttle and International Space Station operations. HZETRN treated diffusive leakage only at the distal surface limiting its application to systems with a large radius of curvature. A revision of HZETRN that included forward and backward diffusion allowed neutron leakage to be evaluated at both the near and distal surfaces. That revision provided a deterministic code of high computational efficiency that was in substantial agreement with Monte Carlo (MC) codes in flat plates (at least to the degree that MC codes agree among themselves). In the present paper, the 3DHZETRN formalism capable of evaluation in general geometry is described. Benchmarking will help quantify uncertainty with MC codes (Geant4, FLUKA, MCNP6, and PHITS) in simple shapes such as spheres within spherical shells and boxes. Connection of the 3DHZETRN to general geometry will be discussed.

An Encoding Method for Compressing Geographical Coordinates in 3d Space

NASA Astrophysics Data System (ADS)

Qian, C.; Jiang, R.; Li, M.

2017-09-01

This paper proposed an encoding method for compressing geographical coordinates in 3D space. By the way of reducing the length of geographical coordinates, it helps to lessen the storage size of geometry information. In addition, the encoding algorithm subdivides the whole space according to octree rules, which enables progressive transmission and loading. Three main steps are included in this method: (1) subdividing the whole 3D geographic space based on octree structure, (2) resampling all the vertices in 3D models, (3) encoding the coordinates of vertices with a combination of Cube Index Code (CIC) and Geometry Code. A series of geographical 3D models were applied to evaluate the encoding method. The results showed that this method reduced the storage size of most test data by 90 % or even more under the condition of a speed of encoding and decoding. In conclusion, this method achieved a remarkable compression rate in vertex bit size with a steerable precision loss. It shall be of positive meaning to the web 3d map storing and transmission.

Realism and Perspectivism: a Reevaluation of Rival Theories of Spatial Vision.

NASA Astrophysics Data System (ADS)

Thro, E. Broydrick

1990-01-01

My study reevaluates two theories of human space perception, a trigonometric surveying theory I call perspectivism and a "scene recognition" theory I call realism. Realists believe that retinal image geometry can supply no unambiguous information about an object's size and distance--and that, as a result, viewers can locate objects in space only by making discretionary interpretations based on familiar experience of object types. Perspectivists, in contrast, think viewers can disambiguate object sizes/distances on the basis of retinal image information alone. More specifically, they believe the eye responds to perspective image geometry with an automatic trigonometric calculation that not only fixes the directions and shapes, but also roughly fixes the sizes and distances of scene elements in space. Today this surveyor theory has been largely superceded by the realist approach, because most vision scientists believe retinal image geometry is ambiguous about the scale of space. However, I show that there is a considerable body of neglected evidence, both past and present, tending to call this scale ambiguity claim into question. I maintain that this evidence against scale ambiguity could hardly be more important, if one considers its subversive implications for the scene recognition theory that is not only today's reigning approach to spatial vision, but also the foundation for computer scientists' efforts to create space-perceiving robots. If viewers were deemed to be capable of automatic surveying calculations, the discretionary scene recognition theory would lose its main justification. Clearly, it would be difficult for realists to maintain that we viewers rely on scene recognition for space perception in spite of our ability to survey. And in reality, as I show, the surveyor theory does a much better job of describing the everyday space we viewers actually see--a space featuring stable, unambiguous relationships among scene elements, and a single horizon and vanishing point for (meter-scale) receding objects. In addition, I argue, the surveyor theory raises fewer philosophical difficulties, because it is more in harmony with our everyday concepts of material objects, human agency and the self.

Common Core State Standards in the Middle Grades: What's New in the Geometry Domain and How Can Teachers Support Student Learning?

ERIC Educational Resources Information Center

Teuscher, Dawn; Tran, Dung; Reys, Barbara J.

2015-01-01

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6-8)…

Kinematics of reflections in subsurface offset and angle-domain image gathers

NASA Astrophysics Data System (ADS)

Dafni, Raanan; Symes, William W.

2018-05-01

Seismic migration in the angle-domain generates multiple images of the earth's interior in which reflection takes place at different scattering-angles. Mechanically, the angle-dependent reflection is restricted to happen instantaneously and at a fixed point in space: Incident wave hits a discontinuity in the subsurface media and instantly generates a scattered wave at the same common point of interaction. Alternatively, the angle-domain image may be associated with space-shift (regarded as subsurface offset) extended migration that artificially splits the reflection geometry. Meaning that, incident and scattered waves interact at some offset distance. The geometric differences between the two approaches amount to a contradictory angle-domain behaviour, and unlike kinematic description. We present a phase space depiction of migration methods extended by the peculiar subsurface offset split and stress its profound dissimilarity. In spite of being in radical contradiction with the general physics, the subsurface offset reveals a link to some valuable angle-domain quantities, via post-migration transformations. The angle quantities are indicated by the direction normal to the subsurface offset extended image. They specifically define the local dip and scattering angles if the velocity at the split reflection coordinates is the same for incident and scattered wave pairs. Otherwise, the reflector normal is not a bisector of the opening angle, but of the corresponding slowness vectors. This evidence, together with the distinguished geometry configuration, fundamentally differentiates the angle-domain decomposition based on the subsurface offset split from the conventional decomposition at a common reflection point. An asymptotic simulation of angle-domain moveout curves in layered media exposes the notion of split versus common reflection point geometry. Traveltime inversion methods that involve the subsurface offset extended migration must accommodate the split geometry in the inversion scheme for a robust and successful convergence at the optimal velocity model.

Image-Based Computational Fluid Dynamics in Blood Vessel Models: Toward Developing a Prognostic Tool to Assess Cardiovascular Function Changes in Prolonged Space Flights

NASA Technical Reports Server (NTRS)

Chatzimavroudis, George P.; Spirka, Thomas A.; Setser, Randolph M.; Myers, Jerry G.

2004-01-01

One of NASA's objectives is to be able to perform a complete, pre-flight, evaluation of cardiovascular changes in astronauts scheduled for prolonged space missions. Computational fluid dynamics (CFD) has shown promise as a method for estimating cardiovascular function during reduced gravity conditions. For this purpose, MRI can provide geometrical information, to reconstruct vessel geometries, and measure all spatial velocity components, providing location specific boundary conditions. The objective of this study was to investigate the reliability of MRI-based model reconstruction and measured boundary conditions for CFD simulations. An aortic arch model and a carotid bifurcation model were scanned in a 1.5T Siemens MRI scanner. Axial MRI acquisitions provided images for geometry reconstruction (slice thickness 3 and 5 mm; pixel size 1x1 and 0.5x0.5 square millimeters). Velocity acquisitions provided measured inlet boundary conditions and localized three-directional steady-flow velocity data (0.7-3.0 L/min). The vessel walls were isolated using NIH provided software (ImageJ) and lofted to form the geometric surface. Constructed and idealized geometries were imported into a commercial CFD code for meshing and simulation. Contour and vector plots of the velocity showed identical features between the MRI velocity data, the MRI-based CFD data, and the idealized-geometry CFD data, with less than 10% differences in the local velocity values. CFD results on models reconstructed from different MRI resolution settings showed insignificant differences (less than 5%). This study illustrated, quantitatively, that reliable CFD simulations can be performed with MRI reconstructed models and gives evidence that a future, subject-specific, computational evaluation of the cardiovascular system alteration during space travel is feasible.

B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements

DTIC Science & Technology

2007-08-01

Infinite plate with a hole: sequence of meshes produced by h-refinement. The geometry of the coarsest mesh...recalled with an emphasis on k -refinement. In Section 3, the use of high-order NURBS within a projection technique is studied in the geometri - cally linear...case with a B̄ method to investigate the choice of approximation and projection spaces with NURBS.

Perceived orientation, spatial layout and the geometry of pictures

NASA Technical Reports Server (NTRS)

Goldstein, E. Bruce

1989-01-01

The purpose is to discuss the role of geometry in determining the perception of spatial layout and perceived orientation in pictures viewed at an angle. This discussion derives from Cutting's (1988) suggestion, based on his analysis of some of the author's data (Goldstein, 1987), that the changes in perceived orientation that occur when pictures are viewed at an angle can be explained in terms of geometrically produced changes in the picture's virtual space.

Mechanical Property Characterization and Modeling of Structural Materials.

DTIC Science & Technology

1982-02-01

ELEMENT ANALYSIS OF TEST SPECIMENS 69 a. Ring and Partial Ring Geometries 69 b. Keyhole and Wide-Notch Specimens 72 c. Three-Dimensional Results for...Figure 12. 45 16 Keyhole Specimen for Short-Crack Investigation (Dimensions in Inches). 47 17 Fatigue-Crack-Growth Rate for a Long Crack in 7075-T651...spacings. A modified keyhole specimen, 1/4-in. thick (shown in Fig. 16 ), was chosen for the investigation. The elongated specimen geometry was

Fast, Large-Area, Wide-Bandgap UV Photodetector for Cherenkov Light Detection

NASA Technical Reports Server (NTRS)

Wrbanek, John D.; Wrbanek, Susan Y.

2013-01-01

Due to limited resources available for power and space for payloads, miniaturizing and integrating instrumentation is a high priority for addressing the challenges of manned and unmanned deep space missions to high Earth orbit (HEO), near Earth objects (NEOs), Lunar and Martian orbits and surfaces, and outer planetary systems, as well as improvements to high-altitude aircraft safety. New, robust, and compact detectors allow future instrumentation packages more options in satisfying specific mission goals. A solid-state ultraviolet (UV) detector was developed with a theoretical fast response time and large detection area intended for application to Cherenkov detectors. The detector is based on the wide-bandgap semiconductor zinc oxide (ZnO), which in a bridge circuit can detect small, fast pulses of UV light like those required for Cherenkov detectors. The goal is to replace the role of photomultiplier tubes in Cherenkov detectors with these solid-state devices, saving on size, weight, and required power. For improving detection geometry, a spherical detector to measure high atomic number and energy (HZE) ions from any direction has been patented as part of a larger space radiation detector system. The detector will require the development of solid-state UV photodetectors fast enough (2 ns response time or better) to detect the shockwave of Cherenkov light emitted as the ions pass through a quartz, sapphire, or acrylic ball. The detector must be small enough to fit in the detector system structure, but have an active area large enough to capture enough Cherenkov light from the sphere. The detector is fabricated on bulk single-crystal undoped ZnO. Inter - digitated finger electrodes and contact pads are patterned via photolithography, and formed by sputtered metal of silver, platinum, or other high-conductivity metal.

Dynamical Connections in a Turbulent Fluid: Experiment and Simulation

NASA Astrophysics Data System (ADS)

Kageorge, Logan; Suri, Balachandra; Tithof, Jeff; Grigoriev, Roman; Schatz, Michael

2017-11-01

Embedded in the state space of a turbulent flow there exist invariant solutions to the Navier-Stokes equation called Exact Coherent Structures (ECS). Recent studies have demonstrated that the geometry of the ECS locally describes the evolution of the turbulent flow. Theory suggests that global connections may serve to guide the flow from the neighborhood of one ECS to that of another. We present here a numerical model of a Kolmogorov-like two-dimensional flow in which such connections have been calculated. Moreover, we present an experimental quasi-two-dimensional realization of this flow in which these connections prove dynamically relevant. This work is supported by the National Science Foundation (NSF CMMI 12-34436) and DARPA (HR0011-16-2-0033 subcontract to Georgia Tech).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Xiaoyao; Hall, Randall W.; Löffler, Frank

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methodsmore » and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Use of a residual distribution Euler solver to study the occurrence of transonic flow in Wells turbine rotor blades

NASA Astrophysics Data System (ADS)

Henriques, J. C. C.; Gato, L. M. C.

The aim of the present study is to investigate the occurrence of transonic flow in several cascade geometries and blade sections that have been considered in the design of Wells turbine rotor blades. The calculations were performed using an implicit Euler solver for two-dimensional flow. The numerical method uses a multi-dimensional upwind matrix residual distribution scheme formulated on a new symmetrized form of the Euler equations, both in time and in space, that decouples the entropy and the enthalpy equations. Second-order accurate steady-state solutions where obtained using a compact three-point stencil. The results show that unwanted transonic flow may occur in the turbine rotor at relatively low mean-flow Mach numbers.