Control of Soft Machines using Actuators Operated by a Braille Display

PubMed Central

Mosadegh, Bobak; Mazzeo, Aaron D.; Shepherd, Robert F.; Morin, Stephen A.; Gupta, Unmukt; Sani, Idin Zhalehdoust; Lai, David; Takayama, Shuichi; Whitesides, George M.

2013-01-01

One strategy for actuating soft machines (e.g., tentacles, grippers, and simple walkers) uses pneumatic inflation of networks of small channels in an elastomeric material. Although the management of a few pneumatic inputs and valves to control pressurized gas is straightforward, the fabrication and operation of manifolds containing many (>50) independent valves is an unsolved problem. Complex pneumatic manifolds—often built for a single purpose—are not easily reconfigured to accommodate the specific inputs (i.e., multiplexing of many fluids, ranges of pressures, and changes in flow rates) required by pneumatic systems. This paper describes a pneumatic manifold comprising a computer-controlled braille display and a micropneumatic device. The braille display provides a compact array of 64 piezoelectric actuators that actively close and open elastomeric valves of a micropneumatic device to route pressurized gas within the manifold. The positioning and geometries of the valves and channels in the micropneumatic device dictate the functionality of the pneumatic manifold, and the use of multi-layer soft lithography permits the fabrication of networks in a wide range of configurations with many possible functions. Simply exchanging micropneumatic devices of different designs enables rapid reconfiguration of the pneumatic manifold. As a proof of principle, a pneumatic manifold controlled a soft machine containing 32 independent actuators to move a ball above a flat surface. PMID:24196070

Minimal measures for Euler-Lagrange flows on finite covering spaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Xia, Zhihong

2016-12-01

In this paper we study the minimal measures for positive definite Lagrangian systems on compact manifolds. We are particularly interested in manifolds with more complicated fundamental groups. Mather’s theory classifies the minimal or action-minimizing measures according to the first (co-)homology group of a given manifold. We extend Mather’s notion of minimal measures to a larger class for compact manifolds with non-commutative fundamental groups, and use finite coverings to study the structure of these extended minimal measures. We also define action-minimizers and minimal measures in the homotopical sense. Our program is to study the structure of homotopical minimal measures by considering Mather’s minimal measures on finite covering spaces. Our goal is to show that, in general, manifolds with a non-commutative fundamental group have a richer set of minimal measures, hence a richer dynamical structure. As an example, we study the geodesic flow on surfaces of higher genus. Indeed, by going to the finite covering spaces, the set of minimal measures is much larger and more interesting.

Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

NASA Astrophysics Data System (ADS)

Liu, Chiu-Chu Melissa; Sheshmani, Artan

2017-07-01

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

A deformation of Sasakian structure in the presence of torsion and supergravity solutions

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Takeuchi, Hiroshi; Yasui, Yukinori

2013-07-01

A deformation of Sasakian structure in the presence of totally skew-symmetric torsion is discussed on odd-dimensional manifolds whose metric cones are Kähler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As their example, we present an explicit expression of local metrics. It is also demonstrated that our example of the metrics admits the existence of hidden symmetry described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an ansatz, we construct exact solutions in five-dimensional minimal gauged/ungauged supergravity and 11-dimensional supergravity. Finally, the global structures of the solutions are discussed. We obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki-Einstein manifolds Yp, q and La, b, c. We also briefly discuss regular metrics on non-compact manifolds in 11 dimensions.

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

NASA Astrophysics Data System (ADS)

de la Ossa, Xenia; Larfors, Magdalena; Svanes, Eirik E.

2016-11-01

We describe the infinitesimal moduli space of pairs ( Y, V) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli {H}_{{overset{ěe }{d}}_A}^1(Y,End(V)) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in {H}_{overset{ěe }{d}θ}^1(Y,TY) , and is given by the kernel of a map overset{ěe }{F} which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map overset{ěe }{F} is given in terms of the curvature of the bundle and maps {H}_{overset{ěe }{d}θ}^1(Y,TY) into {H}_{{overset{ěe }{d}}_A}^2(Y,End(V)) , and moreover can be used to define a cohomology on an extension bundle of TY by End( V). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on ( Y, V) when α' = 0.

GPU accelerated manifold correction method for spinning compact binaries

NASA Astrophysics Data System (ADS)

Ran, Chong-xi; Liu, Song; Zhong, Shuang-ying

2018-04-01

The graphics processing unit (GPU) acceleration of the manifold correction algorithm based on the compute unified device architecture (CUDA) technology is designed to simulate the dynamic evolution of the Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries. The feasibility and the efficiency of parallel computation on GPU have been confirmed by various numerical experiments. The numerical comparisons show that the accuracy on GPU execution of manifold corrections method has a good agreement with the execution of codes on merely central processing unit (CPU-based) method. The acceleration ability when the codes are implemented on GPU can increase enormously through the use of shared memory and register optimization techniques without additional hardware costs, implying that the speedup is nearly 13 times as compared with the codes executed on CPU for phase space scan (including 314 × 314 orbits). In addition, GPU-accelerated manifold correction method is used to numerically study how dynamics are affected by the spin-induced quadrupole-monopole interaction for black hole binary system.

Sigma models with negative curvature

DOE PAGES

Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.

2016-03-16

Here, we construct Higgs Effective Field Theory (HEFT) based on the scalar manifold Hn, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n, 1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.

BPS equations and non-trivial compactifications

NASA Astrophysics Data System (ADS)

Tyukov, Alexander; Warner, Nicholas P.

2018-05-01

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, Y , as opposed to simply a T 6. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact "local model" and take the compactification manifold to be Y={M}_{GH}× {T}^2 , where ℳGH is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on Y . The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of Y depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

The Hantzsche-Wendt manifold in cosmic topology

NASA Astrophysics Data System (ADS)

Aurich, R.; Lustig, S.

2014-08-01

The Hantzsche-Wendt space is one of the 17 multiply connected spaces of the three-dimensional Euclidean space {{{E}}^{3}}. It is a compact and orientable manifold which can serve as a model for a spatial finite universe. Since it possesses much fewer matched back-to-back circle pairs on the cosmic microwave background (CMB) sky than the other compact flat spaces, it can escape the detection by a search for matched circle pairs. The suppression of temperature correlations C(\\vartheta ) on large angular scales on the CMB sky is studied. It is shown that the large-scale correlations are of the same order as for the three-torus topology but express a much larger variability. The Hantzsche-Wendt manifold provides a topological possibility with reduced large-angle correlations that can hide from searches for matched back-to-back circle pairs.

Tops as building blocks for G 2 manifolds

NASA Astrophysics Data System (ADS)

Braun, Andreas P.

2017-10-01

A large number of examples of compact G 2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.

Hopf solitons on compact manifolds

NASA Astrophysics Data System (ADS)

Ward, R. S.

2018-02-01

Hopf solitons in the Skyrme-Faddeev system on R3 typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the Skyrme term (the strong-coupling limit), then the picture simplifies. There is a topological lower bound E ≥ Q on the energy, and the local minima of E can look simple even for large Q. The aim here is to describe and investigate some of these solutions, when M is S3, T3, or S2 × S1. In addition, we review the more elementary baby-Skyrme system, with M being S2 or T2.

A Note on Expansiveness and Hyperbolicity for Generic Geodesic Flows

NASA Astrophysics Data System (ADS)

Bessa, Mário

2018-06-01

In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove that there exists a C 2-residual subset R of metrics on a given compact Riemannian manifold such that if g\\in R, then its associated geodesic flow φ tg is expansive if and only if the closure of the set of periodic orbits of φtg is a uniformly hyperbolic set. For surfaces, we obtain a stronger statement: there exists a C 2-residual R such that if g\\in R, then its associated geodesic flow φtg is expansive if and only if φtg is an Anosov flow.

Asymptotic Behaviour of the Ground State of Singularly Perturbed Elliptic Equations

NASA Astrophysics Data System (ADS)

Piatnitski, Andrey L.

The ground state of a singularly perturbed nonselfadjoint elliptic operator defined on a smooth compact Riemannian manifold with metric aij(x)=(aij(x))-1, is studied. We investigate the limiting behaviour of the first eigenvalue of this operator as μ goes to zero, and find the logarithmic asymptotics of the first eigenfunction everywhere on the manifold. The results are formulated in terms of auxiliary variational problems on the manifold. This approach also allows to study the general singularly perturbed second order elliptic operator on a bounded domain in Rn.

Global embeddings for branes at toric singularities

NASA Astrophysics Data System (ADS)

Balasubramanian, Vijay; Berglund, Per; Braun, Volker; García-Etxebarria, Iñaki

2012-10-01

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) ( dP 0)3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.

Topological properties of a curved spacetime

NASA Astrophysics Data System (ADS)

Agrawal, Gunjan; Shrivastava, Sampada; Godani, Nisha; Sinha, Soami Pyari

2017-12-01

The present paper aims at the study of a topology on Lorentzian manifolds, defined by Göbel [4] using the ideas of Zeeman [16]. Observing that on the Minkowski space it is the same as Zeeman's time topology, it has been found that a Lorentzian manifold with this topology is path connected, nonfirst countable and nonsimply connected while the Minkowski space with time topology is, in addition nonregular and separable. Furthermore, using the notion of Zeno sequences it is obtained that a compact set does not contain a nonempty open set and that a set is compact if and only if each of its infinite subsets has a limit point if and only if each of its sequences has a convergent subsequence.

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

Differential Models for B-Type Open-Closed Topological Landau-Ginzburg Theories

NASA Astrophysics Data System (ADS)

Babalic, Elena Mirela; Doryn, Dmitry; Lazaroiu, Calin Iuliu; Tavakol, Mehdi

2018-05-01

We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair (X,W), where X is any non-compact Calabi-Yau manifold and W is any holomorphic complex-valued function defined on X whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector-valued forms and a twisted Dolbeault category of holomorphic factorizations of W. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed TFT (topological field theory) are satisfied on cohomology and conjecture that the remaining two axioms (namely non-degeneracy of bulk and boundary traces and the topological Cardy constraint) are also satisfied.

An analogue of Weyl’s law for quantized irreducible generalized flag manifolds

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

Matassa, Marco, E-mail: marco.matassa@gmail.com, E-mail: mmatassa@math.uio.no

2015-09-15

We prove an analogue of Weyl’s law for quantized irreducible generalized flag manifolds. This is formulated in terms of a zeta function which, similarly to the classical setting, satisfies the following two properties: as a functional on the quantized algebra it is proportional to the Haar state and its first singularity coincides with the classical dimension. The relevant formulas are given for the more general case of compact quantum groups.

Convergence of spectra of graph-like thin manifolds

NASA Astrophysics Data System (ADS)

Exner, Pavel; Post, Olaf

2005-05-01

We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with Kirchhoff boundary conditions at the vertices. On the other hand, if the shrinking at the vertex parts of the manifold is sufficiently slower comparing to that of the edge parts, the limiting spectrum corresponds to decoupled edges with Dirichlet boundary conditions at the endpoints. At the borderline between the two regimes we have a third possibility when the limiting spectrum can be described by a nontrivial coupling at the vertices.

Localization in abelian Chern-Simons theory

NASA Astrophysics Data System (ADS)

McLellan, B. D. K.

2013-02-01

Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three-manifolds. The torsion part of the abelian Chern-Simons partition function is computed explicitly in terms of Seifert data for a given Sasakian three-manifold.

Maximum Solutions of Normalized Ricci Flow on 4-Manifolds

NASA Astrophysics Data System (ADS)

Fang, Fuquan; Zhang, Yuguang; Zhang, Zhenlei

2008-10-01

We consider the maximum solution g( t), t ∈ [0, + ∞), to the normalized Ricci flow. Among other things, we prove that, if ( M, ω) is a smooth compact symplectic 4-manifold such that {b_2^+(M) > 1} and let g( t), t ∈ [0, ∞), be a solution to (1.3) on M whose Ricci curvature satisfies that |Ric( g( t))| ≤ 3 and additionally χ( M) = 3τ ( M) > 0, then there exists an {min mathbb{N}} , and a sequence of points { x j, k ∈ M}, j = 1, . . . , m, satisfying that, by passing to a subsequence, {{(M, g(tk+t), x_{1,k},ldots, x_{m,k})stackrel{d_{GH}}longrightarrow ({\\coprod limitsm_{j=1}} N_j , g_{infty}, x_{1,infty}, ldots, x_{m,infty}),}} t ∈ [0, ∞), in the m-pointed Gromov-Hausdorff sense for any sequence t k → ∞, where ( N j , g ∞), j = 1, . . . , m, are complete complex hyperbolic orbifolds of complex dimension 2 with at most finitely many isolated orbifold points. Moreover, the convergence is C ∞ in the non-singular part of {\\coprod _1^m Nj} and {text{Vol}_{g0}(M)=sum_{j=1}mtext{Vol}_{g_{infty}}(Nj)} , where χ( M) (resp. τ( M)) is the Euler characteristic (resp. signature) of M.

Nonexistence of stable F-stationary maps of a functional related to pullback metrics.

PubMed

Li, Jing; Liu, Fang; Zhao, Peibiao

2017-01-01

Let [Formula: see text] be a compact convex hypersurface in [Formula: see text]. In this paper, we prove that if the principal curvatures [Formula: see text] of [Formula: see text] satisfy [Formula: see text] and [Formula: see text], then there exists no nonconstant stable F -stationary map between M and a compact Riemannian manifold when (6) or (7) holds.

Absence of positive solutions to the system of differential inequalities on manifolds

NASA Astrophysics Data System (ADS)

Sun, Yuhua

2018-01-01

We investigate the nonexistence of positive solutions to a certain system of differential inequalities on a complete connected non-compact Riemannian manifold. We show that if for some reference point x0, the volume of geodesic ball μ(B(x0, r)) ≤ Crp ln q r holds for all large enough r and for some constant C, then there exists no positive solution to the system. Here the exponents p and q are sharp and cannot be relaxed.

Global uniqueness in an inverse problem for time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M.

2018-01-01

Given (M , g), a compact connected Riemannian manifold of dimension d ⩾ 2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0 , T) × M, T > 0, with time-fractional Caputo derivative of order α ∈ (0 , 1) ∪ (1 , 2). We prove uniqueness in the inverse problem of determining the smooth manifold (M , g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the "flat" case where M is a compact subset of Rd, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ ∂tα u - div (a∇u) + qu = 0 on (0 , T) × M are recovered simultaneously.

Harmonic spinors on a family of Einstein manifolds

NASA Astrophysics Data System (ADS)

Franchetti, Guido

2018-06-01

The purpose of this paper is to study harmonic spinors defined on a 1-parameter family of Einstein manifolds which includes Taub–NUT, Eguchi–Hanson and with the Fubini–Study metric as particular cases. We discuss the existence of and explicitly solve for spinors harmonic with respect to the Dirac operator twisted by a geometrically preferred connection. The metrics examined are defined, for generic values of the parameter, on a non-compact manifold with the topology of and extend to as edge-cone metrics. As a consequence, the subtle boundary conditions of the Atiyah–Patodi–Singer index theorem need to be carefully considered in order to show agreement between the index of the twisted Dirac operator and the result obtained by counting the explicit solutions.

Volume growth and puncture repair in conformal geometry

NASA Astrophysics Data System (ADS)

Eastwood, Michael G.; Gover, A. Rod

2018-04-01

Suppose M is a compact Riemannian manifold and p ∈ M an arbitrary point. We employ estimates on the volume growth around p to prove that the only conformal compactification of M ∖ { p } is M itself.

U(1) mediation of flux supersymmetry breaking

NASA Astrophysics Data System (ADS)

Grimm, Thomas W.; Klemm, Albrecht

2008-10-01

We study the mediation of supersymmetry breaking triggered by background fluxes in Type II string compactifications with Script N = 1 supersymmetry. The mediation arises due to an U(1) vector multiplet coupling to both a hidden supersymmetry breaking flux sector and a visible D-brane sector. The required internal manifolds can be constructed by non-Kähler resolutions of singular Calabi-Yau manifolds. The effective action encoding the U(1) coupling is then determined in terms of the global topological properties of the internal space. We investigate suitable local geometries for the hidden and visible sector in detail. This includes a systematic study of orientifold symmetries of del Pezzo surfaces realized in compact geometries after geometric transition. We construct compact examples admitting the key properties to realize flux supersymmetry breaking and U(1) mediation. Their toric realization allows us to analyze the geometry of curve classes and confirm the topological connection between the hidden and visible sector.

Eigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problems

NASA Astrophysics Data System (ADS)

Xia, Changyu; Wang, Qiaoling

2018-05-01

We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell-Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a bounded domain in a Euclidean space. We study some fourth order Steklov problems and obtain isoperimetric upper bound for the first eigenvalue of them. We also find all the eigenvalues and eigenfunctions for two kind of fourth order Steklov problems on a Euclidean ball.

Gravitational instantons admit hyper-Kähler structure

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

1999-01-01

We construct the explicit form of three almost-complex structures that a Riemannian manifold with self-dual curvature admits and show that their Nijenhuis tensors vanish so that they are integrable. This proves that gravitational instantons with self-dual curvature admit hyper-Kähler structure. In order to arrive at the three vector-valued 1-forms defining almost-complex structure, we give a spinor description of real four-dimensional Riemannian manifolds with Euclidean signature in terms of two independent sets of two-component spinors. This is a version of the original Newman-Penrose formalism that is appropriate to the discussion of the mathematical, as well as physical properties of gravitational instantons. We shall build on the work of Goldblatt who first developed an NP formalism for gravitational instantons but we shall adopt it to differential forms in the NP basis to make the formalism much more compact. We shall show that the spin coefficients, connection 1-form, curvature 2-form, Ricci and Bianchi identities, as well as the Maxwell equations naturally split up into their self-dual and anti-self-dual parts corresponding to the two independent spin frames. We shall give the complex dyad as well as the spinor formulation of the almost-complex structures and show that they reappear under the guise of a triad basis for the Petrov classification of gravitational instantons. Completing the work of Salamon on hyper-Kähler structure, we show that the vanishing of the Nijenhuis tensor for all three almost-complex structures depends on the choice of a self-dual gauge for the connection which is guaranteed by virtue of the fact that the curvature 2-form is self-dual for gravitational instantons.

G-structures and domain walls in heterotic theories

NASA Astrophysics Data System (ADS)

Lukas, Andre; Matti, Cyril

2011-01-01

We consider heterotic string solutions based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold, preserving two supercharges. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be generalized half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that previous heterotic compactifications on half-flat mirror manifolds are based on this class of solutions.

On the Support of Minimizers of Causal Variational Principles

NASA Astrophysics Data System (ADS)

Finster, Felix; Schiefeneder, Daniela

2013-11-01

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed and explicit analysis of the minimizers. On the sphere, we get a connection to packing problems and the Tammes distribution. Moreover, the minimal action is estimated from above and below.

LR: Compact connectivity representation for triangle meshes

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

Gurung, T; Luffel, M; Lindstrom, P

2011-01-28

We propose LR (Laced Ring) - a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constant-time adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearly-Hamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard random-access, constant-time operators formore » traversing a mesh, and show that LR often saves both space and traversal time over competing representations.« less

Grassmann matrix quantum mechanics

DOE PAGES

Anninos, Dionysios; Denef, Frederik; Monten, Ruben

2016-04-21

We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less

Information geometric methods for complexity

NASA Astrophysics Data System (ADS)

Felice, Domenico; Cafaro, Carlo; Mancini, Stefano

2018-03-01

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

NASA Astrophysics Data System (ADS)

Lupo, Umberto

2018-04-01

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

Numerical exploration of the string theory landscape

NASA Astrophysics Data System (ADS)

Metallinos, Konstantinos

String theory is the best candidate to provide a consistent quantum theory of gravity. Its ten dimensional formulation forces us to perform a compactification of the six unobserved dimensions in a very special compact manifold known as Calabi-Yau. The standard way to address this issue is through the flux compactification scenarios. One of the major implications of these scenarios is that the string theory cannot provide a single and unique vacuum as a solution. Rather one can find an extremely large set of solutions, each with its own physical properties. This is the string theory Landscape. In the first part we present the formal description of the flux compactification theory. From the four dimensional point of view this is a supersymmetric theory, fully described only by two functions, the superpotential and the Kahler potential. Their expressions are crucially depend on the geometrical properties of the compact manifold. By writing these functions for the specific Calabi-Yau manifold P41,1,1,6,9 we are looking firstly for supersymmetric and then after breaking the supersymmetry, for non-supersymmetric numerical solutions. These solutions describe the possible vacua and our goal is using statistical analysis to categorize them based on their cosmological properties and to check their stability. Finally we present the existence of stable dS vacua with and without adding an uplifting term on the potential. In the case where there is not an uplifting term the breaking of supersymmetry is done by incorporating alpha' corrections to the Kahler potential. In the second part we construct a KKLT like inflation model, within string theory flux compactifications and, in particular a model of accidental inflation. We investigate the possibility that the apparent fine-tuning of the low energy parameters of the theory needed to have inflation can be generically obtained by scanning the values of the fluxes over the landscape. Furthermore, we find that the existence of a landscape of eternal inflation in this model provides us with a natural theory of initial conditions for the inflationary period in our vacuum. We demonstrate how these two effects work in a small corner of the landscape associated with the complex structure of the Calabi-Yau manifold P41,1,1,6,9 by numerically investigating the flux vacua of a reduced moduli space. This allows us to obtain the distribution of observable parameters for inflation in this mini-landscape directly from the fluxes.

Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications

NASA Astrophysics Data System (ADS)

Ali, Akram; Ozel, Cenap

It is known from [K. Yano and M. Kon, Structures on Manifolds (World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.

Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

NASA Astrophysics Data System (ADS)

Micheli, Mario; Michor, Peter W.; Mumford, David

2013-06-01

Given a finite-dimensional manifold N, the group \\operatorname{Diff}_{ S}(N) of diffeomorphisms diffeomorphism of N which decrease suitably rapidly to the identity, acts on the manifold B(M,N) of submanifolds of N of diffeomorphism-type M, where M is a compact manifold with \\operatorname{dim} M<\\operatorname{dim} N. Given the right-invariant weak Riemannian metric on \\operatorname{Diff}_{ S}(N) induced by a quite general operator L\\colon \\mathfrak{X}_{ S}(N)\\to \\Gamma(T^*N\\otimes\\operatorname{vol}(N)), we consider the induced weak Riemannian metric on B(M,N) and compute its geodesics and sectional curvature. To do this, we derive a covariant formula for the curvature in finite and infinite dimensions, we show how it makes O'Neill's formula very transparent, and we finally use it to compute the sectional curvature on B(M,N).

Topology and Singularities in Cosmological Spacetimes Obeying the Null Energy Condition

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Ling, Eric

2018-06-01

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3 + 1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.

The singular values of the imbedding operators of some classes of analytic functions of several variables

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

Parfenov, O.G.

1994-12-25

We discuss three results. The first exhibits the order of decrease of the s-values as a function of the CR-dimension of a compact set on which we approximate the class of analytic functions being studied. The second is an asymptotic formula for the case when the domain of analyticity and the compact set are Reinhart domains. The third is the computation of the s-values of a special operator that is of interest for approximation theory on one-dimensional manifolds.

Estimation for bilinear stochastic systems

NASA Technical Reports Server (NTRS)

Willsky, A. S.; Marcus, S. I.

1974-01-01

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed.

Ricci curvature of Diff S/sup 1//SL(2,R)

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

Bowick, M.J.; Lahiri, A.

Previous calculations of the Ricci curvature for the manifold Diff Diff(S/sup 1/)/S/sup 1/ are extended to Diff(S/sup 1/)/SL(2R). These manifolds are distinguished by being coadjoint orbits of Diff(S/sup 1/) which admit compatible symphectic and complex structures, making them Kaehler manifolds.

Manifold regularized multitask learning for semi-supervised multilabel image classification.

PubMed

Luo, Yong; Tao, Dacheng; Geng, Bo; Xu, Chao; Maybank, Stephen J

2013-02-01

It is a significant challenge to classify images with multiple labels by using only a small number of labeled samples. One option is to learn a binary classifier for each label and use manifold regularization to improve the classification performance by exploring the underlying geometric structure of the data distribution. However, such an approach does not perform well in practice when images from multiple concepts are represented by high-dimensional visual features. Thus, manifold regularization is insufficient to control the model complexity. In this paper, we propose a manifold regularized multitask learning (MRMTL) algorithm. MRMTL learns a discriminative subspace shared by multiple classification tasks by exploiting the common structure of these tasks. It effectively controls the model complexity because different tasks limit one another's search volume, and the manifold regularization ensures that the functions in the shared hypothesis space are smooth along the data manifold. We conduct extensive experiments, on the PASCAL VOC'07 dataset with 20 classes and the MIR dataset with 38 classes, by comparing MRMTL with popular image classification algorithms. The results suggest that MRMTL is effective for image classification.

Some remarks on the topology of hyperbolic actions of Rn on n-manifolds

NASA Astrophysics Data System (ADS)

Bouloc, Damien

2017-11-01

This paper contains some results on the topology of a nondegenerate action of Rn on a compact connected n-manifold M when the action is totally hyperbolic (i.e. its toric degree is zero). We study the R-action generated by a fixed vector of Rn, that provides some results on the number of hyperbolic domains and the number of fixed points of the action. We study with more details the case of the 2-sphere, in particular we investigate some combinatorial properties of the associated 4-valent graph embedded in S2. We also construct hyperbolic actions in dimension 3, on the sphere S3 and on the projective space RP3.

Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves

NASA Astrophysics Data System (ADS)

Kanazawa, Atsushi

2017-04-01

We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials.

Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions

NASA Astrophysics Data System (ADS)

Hezari, Hamid

2018-02-01

We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.

Hidden symmetries on toric Sasaki-Einstein spaces

NASA Astrophysics Data System (ADS)

Slesar, V.; Visinescu, M.; Vîlcu, G. E.

2015-05-01

We describe the construction of Killing-Yano tensors on toric Sasaki-Einstein manifolds. We use the fact that the metric cones of these spaces are Calabi-Yau manifolds. The description of the Calabi-Yau manifolds in terms of toric data, using the Delzant approach to toric geometries, allows us to find explicitly the complex coordinates and write down the Killing-Yano tensors. As a concrete example we present the complete set of special Killing forms on the five-dimensional homogeneous Sasaki-Einstein manifold T 1,1.

Multispectral embedding-based deep neural network for three-dimensional human pose recovery

NASA Astrophysics Data System (ADS)

Yu, Jialin; Sun, Jifeng

2018-01-01

Monocular image-based three-dimensional (3-D) human pose recovery aims to retrieve 3-D poses using the corresponding two-dimensional image features. Therefore, the pose recovery performance highly depends on the image representations. We propose a multispectral embedding-based deep neural network (MSEDNN) to automatically obtain the most discriminative features from multiple deep convolutional neural networks and then embed their penultimate fully connected layers into a low-dimensional manifold. This compact manifold can explore not only the optimum output from multiple deep networks but also the complementary properties of them. Furthermore, the distribution of each hierarchy discriminative manifold is sufficiently smooth so that the training process of our MSEDNN can be effectively implemented only using few labeled data. Our proposed network contains a body joint detector and a human pose regressor that are jointly trained. Extensive experiments conducted on four databases show that our proposed MSEDNN can achieve the best recovery performance compared with the state-of-the-art methods.

A vacuum manifold for rapid world-to-chip connectivity of complex PDMS microdevices.

PubMed

Cooksey, Gregory A; Plant, Anne L; Atencia, Javier

2009-05-07

The lack of simple interfaces for microfluidic devices with a large number of inlets significantly limits production and utilization of these devices. In this article, we describe the fabrication of a reusable manifold that provides rapid world-to-chip connectivity. A vacuum network milled into a rigid manifold holds microdevices and prevents leakage of fluids injected into the device from ports in the manifold. A number of different manifold designs were explored, and all performed similarly, yielding an average of 100 kPa (15 psi) fluid holding pressure. The wide applicability of this manifold concept is demonstrated by interfacing with a 51-inlet microfluidic chip containing 144 chambers and hundreds of embedded pneumatic valves. Due to the speed of connectivity, the manifolds are ideal for rapid prototyping and are well suited to serve as "universal" interfaces.

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.

Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

NASA Astrophysics Data System (ADS)

Holst, Michael; Meier, Caleb

2015-01-01

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary Σ. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show the existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on Σ, similar to those analyzed previously by Dain (2004 Class. Quantum Grav. 21 555-73), by Maxwell (2004, 2005 Commun. Math. Phys. 253 561-83), and by Holst and Tsogtgerel (2013 Class. Quantum Grav. 30 205011) as a model of black holes in various CMC settings, and by Holst et al (2013 Non-CMC solutions to the einstein constraint equations with apparent horizon boundaries arXiv:1310.2302v1) in the setting of far-from-CMC solutions on compact manifolds with boundary. These ‘marginally trapped surface’ Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region Σ are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assuming a suitable form of weak cosmic censorship, the results presented in this article guarantee the existence of initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new.

Cohomology of line bundles: Applications

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Jurke, Benjamin; Rahn, Thorsten; Roschy, Helmut

2012-01-01

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute cohomology for line bundles on finite group action coset spaces, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrev's formula and its generalizations can be given a one-to-one cohomological interpretation. Furthermore, we derive a combinatorial closed form expression for two Hodge numbers of a codimension two Calabi-Yau fourfold.

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph

2015-09-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces.

Integrative Pericyclic Cascade: An Atom Economic, Multi C-C Bond-Forming Strategy for the Construction of Molecular Complexity.

PubMed

Tejedor, David; Delgado-Hernández, Samuel; Peyrac, Jesús; González-Platas, Javier; García-Tellado, Fernando

2017-07-26

An all-pericyclic manifold is developed for the construction of topologically diverse, structurally complex and natural product-like polycyclic chemotypes. The manifold uses readily accessible tertiary propargyl vinyl ethers as substrates and imidazole as a catalyst to form up to two new rings, three new C-C bonds, six stereogenic centers and one transannular oxo-bridge. The manifold is efficient, scalable and instrumentally simple to perform and entails a propargyl Claisen rearrangement-[1,3]H shift, an oxa-6π-electrocyclization, and an intramolecular Diels-Alder reaction. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Two-dimensional Manifold with Point-like Defects

NASA Astrophysics Data System (ADS)

Gani, V. A.; Dmitriev, A. E.; Rubin, S. G.

We study a class of two-dimensional compact extra spaces isomorphic to the sphere S 2 in the framework of multidimensional gravitation. We show that there exists a family of stationary metrics that depend on the initial (boundary) conditions. All these geometries have a singular point. We also discuss the possibility for these deformed extra spaces to be considered as dark matter candidates.

Algebraic models of local period maps and Yukawa algebras

NASA Astrophysics Data System (ADS)

Bandiera, Ruggero; Manetti, Marco

2018-02-01

We describe some L_{∞} model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.

Apparatus for restraining and transporting dies

DOEpatents

Allison, James W.; LaBarre, Timothy L.

1994-01-01

Apparatus for restraining and transporting dies in punch press operations is provided. A floatation platen for supporting a die on the platen's upper surface has a plurality of recessed gas exhaust ports on the platen's lower surface. A source of pressurized gas delivers gas to a platen manifold, for delivery to orifices located in the gas exhaust ports. The flow of gas is controlled by a first valve adjacent the gas source and a second valve adjacent the manifold, with the second valve being used to control the gas flow during movement of the die. In this fashion, a die may be moved on a cushion of air from one workstation to a selected second workstation. A moveable hydraulically operated restraining fixture is also provided, for clamping the die in position during the compacting phase, and for releasing the die after completion of the compacting phase by releasing the hydraulic pressure on the restraining fixture. When pressure in the hydraulic cylinders on the restraining fixture is reversed, the restraining fixture will retract so that there is no contact between the die and the restraining fixture, thereby allowing the die to be removed from a first workstation and moved to a second selected workstation.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

Representation of complex probabilities and complex Gibbs sampling

NASA Astrophysics Data System (ADS)

Salcedo, Lorenzo Luis

2018-03-01

Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the wellknown sign problem. The complex Langevin approach amounts to effectively construct a positive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension. Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold. Explicit localized representations are obtained for complex probabilities defined on Abelian and non Abelian groups. The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed.

On the equivalence of some spectral sequences for Serre fibrations

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

Onishchenko, Aleksandr Yu; Popelenskii, Fedor Yu

2011-04-30

Several different constructions of a spectral sequence for a Serre fibration {pi}:E{yields}B over a compact simply connected manifold B are considered in this paper. Namely, we consider the spectral sequence for the minimal model ({Lambda}Vx{Lambda}W,d) of the fibration, along with the spectral sequences arising from the Cech filtration in the complexes C*(U,A*{sub PL}({pi}{sup -1}(U))) and C*(U,S*({pi}{sup -1}(U))), where U=(U) is a covering of the base B. It is known that all these spectral sequences have the same terms E{sub 2}*{sup ,}*=H*(X)xH{sup *}(F) and converge to the cohomology of the total space E. A new natural isomorphism of these spectral sequencesmore » is constructed in every term E{sub r} with r{>=}2. It is also proved that in the case of a smooth locally trivial fibration these spectral sequences are isomorphic to the spectral sequences of the complex of smooth forms {Omega}*(E) and of the Cech-de Rham complex. It is therefore established that all these constructions give the same spectral sequence, starting from the E{sub 2} term. Bibliography: 9 titles.« less

On the equivalence of some spectral sequences for Serre fibrations

NASA Astrophysics Data System (ADS)

Onishchenko, Aleksandr Yu; Popelenskii, Fedor Yu

2011-04-01

Several different constructions of a spectral sequence for a Serre fibration \\pi\\colon E \\to B over a compact simply connected manifold B are considered in this paper. Namely, we consider the spectral sequence for the minimal model (\\Lambda V\\otimes \\Lambda W,d) of the fibration, along with the spectral sequences arising from the Čech filtration in the complexes \\check{C}^*(\\mathscr{U}, A_{PL}^*(\\pi^{-1}(U))) and \\check{C}^*(\\mathscr{U}, S^*(\\pi^{-1}(U))), where \\mathscr{U}=\\{U\\} is a covering of the base B. It is known that all these spectral sequences have the same terms E_2^{*,*}=H^*(X)\\otimes H^*(F) and converge to the cohomology of the total space E. A new natural isomorphism of these spectral sequences is constructed in every term E_r with r\\ge2. It is also proved that in the case of a smooth locally trivial fibration these spectral sequences are isomorphic to the spectral sequences of the complex of smooth forms \\Omega^*(E) and of the Čech-de Rham complex. It is therefore established that all these constructions give the same spectral sequence, starting from the E_2 term. Bibliography: 9 titles.

Recent developments in the structural design and optimization of ITER neutral beam manifold

NASA Astrophysics Data System (ADS)

Chengzhi, CAO; Yudong, PAN; Zhiwei, XIA; Bo, LI; Tao, JIANG; Wei, LI

2018-02-01

This paper describes a new design of the neutral beam manifold based on a more optimized support system. A proposed alternative scheme has presented to replace the former complex manifold supports and internal pipe supports in the final design phase. Both the structural reliability and feasibility were confirmed with detailed analyses. Comparative analyses between two typical types of manifold support scheme were performed. All relevant results of mechanical analyses for typical operation scenarios and fault conditions are presented. Future optimization activities are described, which will give useful information for a refined setting of components in the next phase.

Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits

NASA Astrophysics Data System (ADS)

Visinescu, Mihai; Vîlcu, Eduard

2012-08-01

The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. Finally the Killing forms on mixed 3-Sasaki manifolds are briefly described.

Fast spatially resolved exhaust gas recirculation (EGR) distribution measurements in an internal combustion engine using absorption spectroscopy.

PubMed

Yoo, Jihyung; Prikhodko, Vitaly; Parks, James E; Perfetto, Anthony; Geckler, Sam; Partridge, William P

2015-09-01

Exhaust gas recirculation (EGR) in internal combustion engines is an effective method of reducing NOx emissions while improving efficiency. However, insufficient mixing between fresh air and exhaust gas can lead to cycle-to-cycle and cylinder-to-cylinder non-uniform charge gas mixtures of a multi-cylinder engine, which can in turn reduce engine performance and efficiency. A sensor packaged into a compact probe was designed, built and applied to measure spatiotemporal EGR distributions in the intake manifold of an operating engine. The probe promotes the development of more efficient and higher-performance engines by resolving high-speed in situ CO2 concentration at various locations in the intake manifold. The study employed mid-infrared light sources tuned to an absorption band of CO2 near 4.3 μm, an industry standard species for determining EGR fraction. The calibrated probe was used to map spatial EGR distributions in an intake manifold with high accuracy and monitor cycle-resolved cylinder-specific EGR fluctuations at a rate of up to 1 kHz.

Fast Spatially Resolved Exhaust Gas Recirculation (EGR) Distribution Measurements in an Internal Combustion Engine Using Absorption Spectroscopy

DOE PAGES

Yoo, Jihyung; Prikhodko, Vitaly; Parks, James E.; ...

2015-09-01

One effective method of reducing NO x emissions while improving efficiency is exhaust gas recirculation (EGR) in internal combustion engines. But, insufficient mixing between fresh air and exhaust gas can lead to cycle-to-cycle and cylinder-to-cylinder nonuniform charge gas mixtures of a multi-cylinder engine, which can in turn reduce engine performance and efficiency. Furthermore, a sensor packaged into a compact probe was designed, built and applied to measure spatiotemporal EGR distributions in the intake manifold of an operating engine. The probe promotes the development of more efficient and higher-performance engines by resolving high-speed in situ CO 2 concentration at various locationsmore » in the intake manifold. Our study employed mid-infrared light sources tuned to an absorption band of CO 2 near 4.3 μm, an industry standard species for determining EGR fraction. The calibrated probe was used to map spatial EGR distributions in an intake manifold with high accuracy and monitor cycle-resolved cylinder-specific EGR fluctuations at a rate of up to 1 kHz.« less

Cayley transform on Stiefel manifolds

NASA Astrophysics Data System (ADS)

Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel

2018-01-01

The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

PubMed Central

Bianconi, Ginestra; Rahmede, Christoph

2015-01-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces. PMID:26356079

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free.

PubMed

Bianconi, Ginestra; Rahmede, Christoph

2015-09-10

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension d. We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the δ-faces of the d-dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the δ-faces.

Adaptive simplification of complex multiscale systems.

PubMed

Chiavazzo, Eliodoro; Karlin, Ilya

2011-03-01

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step toward extracting essential physical knowledge from complex systems, by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics. Accurate reduced description is achieved, by construction of a hierarchy of slow invariant manifolds, with an embarrassingly simple implementation in any dimension. The method is validated with the autoignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observed.

Camera-pose estimation via projective Newton optimization on the manifold.

PubMed

Sarkis, Michel; Diepold, Klaus

2012-04-01

Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

NASA Technical Reports Server (NTRS)

Gomez, G.; Koon, W. S.; Lo, Martin W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2001-01-01

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

GUTs on Compact Type IIB Orientifolds

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

Blumenhagen, Ralph; /Munich, Max Planck Inst.; Braun, Volker

We systematically analyze globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realization of SU(5) GUTs with gauge symmetry breaking via U(1)Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P{sub 1,1,1,6,9}[18] and of the Quintic P{sub 1,1,1,1,1}[5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of thesemore » geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realize other phenomenological features such as the 10 10 5{sub H} Yukawa coupling and comment on the possibility of moduli stabilization, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds.« less

Decorated Heegaard Diagrams and Combinatorial Heegaard Floer Homology

NASA Astrophysics Data System (ADS)

Hammarsten, Carl

Heegaard Floer homology is a collection of invariants for closed oriented three-manifolds, introduced by Ozsvath and Szabo in 2001. The simplest version is defined as the homology of a chain complex coming from a Heegaard diagram of the three manifold. In the original definition, the differentials count the number of points in certain moduli spaces of holomorphic disks, which are hard to compute in general. More recently, Sarkar and Wang (2006) and Ozsvath, Stipsicz and Szabo, (2009) have determined combinatorial methods for computing this homology with Z2 coefficients. Both methods rely on the construction of very specific Heegaard diagrams for the manifold, which are generally very complicated. Given a decorated Heegaard diagram H for a closed oriented 3-manifold Y, that is a Heegaard diagram together with a collection of embedded paths satisfying certain criteria, we describe a combinatorial recipe for a chain complex CF'[special character omitted]( H). If H satisfies some technical constraints we show that this chain complex is homotopically equivalent to the Heegaard Floer chain complex CF[special character omitted](H) and hence has the Heegaard Floer homology HF[special character omitted](Y) as its homology groups. Using branched spines we give an algorithm to construct a decorated Heegaard diagram which satisfies the necessary technical constraints for every closed oriented Y. We present this diagram graphically in the form of a strip diagram.

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

DOE PAGES

Braun, Volker; Cvetič, Mirjam; Donagi, Ron; ...

2017-07-26

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

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

Braun, Volker; Cvetič, Mirjam; Donagi, Ron

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less

Harmonic maps of S into a complex Grassmann manifold.

PubMed

Chern, S S; Wolfson, J

1985-04-01

Let G(k, n) be the Grassmann manifold of all C(k) in C(n), the complex spaces of dimensions k and n, respectively, or, what is the same, the manifold of all projective spaces P(k-1) in P(n-1), so that G(1, n) is the complex projective space P(n-1) itself. We study harmonic maps of the two-dimensional sphere S(2) into G(k, n). The case k = 1 has been the subject of investigation by several authors [see, for example, Din, A. M. & Zakrzewski, W. J. (1980) Nucl. Phys. B 174, 397-406; Eells, J. & Wood, J. C. (1983) Adv. Math. 49, 217-263; and Wolfson, J. G. Trans. Am. Math. Soc., in press]. The harmonic maps S(2) --> G(2, 4) have been studied by Ramanathan [Ramanathan, J. (1984) J. Differ. Geom. 19, 207-219]. We shall describe all harmonic maps S(2) --> G(2, n). The method is based on several geometrical constructions, which lead from a given harmonic map to new harmonic maps, in which the image projective spaces are related by "fundamental collineations." The key result is the degeneracy of some fundamental collineations, which is a global consequence, following from the fact that the domain manifold is S(2). The method extends to G(k, n).

Complex network view of evolving manifolds

NASA Astrophysics Data System (ADS)

da Silva, Diamantino C.; Bianconi, Ginestra; da Costa, Rui A.; Dorogovtsev, Sergey N.; Mendes, José F. F.

2018-03-01

We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by the condition that at each step, all the faces must be triangles. Stochastic application of these operations leads to random networks with different architectures. We perform extensive numerical simulations and explore the geometries of growing and equilibrium complex networks generated by these transformations and their local structural properties. This characterization includes the Hausdorff and spectral dimensions of the resulting networks, their degree distributions, and various structural correlations. Our results reveal a rich zoo of architectures and geometries of these networks, some of which appear to be small worlds while others are finite dimensional with Hausdorff dimension equal or higher than the original dimensionality of their simplices. The range of spectral dimensions of the evolving triangulations turns out to be from about 1.4 to infinity. Our models include simplicial complexes representing manifolds with evolving topologies, for example, an h -holed torus with a progressively growing number of holes. This evolving graph demonstrates features of a small-world network and has a particularly heavy-tailed degree distribution.

Helicity is the only integral invariant of volume-preserving transformations

PubMed Central

Enciso, Alberto; Peralta-Salas, Daniel; de Lizaur, Francisco Torres

2016-01-01

We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional ℐ defined on exact divergence-free vector fields of class C1 on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that ℐ is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity. PMID:26864201

A short note on the mean exit time of the Brownian motion

NASA Astrophysics Data System (ADS)

Cadeddu, Lucio; Farina, Maria Antonietta

We investigate the functional Ω↦ℰ(Ω) where Ω runs through the set of compact domains of fixed volume v in any Riemannian manifold (M,g) and where ℰ(Ω) is the mean exit time from Ω of the Brownian motion. We give an alternative analytical proof of a well-known fact on its critical points proved by McDonald: the critical points of ℰ(Ω) are harmonic domains.

Discrete symmetry breaking and baryon currents in U(N) and SU(N) gauge theories

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

Lucini, B.; Patella, A.

2009-06-15

In SU(N) gauge theories with fermions in the fundamental or in a two-index (either symmetric or antisymmetric) representation formulated on a manifold with at least one compact dimension with nontrivial holonomy the discrete symmetries C, P, and T are broken at small enough size of the compact direction(s) for certain values of N. We show that for those N in the broken phase a nonzero baryon current wrapping in the compact direction exists, which provides a measurable observable for the breaking of C, P, and T. We prove that in all cases where the current is absent there is nomore » breaking of those discrete symmetries. This includes the limit N{yields}{infinity} of the SU(N) gauge theory with symmetric or antisymmetric fermions and U(N) gauge theory at any value of N. We then argue that the component of the baryon current in the compact direction is the physical order parameter for C, P, and T breaking due to the breaking of Lorentz invariance.« less

Donaldson-Witten theory and indefinite theta functions

NASA Astrophysics Data System (ADS)

Korpas, Georgios; Manschot, Jan

2017-11-01

We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

A note on φ-analytic conformal vector fields

NASA Astrophysics Data System (ADS)

Deshmukh, Sharief; Bin Turki, Nasser

2017-09-01

Taking clue from the analytic vector fields on a complex manifold, φ-analytic conformal vector fields are defined on a Riemannian manifold (Deshmukh and Al-Solamy in Colloq. Math. 112(1):157-161, 2008). In this paper, we use φ-analytic conformal vector fields to find new characterizations of the n-sphere Sn(c) and the Euclidean space (Rn,<,> ).

Averages of Eigenfunctions Over Hypersurfaces

NASA Astrophysics Data System (ADS)

Canzani, Yaiza; Galkowski, Jeffrey; Toth, John A.

2018-06-01

Let ( M, g) be a compact, smooth, Riemannian manifold and φ_h an L 2-normalized sequence of Laplace eigenfunctions with defect measure {μ}. Let H be a smooth hypersurface with unit exterior normal ν. Our main result says that when μ is not concentrated conormally to H, the eigenfunction restrictions to H satisfy \\int_H φ_h dσ_H = o(1) \\quad and \\quad \\int_H h D_{ν} φ_h dσ_H = o(1), {h \\to 0^+}.

Quantization of noncompact coverings and its physical applications

NASA Astrophysics Data System (ADS)

Ivankov, Petr

2018-02-01

A rigorous algebraic definition of noncommutative coverings is developed. In the case of commutative algebras this definition is equivalent to the classical definition of topological coverings of locally compact spaces. The theory has following nontrivial applications: • Coverings of continuous trace algebras, • Coverings of noncommutative tori, • Coverings of the quantum SU(2) group, • Coverings of foliations, • Coverings of isospectral deformations of Spin - manifolds. The theory supplies the rigorous definition of noncommutative Wilson lines.

Signatures of extra dimensions in gravitational waves

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

Andriot, David; Gómez, Gustavo Lucena, E-mail: andriotphysics@gmail.com, E-mail: glucenag@aei.mpg.de

2017-06-01

Considering gravitational waves propagating on the most general 4+ N -dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski{sub 4} times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.

Lamination cooling system formation method

DOEpatents

Rippel, Wally E [Altadena, CA; Kobayashi, Daryl M [Monrovia, CA

2012-06-19

An electric motor, transformer or inductor having a cooling system. A stack of laminations have apertures at least partially coincident with apertures of adjacent laminations. The apertures define straight or angled cooling-fluid passageways through the lamination stack. Gaps between the adjacent laminations are sealed by injecting a heat-cured sealant into the passageways, expelling excess sealant, and heat-curing the lamination stack. Manifold members adjoin opposite ends of the lamination stack, and each is configured with one or more cavities to act as a manifold to adjacent passageway ends. Complex manifold arrangements can create bidirectional flow in a variety of patterns.

Lamination cooling system formation method

DOEpatents

Rippel, Wally E [Altadena, CA; Kobayashi, Daryl M [Monrovia, CA

2009-05-12

An electric motor, transformer or inductor having a cooling system. A stack of laminations have apertures at least partially coincident with apertures of adjacent laminations. The apertures define straight or angled cooling-fluid passageways through the lamination stack. Gaps between the adjacent laminations are sealed by injecting a heat-cured sealant into the passageways, expelling excess sealant, and heat-curing the lamination stack. Manifold members adjoin opposite ends of the lamination stack, and each is configured with one or more cavities to act as a manifold to adjacent passageway ends. Complex manifold arrangements can create bidirectional flow in a variety of patterns.

Complex reflection groups, logarithmic connections and bi-flat F-manifolds

NASA Astrophysics Data System (ADS)

Arsie, Alessandro; Lorenzoni, Paolo

2017-10-01

We show that bi-flat F-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter groups and Veselov's ěe -systems, to the orbit spaces of exceptional well-generated complex reflection groups of rank 2 and 3. On the Veselov's ěe -systems side, we provide a generalization of the notion of ěe -systems that gives rise to a dual connection which coincides with a Dunkl-Kohno-type connection associated with such groups. In particular, this allows us to treat on the same ground several different examples including Coxeter and Shephard groups. Remarkably, as a by-product of our results, we prove that in some examples, basic flat invariants are not uniquely defined. As far as we know, such a phenomenon has never been pointed out before.

Dimensionality reduction of collective motion by principal manifolds

NASA Astrophysics Data System (ADS)

Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.

2015-01-01

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.

Note: A manifold ranking based saliency detection method for camera.

PubMed

Zhang, Libo; Sun, Yihan; Luo, Tiejian; Rahman, Mohammad Muntasir

2016-09-01

Research focused on salient object region in natural scenes has attracted a lot in computer vision and has widely been used in many applications like object detection and segmentation. However, an accurate focusing on the salient region, while taking photographs of the real-world scenery, is still a challenging task. In order to deal with the problem, this paper presents a novel approach based on human visual system, which works better with the usage of both background prior and compactness prior. In the proposed method, we eliminate the unsuitable boundary with a fixed threshold to optimize the image boundary selection which can provide more precise estimations. Then, the object detection, which is optimized with compactness prior, is obtained by ranking with background queries. Salient objects are generally grouped together into connected areas that have compact spatial distributions. The experimental results on three public datasets demonstrate that the precision and robustness of the proposed algorithm have been improved obviously.

Role of histone deacetylases in gene regulation at nuclear lamina.

PubMed

Milon, Beatrice C; Cheng, Haibo; Tselebrovsky, Mikhail V; Lavrov, Sergei A; Nenasheva, Valentina V; Mikhaleva, Elena A; Shevelyov, Yuri Y; Nurminsky, Dmitry I

2012-01-01

Theoretical models suggest that gene silencing at the nuclear periphery may involve "closing" of chromatin by transcriptional repressors, such as histone deacetylases (HDACs). Here we provide experimental evidence confirming these predictions. Histone acetylation, chromatin compactness, and gene repression in lamina-interacting multigenic chromatin domains were analyzed in Drosophila S2 cells in which B-type lamin, diverse HDACs, and lamina-associated proteins were downregulated by dsRNA. Lamin depletion resulted in decreased compactness of the repressed multigenic domain associated with its detachment from the lamina and enhanced histone acetylation. Our data reveal the major role for HDAC1 in mediating deacetylation, chromatin compaction, and gene silencing in the multigenic domain, and an auxiliary role for HDAC3 that is required for retention of the domain at the lamina. These findings demonstrate the manifold and central involvement of class I HDACs in regulation of lamina-associated genes, illuminating a mechanism by which these enzymes can orchestrate normal and pathological development.

Methodology for CFD Design Analysis of National Launch System Nozzle Manifold

NASA Technical Reports Server (NTRS)

Haire, Scot L.

1993-01-01

The current design environment dictates that high technology CFD (Computational Fluid Dynamics) analysis produce quality results in a timely manner if it is to be integrated into the design process. The design methodology outlined describes the CFD analysis of an NLS (National Launch System) nozzle film cooling manifold. The objective of the analysis was to obtain a qualitative estimate for the flow distribution within the manifold. A complex, 3D, multiple zone, structured grid was generated from a 3D CAD file of the geometry. A Euler solution was computed with a fully implicit compressible flow solver. Post processing consisted of full 3D color graphics and mass averaged performance. The result was a qualitative CFD solution that provided the design team with relevant information concerning the flow distribution in and performance characteristics of the film cooling manifold within an effective time frame. Also, this design methodology was the foundation for a quick turnaround CFD analysis of the next iteration in the manifold design.

Bearing diagnostics: A method based on differential geometry

NASA Astrophysics Data System (ADS)

Tian, Ye; Wang, Zili; Lu, Chen; Wang, Zhipeng

2016-12-01

The structures around bearings are complex, and the working environment is variable. These conditions cause the collected vibration signals to become nonlinear, non-stationary, and chaotic characteristics that make noise reduction, feature extraction, fault diagnosis, and health assessment significantly challenging. Thus, a set of differential geometry-based methods with superiorities in nonlinear analysis is presented in this study. For noise reduction, the Local Projection method is modified by both selecting the neighborhood radius based on empirical mode decomposition and determining noise subspace constrained by neighborhood distribution information. For feature extraction, Hessian locally linear embedding is introduced to acquire manifold features from the manifold topological structures, and singular values of eigenmatrices as well as several specific frequency amplitudes in spectrograms are extracted subsequently to reduce the complexity of the manifold features. For fault diagnosis, information geometry-based support vector machine is applied to classify the fault states. For health assessment, the manifold distance is employed to represent the health information; the Gaussian mixture model is utilized to calculate the confidence values, which directly reflect the health status. Case studies on Lorenz signals and vibration datasets of bearings demonstrate the effectiveness of the proposed methods.

Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators

NASA Astrophysics Data System (ADS)

Campbell, J.; Latushkin, Y.

A matrix coefficient transfer operator , on the space of -sections of an m-dimensional vector bundle over n-dimensional compact manifold is considered. The spectral radius of is estimated bya; and the essential spectral radius by Here is the set of ergodic f-invariant measures, and for is the measure-theoretic entropy of f, is the largest Lyapunov exponent of the cocycle over f generated by , and is the smallest Lyapunov exponent of the differential of f.

The Bach equations in spin-coefficient form

NASA Astrophysics Data System (ADS)

Forbes, Hamish

2018-06-01

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

Inequivalent coherent state representations in group field theory

NASA Astrophysics Data System (ADS)

Kegeles, Alexander; Oriti, Daniele; Tomlin, Casey

2018-06-01

In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.

Flux compactification of M-theory on compact manifolds with spin(7) holonomy

NASA Astrophysics Data System (ADS)

Constantin, Dragos Eugeniu

2005-11-01

At the leading order, M-theory admits minimal supersymmetric compactifications if the internal manifold has exceptional holonomy. The inclusion of non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory, which depends on the fluxes. In this work, we check the conjectured form of this superpotential in the case of warped M-theory compactifications on Spin (7) holonomy manifolds. We perform a Kaluza-Klein reduction of the eleven-dimensional supersymmetry transformation for the gravitino and we find by direct comparison the superpotential expression. We check the conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well. The conjecture can be checked indirectly by inspecting the scalar potential obtained after the compactification of M-theory on Spin (7) holonomy manifolds with non-vanishing fluxes. The scalar potential can be written in terms of the superpotential and we show that this potential stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. All the above analyses require the knowledge of the minimal supergravity action in three dimensions. Therefore we calculate the most general causal N = 1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using Ectoplasmic integration theory. We also show that the three-dimensional theory which results from the compactification is in agreement with the more general supergravity construction. The compactification procedure takes into account higher order quantum correction terms in the low energy effective action. We analyze the properties of these terms on a Spin (7) background. We derive a perturbative set of solutions which emerges from a warped compactification on a Spin (7) holonomy manifold with non-vanishing flux for the M-theory field strength and we show that in general the Ricci flatness of the internal manifold is lost, which means that the supergravity vacua are deformed away from the exceptional holonomy. Using the superpotential form we identify the supersymmetric vacua out of this general set of solutions.

Feature extraction based on semi-supervised kernel Marginal Fisher analysis and its application in bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Jiang, Li; Xuan, Jianping; Shi, Tielin

2013-12-01

Generally, the vibration signals of faulty machinery are non-stationary and nonlinear under complicated operating conditions. Therefore, it is a big challenge for machinery fault diagnosis to extract optimal features for improving classification accuracy. This paper proposes semi-supervised kernel Marginal Fisher analysis (SSKMFA) for feature extraction, which can discover the intrinsic manifold structure of dataset, and simultaneously consider the intra-class compactness and the inter-class separability. Based on SSKMFA, a novel approach to fault diagnosis is put forward and applied to fault recognition of rolling bearings. SSKMFA directly extracts the low-dimensional characteristics from the raw high-dimensional vibration signals, by exploiting the inherent manifold structure of both labeled and unlabeled samples. Subsequently, the optimal low-dimensional features are fed into the simplest K-nearest neighbor (KNN) classifier to recognize different fault categories and severities of bearings. The experimental results demonstrate that the proposed approach improves the fault recognition performance and outperforms the other four feature extraction methods.

Bianchi IX dynamics in bouncing cosmologies: homoclinic chaos and the BKL conjecture

NASA Astrophysics Data System (ADS)

Maier, Rodrigo; Damião Soares, Ivano; Valentino Tonini, Eduardo

2015-12-01

We examine the dynamics of a Bianchi IX model with three scale factors on a 4-dim Lorentzian brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. The matter content is a pressureless perfect fluid restricted to the brane, with the embedding consistently satisfying the Gauss-Codazzi equations. The 4-dim Einstein equations on the brane reduce to a 6-dim Hamiltonian dynamical system with additional terms (due to the bulk-brane interaction) that avoid the singularity and implement nonsingular bounces in the model. We examine the complex Bianchi IX dynamics in its approach to the neighborhood of the bounce which replaces the cosmological singularity of general relativity. The phase space of the model presents (i) two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, (ii) two asymptotic de Sitter critical points at infinity, one acting as an attractor to late-time acceleration and (iii) a 2-dim invariant plane, which together organize the dynamics of the phase space. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders R × S 3, where R is a saddle direction and S 3 is the center manifold of unstable periodic orbits, the latter being the nonlinear extension of the center-center sector. By a proper canonical transformation the degrees of freedom of the dynamics are separated into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom associated with the center manifold S 3. The typical dynamical flow is thus an oscillatory mode about the orbits of the invariant plane. The stable and unstable cylinders are spanned by oscillatory orbits about the separatrix towards the bounce, leading to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct simulations. The homoclinic intersection manifold has the topology of R × S 2 consisting of homoclinic orbits biasymptotic to the center manifold S 3. This behavior defines a chaotic saddle associated with S 3, indicating that the intersection points of the cylinders have the nature of a Cantor set with compact support S 2. This is an invariant signature of chaos in the model. We discuss the connection between these properties of the dynamics, namely the oscillatory approach to the bounce together with its chaotic behavior, and analogous features present in the BKL conjecture in general relativity.

Multilayer Joint Gait-Pose Manifolds for Human Gait Motion Modeling.

PubMed

Ding, Meng; Fan, Guolian

2015-11-01

We present new multilayer joint gait-pose manifolds (multilayer JGPMs) for complex human gait motion modeling, where three latent variables are defined jointly in a low-dimensional manifold to represent a variety of body configurations. Specifically, the pose variable (along the pose manifold) denotes a specific stage in a walking cycle; the gait variable (along the gait manifold) represents different walking styles; and the linear scale variable characterizes the maximum stride in a walking cycle. We discuss two kinds of topological priors for coupling the pose and gait manifolds, i.e., cylindrical and toroidal, to examine their effectiveness and suitability for motion modeling. We resort to a topologically-constrained Gaussian process (GP) latent variable model to learn the multilayer JGPMs where two new techniques are introduced to facilitate model learning under limited training data. First is training data diversification that creates a set of simulated motion data with different strides. Second is the topology-aware local learning to speed up model learning by taking advantage of the local topological structure. The experimental results on the Carnegie Mellon University motion capture data demonstrate the advantages of our proposed multilayer models over several existing GP-based motion models in terms of the overall performance of human gait motion modeling.

The Design-To-Cost Manifold

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1990-01-01

Design-to-cost is a popular technique for controlling costs. Although qualitative techniques exist for implementing design to cost, quantitative methods are sparse. In the launch vehicle and spacecraft engineering process, the question whether to minimize mass is usually an issue. The lack of quantification in this issue leads to arguments on both sides. This paper presents a mathematical technique which both quantifies the design-to-cost process and the mass/complexity issue. Parametric cost analysis generates and applies mathematical formulas called cost estimating relationships. In their most common forms, they are continuous and differentiable. This property permits the application of the mathematics of differentiable manifolds. Although the terminology sounds formidable, the application of the techniques requires only a knowledge of linear algebra and ordinary differential equations, common subjects in undergraduate scientific and engineering curricula. When the cost c is expressed as a differentiable function of n system metrics, setting the cost c to be a constant generates an n-1 dimensional subspace of the space of system metrics such that any set of metric values in that space satisfies the constant design-to-cost criterion. This space is a differentiable manifold upon which all mathematical properties of a differentiable manifold may be applied. One important property is that an easily implemented system of ordinary differential equations exists which permits optimization of any function of the system metrics, mass for example, over the design-to-cost manifold. A dual set of equations defines the directions of maximum and minimum cost change. A simplified approximation of the PRICE H(TM) production-production cost is used to generate this set of differential equations over [mass, complexity] space. The equations are solved in closed form to obtain the one dimensional design-to-cost trade and design-for-cost spaces. Preliminary results indicate that cost is relatively insensitive to changes in mass and that the reduction of complexity, both in the manufacturing process and of the spacecraft, is dominant in reducing cost.

Water pentamer: characterization of the torsional-puckering manifold by terahertz VRT spectroscopy.

PubMed

Harker, Heather A; Viant, Mark R; Keutsch, Frank N; Michael, Ernest A; McLaughlin, Ryan P; Saykally, Richard J

2005-07-28

We present the measurement and analysis of five new (D2O)5 bands via vibration-rotation-tunneling (VRT) spectroscopy as well as a preliminary description of a second (H2O)5 band. The vibrationally averaged rotational constants of all five fitted bands agree well with those from the two previously observed (D2O)5 bands and confirm that the pentamer averages to a symmetric, quasi-planar structure on the time scale of our experiment. While the spectrum of the first two bands, located at 50.7 cm(-1) (1.52 THz) and 27.3 cm(-1) (0.82 THz) are indicative of unperturbed oblate rotors, the three remaining (D2O)5 bands centered at 47.7 cm(-1) (1.43 THz), 45.4 cm(-1) (1.36 THz), and 45.0 cm(-1) (1.35 THz) are severely perturbed by first-order Coriolis coupling. This represents the first observation of this perturbation in the perdeuterated water pentamer, as well as the first observation of transitions between degenerate states of the torsional-puckering manifold. Unlike transitions from the (H2O)5 band observed by Brown et al. at 89.0 cm(-1) and the 103.8 cm(-1) band that we report here, none of the individual rovibrational transitions of any of the five (D2O)5 bands demonstrate spectral splittings due to bifurcation tunneling. We conclude, through careful analysis of these water pentamer bands, that at least three torsional-puckering manifolds have been probed and that the lowest-energy manifold is highly compacted. A plausible water pentamer torsional-puckering correlation diagram is proposed, though additional experimental data are required to unambiguously establish the energies of the torsional-puckering levels.

Nonlinear sigma models with compact hyperbolic target spaces

NASA Astrophysics Data System (ADS)

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James

2016-06-01

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

Nonlinear sigma models with compact hyperbolic target spaces

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

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in themore » O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. In conclusion, the diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.« less

Nonlinear sigma models with compact hyperbolic target spaces

DOE PAGES

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; ...

2016-06-23

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in themore » O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. In conclusion, the diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.« less

Global differential geometry: An introduction for control engineers

NASA Technical Reports Server (NTRS)

Doolin, B. F.; Martin, C. F.

1982-01-01

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Circuit-level optimisation of a:Si TFT-based AMOLED pixel circuits for maximum hold current

NASA Astrophysics Data System (ADS)

Foroughi, Aidin; Mehrpoo, Mohammadreza; Ashtiani, Shahin J.

2013-11-01

Design of AMOLED pixel circuits has manifold constraints and trade-offs which provides incentive for circuit designers to seek optimal solutions for different objectives. In this article, we present a discussion on the viability of an optimal solution to achieve the maximum hold current. A compact formula for component sizing in a conventional 2T1C pixel is, therefore, derived. Compared to SPICE simulation results, for several pixel sizes, our predicted optimum sizing yields maximum currents with errors less than 0.4%.

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

Poerschke, Andrew; Rudd, Armin

This report investigates the feasibility of using a home-run manifold small-diameter duct system to provide space-conditioning air to individual thermal zones in a low-load home. This compact layout allows duct systems to easily be brought within conditioned space via interior partition walls. Centrally locating the air handling unit in the house significantly reduces duct lengths. The plenum box is designed so that each connected duct receives a similar amount of airflow—regardless of its position on the box. Furthermore, within a reasonable set of length restrictions each duct continues to receive similar airflow.

Target space pseudoduality in supersymmetric sigma models on symmetric spaces

NASA Astrophysics Data System (ADS)

Sarisaman, Mustafa

We discuss the target space pseudoduality in supersymmetric sigma models on symmetric spaces. We first consider the case where sigma models based on real compact connected Lie groups of the same dimensionality and give examples using three dimensional models on target spaces. We show explicit construction of nonlocal conserved currents on the pseudodual manifold. We then switch the Lie group valued pseudoduality equations to Lie algebra valued ones, which leads to an infinite number of pseudoduality equations. We obtain an infinite number of conserved currents on the tangent bundle of the pseudo-dual manifold. Since pseudoduality imposes the condition that sigma models pseudodual to each other are based on symmetric spaces with opposite curvatures (i.e. dual symmetric spaces), we investigate pseudoduality transformation on the symmetric space sigma models in the third chapter. We see that there can be mixing of decomposed spaces with each other, which leads to mixings of the following expressions. We obtain the pseudodual conserved currents which are viewed as the orthonormal frame on the pullback bundle of the tangent space of G˜ which is the Lie group on which the pseudodual model based. Hence we obtain the mixing forms of curvature relations and one loop renormalization group beta function by means of these currents. In chapter four, we generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold M and by orthonormal coframe method on manifold SO( M). The component method produces the result that pseudoduality transformation is not invertible at all points and occurs from all points on one manifold to only one point where riemann normal coordinates valid on the second manifold. Torsion of the sigma model on M must vanish while it is nonvanishing on M˜, and curvatures of the manifolds must be constant and the same because of anticommuting grassmann numbers. We obtain the similar results with the classical case in orthonormal coframe method. In case of super WZW sigma models pseudoduality equations result in three different pseudoduality conditions; flat space, chiral and antichiral pseudoduality. Finally we study the pseudoduality transformations on symmetric spaces using two different methods again. These two methods yield similar results to the classical cases with the exception that commuting bracket relations in classical case turns out to be anticommuting ones because of the appearance of grassmann numbers. It is understood that constraint relations in case of non-mixing pseudoduality are the remnants of mixing pseudoduality. Once mixing terms are included in the pseudoduality the constraint relations disappear.

New dimensions for wound strings: The modular transformation of geometry to topology

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

McGreevy, John; Silverstein, Eva; Starr, David

2007-02-15

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in E. Silverstein, Phys. Rev. D 73, 086004 (2006).. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponential growth of its fundamental group, which translates in string theory to a higher effective central charge arising from winding strings. This exponential density of winding modes is related by modular invariance to the infrared small perturbation spectrum. Using self-consistent approximations valid at large radius, we analyze this correspondencemore » explicitly in a broad set of time-dependent solutions, finding precise agreement between the effective central charge and the corresponding infrared small perturbation spectrum. This indicates a basic relation between geometry, topology, and dimensionality in string theory.« less

Hidden symmetries on Kerr-NUT-(A)dS metrics of Einstein-Sasaki type

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2013-01-01

The hidden symmetries of higher dimensional Euclideanised Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. As a concrete example we present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

{\\ {PT}}-symmetric models in curved manifolds

NASA Astrophysics Data System (ADS)

Krejčiřík, David; Siegl, Petr

2010-12-01

We consider the Laplace-Beltrami operator in tubular neighborhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.

Comparison of Space Shuttle Hot Gas Manifold analysis to air flow data

NASA Technical Reports Server (NTRS)

Mcconnaughey, P. K.

1988-01-01

This paper summarizes several recent analyses of the Space Shuttle Main Engine Hot Gas Manifold and compares predicted flow environments to air flow data. Codes used in these analyses include INS3D, PAGE, PHOENICS, and VAST. Both laminar (Re = 250, M = 0.30) and turbulent (Re = 1.9 million, M = 0.30) results are discussed, with the latter being compared to data for system losses, outer wall static pressures, and manifold exit Mach number profiles. Comparison of predicted results for the turbulent case to air flow data shows that the analysis using INS3D predicted system losses within 1 percent error, while the PHOENICS, PAGE, and VAST codes erred by 31, 35, and 47 percent, respectively. The INS3D, PHOENICS, and PAGE codes did a reasonable job of predicting outer wall static pressure, while the PHOENICS code predicted exit Mach number profiles with acceptable accuracy. INS3D was approximately an order of magnitude more efficient than the other codes in terms of code speed and memory requirements. In general, it is seen that complex internal flows in manifold-like geometries can be predicted with a limited degree of confidence, and further development is necessary to improve both efficiency and accuracy of codes if they are to be used as design tools for complex three-dimensional geometries.

Lamination cooling system

DOEpatents

Rippel, Wally E.; Kobayashi, Daryl M.

2005-10-11

An electric motor, transformer or inductor having a lamination cooling system including a stack of laminations, each defining a plurality of apertures at least partially coincident with apertures of adjacent laminations. The apertures define a plurality of cooling-fluid passageways through the lamination stack, and gaps between the adjacent laminations are sealed to prevent a liquid cooling fluid in the passageways from escaping between the laminations. The gaps are sealed by injecting a heat-cured sealant into the passageways, expelling excess sealant, and heat-curing the lamination stack. The apertures of each lamination can be coincident with the same-sized apertures of adjacent laminations to form straight passageways, or they can vary in size, shape and/or position to form non-axial passageways, angled passageways, bidirectional passageways, and manifold sections of passageways that connect a plurality of different passageway sections. Manifold members adjoin opposite ends of the lamination stack, and each is configured with one or more cavities to act as a manifold to adjacent passageway ends. Complex manifold arrangements can create bidirectional flow in a variety of patterns.

Exotic differentiable structures and general relativity

NASA Astrophysics Data System (ADS)

Brans, Carl H.; Randall, Duane

1993-02-01

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (“fake” or “exotic”) differentiable structures on topologically simple manifolds such asS 7, ℝ4 andS 3 X ℝ1. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.

Wave maps from Gödel's universe

NASA Astrophysics Data System (ADS)

Barletta, Elisabetta; Dragomir, Sorin; Magliaro, Marco

2014-10-01

Using a result by Koch (1988 Trans. Am. Math. Soc. 307 827-41) we realize Gödel's universe G_{α }^{4}=({{{R}}^{4}},{{g}_{α}}) as the total space of a principal {R}-bundle over a strictly pseudo-convex CR manifold M3 and exploit the analogy between {{g}_{Yalpha;}} and Fefferman's metric {{F}_{θ}} (Fefferman 1976 Ann. Math. 103 395-416 104 393-4) to show that for any {R}-invariant wave map Φ of G_{α}^{4} into a Riemannian manifold N, the corresponding base map φ :{{M}^{3}}\\to N is subelliptic harmonic, with respect to a canonical choice of contact form θ on M3. We show that the subelliptic Jacobi operator J_{b}^{φ} of ϕ has a discrete Dirichlet spectrum on any bounded domain D\\subset {{M}^{3}} supporting the Poincaré inequality on \\mathop{W}\\limits^{\\circ }{}_{H}^{1,2}(D,{{φ}^{-1}}TN) and Kondrakov compactness, i.e. compactness of the embedding \\mathop{W}\\limits^{\\circ }{}_{H}^{1,2}(D,{{φ }^{-1}}TN)\\hookrightarrow {{L}^{2}}(D,{{φ}^{-1}}TN). We exhibit an explicit solution π :G_{α}^{4}\\to {{M}^{3}} to the wave map system on G_{α}^{4}, of index in{{d}^{Ω}}(π)\\geqslant 1 for any bounded domain Ω \\subset G_{α}^{4}. Mounoud's distance (Mounoud 2001 Differ. Geom. Appl. 15 47-57) d_{{{G}_{0}}, Ω }^{∞}({{g}_{α }}, {{F}_{θ}}) is bounded below by a constant depending only on the rotation frequency of Gödel's universe, thus giving a measure of the bias of {{g}_{α}} from being Fefferman like in the region Ω \\subset {{{R}}^{4}}.

Saddle Slow Manifolds and Canard Orbits in [Formula: see text] and Application to the Full Hodgkin-Huxley Model.

PubMed

Hasan, Cris R; Krauskopf, Bernd; Osinga, Hinke M

2018-04-19

Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin-Huxley model is well known for explaining the ionic mechanism that generates the action potential in the squid giant axon. Rubin and Wechselberger (Biol. Cybern. 97:5-32, 2007) nondimensionalized this model and obtained a singularly perturbed system with two fast, two slow variables, and an explicit time-scale ratio ε. The dynamics of this system are complex and feature periodic orbits with a series of action potentials separated by small-amplitude oscillations (SAOs); also referred to as mixed-mode oscillations (MMOs). The slow dynamics of this system are organized by two-dimensional locally invariant manifolds called slow manifolds which can be either attracting or of saddle type.In this paper, we introduce a general approach for computing two-dimensional saddle slow manifolds and their stable and unstable fast manifolds. We also develop a technique for detecting and continuing associated canard orbits, which arise from the interaction between attracting and saddle slow manifolds, and provide a mechanism for the organization of SAOs in [Formula: see text]. We first test our approach with an extended four-dimensional normal form of a folded node. Our results demonstrate that our computations give reliable approximations of slow manifolds and canard orbits of this model. Our computational approach is then utilized to investigate the role of saddle slow manifolds and associated canard orbits of the full Hodgkin-Huxley model in organizing MMOs and determining the firing rates of action potentials. For ε sufficiently large, canard orbits are arranged in pairs of twin canard orbits with the same number of SAOs. We illustrate how twin canard orbits partition the attracting slow manifold into a number of ribbons that play the role of sectors of rotations. The upshot is that we are able to unravel the geometry of slow manifolds and associated canard orbits without the need to reduce the model.

Kernel Manifold Alignment for Domain Adaptation.

PubMed

Tuia, Devis; Camps-Valls, Gustau

2016-01-01

The wealth of sensory data coming from different modalities has opened numerous opportunities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. However, multimodal architectures must rely on models able to adapt to changes in the data distribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation problem as domain adaptation. In this paper, instead of adapting the trained models themselves, we alternatively focus on finding mappings of the data sources into a common, semantically meaningful, representation domain. This field of manifold alignment extends traditional techniques in statistics such as canonical correlation analysis (CCA) to deal with nonlinear adaptation and possibly non-corresponding data pairs between the domains. We introduce a kernel method for manifold alignment (KEMA) that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a discriminative alignment preserving each manifold inner structure, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible, which allows transfer across-domains and data synthesis. To authors' knowledge this is the first method addressing all these important issues at once. We also present a reduced-rank version of KEMA for computational efficiency, and discuss the generalization performance of KEMA under Rademacher principles of stability. Aligning multimodal data with KEMA reports outstanding benefits when used as a data pre-conditioner step in the standard data analysis processing chain. KEMA exhibits very good performance over competing methods in synthetic controlled examples, visual object recognition and recognition of facial expressions tasks. KEMA is especially well-suited to deal with high-dimensional problems, such as images and videos, and under complicated distortions, twists and warpings of the data manifolds. A fully functional toolbox is available at https://github.com/dtuia/KEMA.git.

Refined 3d-3d correspondence

NASA Astrophysics Data System (ADS)

Alday, Luis F.; Genolini, Pietro Benetti; Bullimore, Mathew; van Loon, Mark

2017-04-01

We explore aspects of the correspondence between Seifert 3-manifolds and 3d N = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N = 2 theories constructed from boundary conditions and interfaces in a 4d N = 2∗ theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d N = 2∗ theory. In the presence of a mass parameter cfor the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.

An intelligent fault diagnosis method of rolling bearings based on regularized kernel Marginal Fisher analysis

NASA Astrophysics Data System (ADS)

Jiang, Li; Shi, Tielin; Xuan, Jianping

2012-05-01

Generally, the vibration signals of fault bearings are non-stationary and highly nonlinear under complicated operating conditions. Thus, it's a big challenge to extract optimal features for improving classification and simultaneously decreasing feature dimension. Kernel Marginal Fisher analysis (KMFA) is a novel supervised manifold learning algorithm for feature extraction and dimensionality reduction. In order to avoid the small sample size problem in KMFA, we propose regularized KMFA (RKMFA). A simple and efficient intelligent fault diagnosis method based on RKMFA is put forward and applied to fault recognition of rolling bearings. So as to directly excavate nonlinear features from the original high-dimensional vibration signals, RKMFA constructs two graphs describing the intra-class compactness and the inter-class separability, by combining traditional manifold learning algorithm with fisher criteria. Therefore, the optimal low-dimensional features are obtained for better classification and finally fed into the simplest K-nearest neighbor (KNN) classifier to recognize different fault categories of bearings. The experimental results demonstrate that the proposed approach improves the fault classification performance and outperforms the other conventional approaches.

On the approximation of Lyapunov exponents and a question suggested by Anatole Katok

NASA Astrophysics Data System (ADS)

Dai, Xiongping

2010-03-01

Let \\mathcal {F}\\colon X\\times\\mathbb{Z}_+\\rightarrow \\rm{GL}(n,\\mathbb{R}) be a Hölder-continuous linear cocycle whose driving semiflow f\\colon X\\times\\mathbb{Z}_+\\rightarrow X preserves a probability μ on a compact metric space X. Using the concept of two-sided quasi-Pesin orbits introduced in this paper, we show that the Lyapunov characteristic spectrum of μ can be approached arbitrarily by that of periodic points of f. So, if all periodic points of f have only positive Lyapunov exponents and such exponents are uniformly bounded away from zero, then μ also has only positive exponents. In our arguments, the exponential closing property of the driving semiflow is a basic condition, and it is easy to check that every C1-expanding map of a closed manifold obeys this closing property. Consequently, if f is a C1+Hölder local diffeomorphism of a closed manifold and if it is Hölder conjugated to some C1-expanding map, then f is itself expanding. This gives a positive answer to a question suggested by Anatole Katok.

Foliated eight-manifolds for M-theory compactification

NASA Astrophysics Data System (ADS)

Babalic, Elena Mirela; Lazaroiu, Calin Iuliu

2015-01-01

We characterize compact eight-manifolds M which arise as internal spaces in flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part ξ of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation of M which carries a leafwise G 2 structure, such that the O'Neill-Gray tensors, non-adapted part of the normal connection and the torsion classes of the G 2 structure are given in terms of the supergravity four-form field strength by explicit formulas which we derive. We discuss the topology of such foliations, showing that the C * algebra is a noncommutative torus of dimension given by the irrationality rank of a certain cohomology class constructed from G, which must satisfy the Latour obstruction. We also give a criterion in terms of this class for when such foliations are fibrations over the circle. When the criterion is not satisfied, each leaf of is dense in M.

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.

Wave computation on the Poincaré dodecahedral space

NASA Astrophysics Data System (ADS)

Bachelot-Motet, Agnès

2013-12-01

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non-trivial topology: the Poincaré dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace-Beltrami operator.

Dual-phase reactor plant with partitioned isolation condenser

DOEpatents

Hui, Marvin M.

1992-01-01

A nuclear energy plant housing a boiling-water reactor utilizes an isolation condenser in which a single chamber is partitioned into a distributor plenum and a collector plenum. Steam accumulates in the distributor plenum and is conveyed to the collector plenum through an annular manifold that includes tubes extending through a condenser pool. The tubes provide for a transfer of heat from the steam, forming a condensate. The chamber has a disk-shaped base, a cylindrical sidewall, and a semispherical top. This geometry results in a compact design that exhibits significant performance and cost advantages over prior designs.

Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.

PubMed

Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof

2018-01-01

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Transition Manifolds of Complex Metastable Systems

NASA Astrophysics Data System (ADS)

Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof

2018-04-01

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Reading off the nongeometric scalar potentials via the topological data of the compactifying Calabi-Yau manifolds

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2016-10-01

In the context of studying the 4D-effective potentials of type IIB nongeometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level nongeometric scalar potential arising from a flux superpotential which includes the S-dual pairs of nongeometric fluxes (Q , P ), the standard NS-NS and RR three-form fluxes (F3 , H3 ), and the geometric flux (ω ). This "symplectic formulation" is valid for arbitrary numbers of Kähler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as Hodge numbers and the triple-intersection numbers) of the compactifying threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kähler and superpotentials.

Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations

NASA Astrophysics Data System (ADS)

Giovanis, D. G.; Shields, M. D.

2018-07-01

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an adaptive stochastic simulation-based methodology is introduced that refines the probability space based on Grassmann manifold variations. The proposed method has a multi-element character discretizing the probability space into simplex elements using a Delaunay triangulation. For every simplex, the high-dimensional solutions corresponding to its vertices (sample points) are projected onto the Grassmann manifold. The pairwise distances between these points are calculated using appropriately defined metrics and the elements with large total distance are sub-sampled and refined. As a result, regions of the probability space that produce significant changes in the full-field solution are accurately resolved. An added benefit is that an approximation of the solution within each element can be obtained by interpolation on the Grassmann manifold. The method is applied to study the probability of shear band formation in a bulk metallic glass using the shear transformation zone theory.

Improving CNN Performance Accuracies With Min-Max Objective.

PubMed

Shi, Weiwei; Gong, Yihong; Tao, Xiaoyu; Wang, Jinjun; Zheng, Nanning

2017-06-09

We propose a novel method for improving performance accuracies of convolutional neural network (CNN) without the need to increase the network complexity. We accomplish the goal by applying the proposed Min-Max objective to a layer below the output layer of a CNN model in the course of training. The Min-Max objective explicitly ensures that the feature maps learned by a CNN model have the minimum within-manifold distance for each object manifold and the maximum between-manifold distances among different object manifolds. The Min-Max objective is general and able to be applied to different CNNs with insignificant increases in computation cost. Moreover, an incremental minibatch training procedure is also proposed in conjunction with the Min-Max objective to enable the handling of large-scale training data. Comprehensive experimental evaluations on several benchmark data sets with both the image classification and face verification tasks reveal that employing the proposed Min-Max objective in the training process can remarkably improve performance accuracies of a CNN model in comparison with the same model trained without using this objective.

Structural maintenance of chromosome complexes differentially compact mitotic chromosomes according to genomic context

PubMed Central

Schalbetter, S. A.; Goloborodko, A.; Fudenberg, G.; Belton, J.-M.; Miles, C.; Yu, M.; Dekker, J.; Mirny, L.; Baxter, J.

2017-01-01

Structural Maintenance of Chromosomes (SMC) protein complexes are key determinants of chromosome conformation. Using Hi-C and polymer modeling, we study how cohesin and condensin, two deeply conserved SMC complexes, organize chromosomes in the budding yeast Saccharomyces cerevisiae. The canonical role of cohesin is to co-align sister chromatids whilst condensin generally compacts mitotic chromosomes. We find strikingly different roles for the two complexes in budding yeast mitosis. First, cohesin is responsible for compacting mitotic chromosome arms, independently of sister chromatid cohesion. Polymer simulations demonstrate this role can be fully accounted for through cis-looping of chromatin. Second, condensin is generally dispensable for compaction along chromosome arms. Instead it plays a targeted role compacting the rDNA proximal regions and promoting resolution of peri-centromeric regions. Our results argue that the conserved mechanism of SMC complexes is to form chromatin loops and that distinct SMC-dependent looping activities are selectively deployed to appropriately compact chromosomes. PMID:28825700

Blanket activation and afterheat for the Compact Reversed-Field Pinch Reactor

NASA Astrophysics Data System (ADS)

Davidson, J. W.; Battat, M. E.

A detailed assessment has been made of the activation and afterheat for a Compact Reversed-Field Pinch Reactor (CRFPR) blanket using a two-dimensional model that included the limiter, the vacuum ducts, and the manifolds and headers for cooling the limiter and the first and second walls. Region-averaged, multigroup fluxes and prompt gamma-ray/neutron heating rates were calculated using the two-dimensional, discrete-ordinates code TRISM. Activation and depletion calculations were performed with the code FORIG using one-group cross sections generated with the TRISM region-averaged fluxes. Afterheat calculations were performed for regions near the plasma, i.e., the limiter, first wall, etc. assuming a 10-day irradiation. Decay heats were computed for decay periods up to 100 minutes. For the activation calculations, the irradiation period was taken to be one year and blanket activity inventories were computed for decay times to 4 x 10 years. These activities were also calculated as the toxicity-weighted biological hazard potential (BHP).

Decoding Lifespan Changes of the Human Brain Using Resting-State Functional Connectivity MRI

PubMed Central

Wang, Lubin; Su, Longfei; Shen, Hui; Hu, Dewen

2012-01-01

The development of large-scale functional brain networks is a complex, lifelong process that can be investigated using resting-state functional connectivity MRI (rs-fcMRI). In this study, we aimed to decode the developmental dynamics of the whole-brain functional network in seven decades (8–79 years) of the human lifespan. We first used parametric curve fitting to examine linear and nonlinear age effect on the resting human brain, and then combined manifold learning and support vector machine methods to predict individuals' “brain ages” from rs-fcMRI data. We found that age-related changes in interregional functional connectivity exhibited spatially and temporally specific patterns. During brain development from childhood to senescence, functional connections tended to linearly increase in the emotion system and decrease in the sensorimotor system; while quadratic trajectories were observed in functional connections related to higher-order cognitive functions. The complex patterns of age effect on the whole-brain functional network could be effectively represented by a low-dimensional, nonlinear manifold embedded in the functional connectivity space, which uncovered the inherent structure of brain maturation and aging. Regression of manifold coordinates with age further showed that the manifold representation extracted sufficient information from rs-fcMRI data to make prediction about individual brains' functional development levels. Our study not only gives insights into the neural substrates that underlie behavioral and cognitive changes over age, but also provides a possible way to quantitatively describe the typical and atypical developmental progression of human brain function using rs-fcMRI. PMID:22952990

Decoding lifespan changes of the human brain using resting-state functional connectivity MRI.

PubMed

Wang, Lubin; Su, Longfei; Shen, Hui; Hu, Dewen

2012-01-01

The development of large-scale functional brain networks is a complex, lifelong process that can be investigated using resting-state functional connectivity MRI (rs-fcMRI). In this study, we aimed to decode the developmental dynamics of the whole-brain functional network in seven decades (8-79 years) of the human lifespan. We first used parametric curve fitting to examine linear and nonlinear age effect on the resting human brain, and then combined manifold learning and support vector machine methods to predict individuals' "brain ages" from rs-fcMRI data. We found that age-related changes in interregional functional connectivity exhibited spatially and temporally specific patterns. During brain development from childhood to senescence, functional connections tended to linearly increase in the emotion system and decrease in the sensorimotor system; while quadratic trajectories were observed in functional connections related to higher-order cognitive functions. The complex patterns of age effect on the whole-brain functional network could be effectively represented by a low-dimensional, nonlinear manifold embedded in the functional connectivity space, which uncovered the inherent structure of brain maturation and aging. Regression of manifold coordinates with age further showed that the manifold representation extracted sufficient information from rs-fcMRI data to make prediction about individual brains' functional development levels. Our study not only gives insights into the neural substrates that underlie behavioral and cognitive changes over age, but also provides a possible way to quantitatively describe the typical and atypical developmental progression of human brain function using rs-fcMRI.

Automated Simplification of Full Chemical Mechanisms

NASA Technical Reports Server (NTRS)

Norris, A. T.

1997-01-01

A code has been developed to automatically simplify full chemical mechanisms. The method employed is based on the Intrinsic Low Dimensional Manifold (ILDM) method of Maas and Pope. The ILDM method is a dynamical systems approach to the simplification of large chemical kinetic mechanisms. By identifying low-dimensional attracting manifolds, the method allows complex full mechanisms to be parameterized by just a few variables; in effect, generating reduced chemical mechanisms by an automatic procedure. These resulting mechanisms however, still retain all the species used in the full mechanism. Full and skeletal mechanisms for various fuels are simplified to a two dimensional manifold, and the resulting mechanisms are found to compare well with the full mechanisms, and show significant improvement over global one step mechanisms, such as those by Westbrook and Dryer. In addition, by using an ILDM reaction mechanism in a CID code, a considerable improvement in turn-around time can be achieved.

Numerical simulation of flow path in the oxidizer side hot gas manifold of the Space Shuttle main engine

NASA Technical Reports Server (NTRS)

Lin, S. J.; Yang, R. J.; Chang, James L. C.; Kwak, D.

1987-01-01

The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside the oxidizer side Hot Gas Manifold of the Space Shuttle Main Engine. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is developed to overcome the complexity of the geometry. In the present study, the laminar and turbulent flows in the oxidizer side Hot Gas Manifold have been computed. The study reveals that: (1) there exists large recirculation zones inside the bowl if no vanes are present; (2) strong secondary flows are observed in the transfer tube; and (3) properly shaped and positioned guide vanes are effective in eliminating flow separation.

Nickel-catalyzed cross-coupling of photoredox-generated radicals: uncovering a general manifold for stereoconvergence in nickel-catalyzed cross-couplings.

PubMed

Gutierrez, Osvaldo; Tellis, John C; Primer, David N; Molander, Gary A; Kozlowski, Marisa C

2015-04-22

The cross-coupling of sp(3)-hybridized organoboron reagents via photoredox/nickel dual catalysis represents a new paradigm of reactivity for engaging alkylmetallic reagents in transition-metal-catalyzed processes. Reported here is an investigation into the mechanistic details of this important transformation using density functional theory. Calculations bring to light a new reaction pathway involving an alkylnickel(I) complex generated by addition of an alkyl radical to Ni(0) that is likely to operate simultaneously with the previously proposed mechanism. Analysis of the enantioselective variant of the transformation reveals an unexpected manifold for stereoinduction involving dynamic kinetic resolution (DKR) of a Ni(III) intermediate wherein the stereodetermining step is reductive elimination. Furthermore, calculations suggest that the DKR-based stereoinduction manifold may be responsible for stereoselectivity observed in numerous other stereoconvergent Ni-catalyzed cross-couplings and reductive couplings.

LETTER TO THE EDITOR: Anti-self-dual Riemannian metrics without Killing vectors: can they be realized on K3?

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2003-11-01

Explicit Riemannian metrics with Euclidean signature and anti-self-dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogeneous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coordinates and parameters it can be the metric on a compact manifold. Then, by the theorem of Hitchin, it could be a class of metrics on K3, or on surfaces whose universal covering is K3.

Self-dual geometry of generalized Hermitian surfaces

NASA Astrophysics Data System (ADS)

Arsen'eva, O. E.; Kirichenko, V. F.

1998-02-01

Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces.

The model for self-dual chiral bosons as a Hodge theory

NASA Astrophysics Data System (ADS)

Upadhyay, Sudhaker; Mandal, Bhabani Prasad

2011-09-01

We consider (1+1) dimensional theory for a single self-dual chiral boson as a classical model for gauge theory. Using the Batalin-Fradkin-Vilkovisky (BFV) technique, the nilpotent BRST and anti-BRST symmetry transformations for this theory have been studied. In this model other forms of nilpotent symmetry transformations like co-BRST and anti-co-BRST, which leave the gauge-fixing part of the action invariant, are also explored. We show that the nilpotent charges for these symmetry transformations satisfy the algebra of the de Rham cohomological operators in differential geometry. The Hodge decomposition theorem on compact manifold is also studied in the context of conserved charges.

Gauged BPS baby Skyrmions with quantized magnetic flux

NASA Astrophysics Data System (ADS)

Adam, C.; Wereszczynski, A.

2017-06-01

A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of 2 π , which allows, in principle, to define this theory on a compact manifold without boundary, unlike all gauged baby Skyrme models considered so far.

Total Mean Curvature, Scalar Curvature, and a Variational Analog of Brown-York Mass

NASA Astrophysics Data System (ADS)

Mantoulidis, Christos; Miao, Pengzi

2017-06-01

We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric. We establish an additivity property for this supremum and exhibit rigidity for maximizers assuming the supremum is attained. When the boundary consists of 2-spheres, we demonstrate that the finiteness of the supremum follows from the previous work of Shi-Tam and Wang-Yau on the quasi-local mass problem in general relativity. In turn, we define a variational analog of Brown-York quasi-local mass without assuming that the boundary 2-sphere has positive Gauss curvature.

Multi-leg heat pipe evaporator

NASA Technical Reports Server (NTRS)

Alario, J. P.; Haslett, R. A. (Inventor)

1986-01-01

A multileg heat pipe evaporator facilitates the use and application of a monogroove heat pipe by providing an evaporation section which is compact in area and structurally more compatible with certain heat exchangers or heat input apparatus. The evaporation section of a monogroove heat pipe is formed by a series of parallel legs having a liquid and a vapor channel and a communicating capillary slot therebetween. The liquid and vapor channels and interconnecting capillary slots of the evaporating section are connected to the condensing section of the heat pipe by a manifold connecting liquid and vapor channels of the parallel evaporation section legs with the corresponding liquid and vapor channels of the condensing section.

Everyday Matters in Science and Mathematics: Studies of Complex Classroom Events

ERIC Educational Resources Information Center

Nemirovsky, Ricardo, Ed.; Rosebery, Ann S., Ed.; Solomon, Jesse, Ed.; Warren, Beth, Ed.

2005-01-01

This book re-examines the dichotomy between the everyday and the disciplinary in mathematics and science education, and explores alternatives to this opposition from points of view grounded in the close examination of complex classroom events. It makes the case that students' everyday experience and knowledge in their entire manifold forms matter…

Tunnelling with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Gibbons, G. W.

1996-02-01

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.

Direct biomechanical modeling of trabecular bone using a nonlinear manifold-based volumetric representation

NASA Astrophysics Data System (ADS)

Jin, Dakai; Lu, Jia; Zhang, Xiaoliu; Chen, Cheng; Bai, ErWei; Saha, Punam K.

2017-03-01

Osteoporosis is associated with increased fracture risk. Recent advancement in the area of in vivo imaging allows segmentation of trabecular bone (TB) microstructures, which is a known key determinant of bone strength and fracture risk. An accurate biomechanical modelling of TB micro-architecture provides a comprehensive summary measure of bone strength and fracture risk. In this paper, a new direct TB biomechanical modelling method using nonlinear manifold-based volumetric reconstruction of trabecular network is presented. It is accomplished in two sequential modules. The first module reconstructs a nonlinear manifold-based volumetric representation of TB networks from three-dimensional digital images. Specifically, it starts with the fuzzy digital segmentation of a TB network, and computes its surface and curve skeletons. An individual trabecula is identified as a topological segment in the curve skeleton. Using geometric analysis, smoothing and optimization techniques, the algorithm generates smooth, curved, and continuous representations of individual trabeculae glued at their junctions. Also, the method generates a geometrically consistent TB volume at junctions. In the second module, a direct computational biomechanical stress-strain analysis is applied on the reconstructed TB volume to predict mechanical measures. The accuracy of the method was examined using micro-CT imaging of cadaveric distal tibia specimens (N = 12). A high linear correlation (r = 0.95) between TB volume computed using the new manifold-modelling algorithm and that directly derived from the voxel-based micro-CT images was observed. Young's modulus (YM) was computed using direct mechanical analysis on the TB manifold-model over a cubical volume of interest (VOI), and its correlation with the YM, computed using micro-CT based conventional finite-element analysis over the same VOI, was examined. A moderate linear correlation (r = 0.77) was observed between the two YM measures. This preliminary results show the accuracy of the new nonlinear manifold modelling algorithm for TB, and demonstrate the feasibility of a new direct mechanical strain-strain analysis on a nonlinear manifold model of a highly complex biological structure.

3D GIS spatial operation based on extended Euler operators

NASA Astrophysics Data System (ADS)

Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing

2008-10-01

The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.

M-Isomap: Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction.

PubMed

Zhang, Zhao; Chow, Tommy W S; Zhao, Mingbo

2013-02-01

Isomap is a well-known nonlinear dimensionality reduction (DR) method, aiming at preserving geodesic distances of all similarity pairs for delivering highly nonlinear manifolds. Isomap is efficient in visualizing synthetic data sets, but it usually delivers unsatisfactory results in benchmark cases. This paper incorporates the pairwise constraints into Isomap and proposes a marginal Isomap (M-Isomap) for manifold learning. The pairwise Cannot-Link and Must-Link constraints are used to specify the types of neighborhoods. M-Isomap computes the shortest path distances over constrained neighborhood graphs and guides the nonlinear DR through separating the interclass neighbors. As a result, large margins between both interand intraclass clusters are delivered and enhanced compactness of intracluster points is achieved at the same time. The validity of M-Isomap is examined by extensive simulations over synthetic, University of California, Irvine, and benchmark real Olivetti Research Library, YALE, and CMU Pose, Illumination, and Expression databases. The data visualization and clustering power of M-Isomap are compared with those of six related DR methods. The visualization results show that M-Isomap is able to deliver more separate clusters. Clustering evaluations also demonstrate that M-Isomap delivers comparable or even better results than some state-of-the-art DR algorithms.

Magnetohydrodynamic pressure drop and flow balancing of liquid metal flow in a prototypic fusion blanket manifold

NASA Astrophysics Data System (ADS)

Rhodes, Tyler J.; Smolentsev, Sergey; Abdou, Mohamed

2018-05-01

Understanding magnetohydrodynamic (MHD) phenomena associated with the flow of electrically conducting fluids in complex geometry ducts subject to a strong magnetic field is required to effectively design liquid metal (LM) blankets for fusion reactors. Particularly, accurately predicting the 3D MHD pressure drop and flow distribution is important. To investigate these topics, we simulate a LM MHD flow through an electrically non-conducting prototypic manifold for a wide range of flow and geometry parameters using a 3D MHD solver, HyPerComp incompressible MHD solver for arbitrary geometry. The reference manifold geometry consists of a rectangular feeding duct which suddenly expands such that the duct thickness in the magnetic field direction abruptly increases by a factor rexp. Downstream of the sudden expansion, the LM is distributed into several parallel channels. As a first step in qualifying the flow, a magnitude of the curl of the induced Lorentz force was used to distinguish between inviscid, irrotational core flows and boundary and internal shear layers where inertia and/or viscous forces are important. Scaling laws have been obtained which characterize the 3D MHD pressure drop and flow balancing as a function of the flow parameters and the manifold geometry. Associated Hartmann and Reynolds numbers in the computations were ˜103 and ˜101-103, respectively, while rexp was varied from 4 to 12. An accurate model for the pressure drop was developed for the first time for inertial-electromagnetic and viscous-electromagnetic regimes based on 96 computed cases. Analysis shows that flow balance can be improved by lengthening the distance between the manifold inlet and the entrances of the parallel channels by utilizing the effect of flow transitioning to a quasi-two-dimensional state in the expansion region of the manifold.

Energy minimization on manifolds for docking flexible molecules

PubMed Central

Mirzaei, Hanieh; Zarbafian, Shahrooz; Villar, Elizabeth; Mottarella, Scott; Beglov, Dmitri; Vajda, Sandor; Paschalidis, Ioannis Ch.; Vakili, Pirooz; Kozakov, Dima

2015-01-01

In this paper we extend a recently introduced rigid body minimization algorithm, defined on manifolds, to the problem of minimizing the energy of interacting flexible molecules. The goal is to integrate moving the ligand in six dimensional rotational/translational space with internal rotations around rotatable bonds within the two molecules. We show that adding rotational degrees of freedom to the rigid moves of the ligand results in an overall optimization search space that is a manifold to which our manifold optimization approach can be extended. The effectiveness of the method is shown for three different docking problems of increasing complexity. First we minimize the energy of fragment-size ligands with a single rotatable bond as part of a protein mapping method developed for the identification of binding hot spots. Second, we consider energy minimization for docking a flexible ligand to a rigid protein receptor, an approach frequently used in existing methods. In the third problem we account for flexibility in both the ligand and the receptor. Results show that minimization using the manifold optimization algorithm is substantially more efficient than minimization using a traditional all-atom optimization algorithm while producing solutions of comparable quality. In addition to the specific problems considered, the method is general enough to be used in a large class of applications such as docking multidomain proteins with flexible hinges. The code is available under open source license (at http://cluspro.bu.edu/Code/Code_Rigtree.tar), and with minimal effort can be incorporated into any molecular modeling package. PMID:26478722

Symplectic homoclinic tangles of the ideal separatrix of the DIII-D from type I ELMs

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima

2012-10-01

The ideal separatrix of the divertor tokamaks is a degenerate manifold where both the stable and unstable manifolds coincide. Non-axisymmetric magnetic perturbations remove the degeneracy; and split the separatrix manifold. This creates an extremely complex topological structure, called homoclinic tangles. The unstable manifold intersects the stable manifold and creates alternating inner and outer lobes at successive homoclinic points. The Hamiltonian system must preserve the symplectic topological invariance, and this controls the size and radial extent of the lobes. Very recently, lobes near the X-point have been experimentally observed in MAST [A. Kirk et al, PRL 108, 255003 (2012)]. We have used the DIII-D map [A. Punjabi, NF 49, 115020 (2009)] to calculate symplectic homoclinic tangles of the ideal separatrix of the DIII-D from the type I ELMs represented by the peeling-ballooning modes (m,n)=(30,10)+(40,10). The DIII-D map is symplectic, accurate, and is in natural canonical coordinates which are invertible to physical coordinates [A. Punjabi and H. Ali, POP 15, 122502 (2008)]. To our knowledge, we are the first to symplectically calculate these tangles in physical space. Homoclinic tangles of separatrix can cause radial displacement of mobile passing electrons and create sheared radial electric fields and currents, resulting in radial flows, drifts, differential spinning, and reduction in turbulence, and other effects. This work is supported by the grants DE-FG02-01ER54624 and DE-FG02-04ER54793.

A unified approach to χ2 discriminators for searches of gravitational waves from compact binary coalescences

NASA Astrophysics Data System (ADS)

Dhurandhar, Sanjeev; Gupta, Anuradha; Gadre, Bhooshan; Bose, Sukanta

2017-11-01

We describe a general mathematical framework for χ2 discriminators in the context of the compact binary coalescence (CBC) search. We show that with any χ2 is associated a vector bundle over the signal manifold, that is, the manifold traced out by the signal waveforms in the function space of data segments. The χ2 is then defined as the square of the L2 norm of the data vector projected onto a finite-dimensional subspace (the fibre) of the Hilbert space of data trains and orthogonal to the signal waveform. Any such fibre leads to a χ2 discriminator, and the full vector bundle comprising the subspaces and the base manifold constitute the χ2 discriminator. We show that the χ2 discriminators used so far in the CBC searches correspond to different fibre structures constituting different vector bundles on the same base manifold, namely, the parameter space. Several benefits accrue from this general formulation. It most importantly shows that there are a plethora of χ2's available and further gives useful insights into the vetoing procedure. It indicates procedures to formulate new χ2's that could be more effective in discriminating against commonly occurring glitches in the data. It also shows that no χ2 with a reasonable number of degrees of freedom is foolproof. It could also shed light on understanding why the traditional χ2 works so well. We show how to construct a generic χ2 given an arbitrary set of vectors in the function space of data segments. These vectors could be chosen such that glitches have maximum projection on them. Further, for glitches that can be modeled, we are able to quantify the efficiency of a given χ2 discriminator by a probability. Second, we propose a family of ambiguity χ2 discriminators that is an alternative to the traditional one [B. Allen, Phys. Rev. D 71, 062001 (2005), 10.1103/PhysRevD.71.062001, B. Allen et al., Phys. Rev. D 85, 122006 (2012)., 10.1103/PhysRevD.85.122006]. Any such ambiguity χ2 makes use of the filtered output of the template bank, thus adding negligible cost to the overall search. It is termed so because it makes significant use of the ambiguity function. We first describe the formulation with the help of the Newtonian waveform, apply the ambiguity χ2 to the spinless TaylorF2 waveforms, and test it on simulated data. We show that the ambiguity χ2 essentially gives a clean separation between glitches and signals. We indicate how the ambiguity χ2 can be generalized to detector networks for coherent observations. The effects of mismatch between signal and templates on a χ2 discriminator using general arguments and the geometrical framework are also investigated.

Spectroscopic study of trivalent praseodymium in barium yttrium fluoride

NASA Astrophysics Data System (ADS)

Bowlby, Brian Edward

1998-09-01

This work investigates the spectroscopic properties of trivalent praseodymium (Pr3+) in barium yttrium fluoride (BaY2F8). Two doping concentrations were studied: BaY2F8:Pr3+ (.3%) and BaY2F8:Pr3+ (1%). Absorption spectra were taken at 77K and 300K and these were then used to calculate the Judd-Ofelt coefficients for both samples. These coefficients were then used to calculate the theoretical lifetimes and radiative branching ratios for all manifolds. Continuous luminescence spectra and lifetime measurements were also performed, and from these, experimentally determined values for the branching ratio and lifetimes were determined. These were then compared to their theoretical counterparts. It was found that while the theory gave values that were qualitatively correct, the quantitative correlation between theory and experiment shows the complexity of the physical reality and the difficulty of synthesizing an encompassing theoretical model. Absorption spectra and continuous luminescence spectra were also used to determine the energy levels of all manifolds in both samples. A total of 59 energy levels in 11 manifolds were identified in the BaY2F8:Pr3+ (1%) sample, while 51 levels in 11 manifolds were identified in the BaY2F8:Pr3+ (.3%) sample. Finally, the effects of temperature on the line width and line position for several radiative transitions was studied. It was found that while most transitions exhibited the expected broadening and shifting towards longer wavelengths at higher temperatures (a 'red shift'), the transition from the 3P0 level to the 3H4 ground state showed a shift towards shorter wavelengths at higher temperature (a 'blue shift'). Again this highlights the complexity of the ion- host interaction.

The closed MTIP-MyosinA-tail complex from the malaria parasite invasion machinery

PubMed Central

Bosch, Jürgen; Turley, Stewart; Roach, Claudia M.; Daly, Thomas M.; Bergman, Lawrence W.; Hol, Wim G. J.

2009-01-01

The Myosin A-tail Interacting Protein (MTIP) of the malaria parasite links the actomyosin motor of the host cell invasion machinery to its inner membrane complex. We report here that at neutral pH Plasmodium falciparum MTIP in complex with Myosin A adopts a compact conformation, with its two domains completely surrounding the Myosin A-tail helix, dramatically different from previously observed extended MTIP structures. Crystallographic and mutagenesis studies show that H810 and K813 of Myosin A are key players in the formation of the compact MTIP:Myosin A complex. Only the unprotonated state of Myosin A-H810 is compatible with the compact complex. Most surprisingly, every side chain atom of Myosin A-K813 is engaged in contacts with MTIP. While this side chain was previously considered to prevent a compact conformation of MTIP with Myosin A, it actually appears to be essential for the formation of the compact complex. The hydrophobic pockets and adaptability seen in the available series of MTIP structures bodes well for the discovery of inhibitors of cell invasion by malaria parasites. PMID:17628590

Space shuttle main engine computed tomography applications

NASA Technical Reports Server (NTRS)

Sporny, Richard F.

1990-01-01

For the past two years the potential applications of computed tomography to the fabrication and overhaul of the Space Shuttle Main Engine were evaluated. Application tests were performed at various government and manufacturer facilities with equipment produced by four different manufacturers. The hardware scanned varied in size and complexity from a small temperature sensor and turbine blades to an assembled heat exchanger and main injector oxidizer inlet manifold. The evaluation of capabilities included the ability to identify and locate internal flaws, measure the depth of surface cracks, measure wall thickness, compare manifold design contours to actual part contours, perform automatic dimensional inspections, generate 3D computer models of actual parts, and image the relationship of the details in a complex assembly. The capabilities evaluated, with the exception of measuring the depth of surface flaws, demonstrated the existing and potential ability to perform many beneficial Space Shuttle Main Engine applications.

Data-Driven Modeling of Complex Systems by means of a Dynamical ANN

NASA Astrophysics Data System (ADS)

Seleznev, A.; Mukhin, D.; Gavrilov, A.; Loskutov, E.; Feigin, A.

2017-12-01

The data-driven methods for modeling and prognosis of complex dynamical systems become more and more popular in various fields due to growth of high-resolution data. We distinguish the two basic steps in such an approach: (i) determining the phase subspace of the system, or embedding, from available time series and (ii) constructing an evolution operator acting in this reduced subspace. In this work we suggest a novel approach combining these two steps by means of construction of an artificial neural network (ANN) with special topology. The proposed ANN-based model, on the one hand, projects the data onto a low-dimensional manifold, and, on the other hand, models a dynamical system on this manifold. Actually, this is a recurrent multilayer ANN which has internal dynamics and capable of generating time series. Very important point of the proposed methodology is the optimization of the model allowing us to avoid overfitting: we use Bayesian criterion to optimize the ANN structure and estimate both the degree of evolution operator nonlinearity and the complexity of nonlinear manifold which the data are projected on. The proposed modeling technique will be applied to the analysis of high-dimensional dynamical systems: Lorenz'96 model of atmospheric turbulence, producing high-dimensional space-time chaos, and quasi-geostrophic three-layer model of the Earth's atmosphere with the natural orography, describing the dynamics of synoptical vortexes as well as mesoscale blocking systems. The possibility of application of the proposed methodology to analyze real measured data is also discussed. The study was supported by the Russian Science Foundation (grant #16-12-10198).

Self-dual geometry of generalized Hermitian surfaces

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

Arsen'eva, O E; Kirichenko, V F

Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chenmore » problem in this class of Hermitian surfaces.« less

Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary

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

Gorshkov, Aleksei V

2012-09-30

The problem of stabilizing a solution of the 2D Navier-Stokes system defined in the exterior of a bounded domain with smooth boundary is investigated. For a given initial velocity field a control on the boundary of the domain must be constructed such that the solution stabilizes to a prescribed vortex solution or trivial solution at the rate of 1/t{sup k}. On the way, related questions are investigated, concerning the behaviour of the spectrum of an operator under a relatively compact perturbation and the existence of attracting invariant manifolds. Bibliography: 21 titles.

N-Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation

NASA Astrophysics Data System (ADS)

Wang, Xin; Geng, Xian-Guo

2017-08-01

We derive the Lax pair and Darboux transformation for the (2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlevé analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively. Supported by National Natural Science Foundation of China under Grant No. 11331008 and China Postdoctoral Science Foundation Funded Sixtieth Batches (2016M602252)

Refining the boundaries of the classical de Sitter landscape

NASA Astrophysics Data System (ADS)

Andriot, David; Blåbäck, Johan

2017-03-01

We derive highly constraining no-go theorems for classical de Sitter backgrounds of string theory, with parallel sources; this should impact the embedding of cosmological models. We study ten-dimensional vacua of type II supergravities with parallel and backreacted orientifold O p -planes and D p -branes, on four-dimensional de Sitter spacetime times a compact manifold. Vacua for p = 3, 7 or 8 are completely excluded, and we obtain tight constraints for p = 4, 5, 6. This is achieved through the derivation of an enlightening expression for the four-dimensional Ricci scalar. Further interesting expressions and no-go theorems are obtained. The paper is self-contained so technical aspects, including conventions, might be of more general interest.

Conformal symmetries of Einstein's field equations and initial data

NASA Astrophysics Data System (ADS)

Sharma, Ramesh

2005-04-01

This paper examines the initial data for the evolution of the space-time solution of Einstein's equations admitting a conformal symmetry. Under certain conditions on the extrinsic curvature of the initial complete spacelike hypersurface and sectional curvature of the space-time with respect to sections containing the normal vector field, we have shown that the initial hypersurface is conformally diffeomorphic to a sphere or a flat space or a hyperbolic space or the product of an open real interval and a complete 2-manifold. It has been further shown that if the initial hypersurface is compact, then it is conformally diffeomorphic to a sphere. Finally, the conformal symmetries of a generalized Robertson-Walker space-time have been described.

Compact fuel cell

DOEpatents

Jacobson, Craig; DeJonghe, Lutgard C.; Lu, Chun

2010-10-19

A novel electrochemical cell which may be a solid oxide fuel cell (SOFC) is disclosed where the cathodes (144, 140) may be exposed to the air and open to the ambient atmosphere without further housing. Current collector (145) extends through a first cathode on one side of a unit and over the unit through the cathode on the other side of the unit and is in electrical contact via lead (146) with housing unit (122 and 124). Electrical insulator (170) prevents electrical contact between two units. Fuel inlet manifold (134) allows fuel to communicate with internal space (138) between the anodes (154 and 156). Electrically insulating members (164 and 166) prevent the current collector from being in electrical contact with the anode.

Multifractal vector fields and stochastic Clifford algebra.

PubMed

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2015-12-01

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

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

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge upmore » the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.« less

Compactifications of deformed conifolds, branes and the geometry of qubits

NASA Astrophysics Data System (ADS)

Cvetič, M.; Gibbons, G. W.; Pope, C. N.

2016-01-01

We present three families of exact, cohomogeneity-one Einstein metrics in (2 n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces C{P}^{n+1} , written in a Stenzel form, whose principal orbits are the Stiefel manifolds {V}_2(R}^{n+2})=SO(n+2)/SO(n) divided by {Z}_2 . The second family are also Einstein-Kähler metrics, now on the Grassmannian manifolds {G}_2({{R}}^{n+3})=SO(n+3)/((SO(n+1)× SO(2)), whose principal orbits are the Stiefel manifolds {V}_2({{R}}^{n+2}) (with no {{Z}}_2 factoring in this case). The third family are Einstein metrics on the product manifolds S n+1 × S n+1, and are Kähler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Kähler geometry of Fubini-Study metrics on {C}{{P}}^{n+1} , and we apply the formalism to study the quantum entanglement of qubits.

Compactifications of deformed conifolds, branes and the geometry of qubits $\\mathfrak S

DOE PAGES

Cvetič, M.; Gibbons, G. W.; Pope, C. N.

2016-01-22

We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces CP n+1, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V 2(more » $$\\mathbb R^{2+3}$$) = SO(n+2)/SO(n) divided by Z 2. The second family are also Einstein-Kahler metrics, now on the Grassmannian manifolds G 2(R n+3) = SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V 2($$\\mathbb R^{2+3}$$) (with no Z 2 factoring in this case). Furthermore, the third family are Einstein metrics on the product manifolds S n+1 × S n+1, and are Kahler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. Also, we elaborate on the geometric approach to quantum mechanics based on the Kahler geometry of Fubini-Study metrics on $$\\mathbb CP^{n+1}$$, and we apply the formalism to study the quantum entanglement of qubits.« less

Quaternionic Kähler Detour Complexes and {mathcal{N} = 2} Supersymmetric Black Holes

NASA Astrophysics Data System (ADS)

Cherney, D.; Latini, E.; Waldron, A.

2011-03-01

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional {{mathcal N} = 2} supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generate special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston’s complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.

The large N limit of superconformal field theories and supergravity

NASA Astrophysics Data System (ADS)

Maldacena, Juan

1999-07-01

We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 3+1N=4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.

Emergence of gravity, fermion, gauge and Chern-Simons fields during formation of N-dimensional manifolds from joining point-like ones

NASA Astrophysics Data System (ADS)

Sepehri, Alireza; Shoorvazi, Somayyeh

In this paper, we will consider the birth and evolution of fields during formation of N-dimensional manifolds from joining point-like ones. We will show that at the beginning, only there are point-like manifolds which some strings are attached to them. By joining these manifolds, 1-dimensional manifolds are appeared and gravity, fermion, and gauge fields are emerged. By coupling these manifolds, higher dimensional manifolds are produced and higher orders of fermion, gauge fields and gravity are emerged. By decaying N-dimensional manifold, two child manifolds and a Chern-Simons one are born and anomaly is emerged. The Chern-Simons manifold connects two child manifolds and leads to the energy transmission from the bulk to manifolds and their expansion. We show that F-gravity can be emerged during the formation of N-dimensional manifold from point-like manifolds. This type of F-gravity includes both type of fermionic and bosonic gravity. G-fields and also C-fields which are produced by fermionic strings produce extra energy and change the gravity.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

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

Means, Gregory Scott; Boardman, Gregory Allen; Berry, Jonathan Dwight

A combustor for a gas turbine generally includes a radial flow fuel nozzle having a fuel distribution manifold, and a fuel injection manifold axially separated from the fuel distribution manifold. The fuel injection manifold generally includes an inner side portion, an outer side portion, and a plurality of circumferentially spaced fuel ports that extend through the outer side portion. A plurality of tubes provides axial separation between the fuel distribution manifold and the fuel injection manifold. Each tube defines a fluid communication path between the fuel distribution manifold and the fuel injection manifold.

Oxidative demetalation of cyclohexadienyl ruthenium(II) complexes: a net Ru-mediated dearomatization.

PubMed

Pigge, F Christopher; Coniglio, John J; Rath, Nigam P

2003-05-29

[reaction: see text] An experimentally simple method for the demetalation of spirocyclic cyclohexadienylruthenium(II) complexes has been developed. Treatment of an alkoxy-substituted cyclohexadienyl complex with CuCl(2) affords either azaspiro[4.5]decane derivatives or heavily functionalized tetrahydroisoquinolines. The former reaction manifold completes a net Ru-mediated dearomatization as the organometallic starting materials are prepared from (eta(6)-arene)Ru(II) precursors. Both of these heterocyclic products are well suited for further synthetic elaboration.

(U) Influence of Compaction Model Form on Planar and Cylindrical Compaction Geometries

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

Fredenburg, David A.; Carney, Theodore Clayton; Fichtl, Christopher Allen

The dynamic compaction response of CeO 2 is examined within the frameworks of the Ramp and P-a compaction models. Hydrocode calculations simulating the dynamic response of CeO 2 at several distinct pressures within the compaction region are investigated in both planar and cylindrically convergent geometries. Findings suggest additional validation of the compaction models is warranted under complex loading configurations.

A compact model for electroosmotic flows in microfluidic devices

NASA Astrophysics Data System (ADS)

Qiao, R.; Aluru, N. R.

2002-09-01

A compact model to compute flow rate and pressure in microfluidic devices is presented. The microfluidic flow can be driven by either an applied electric field or a combined electric field and pressure gradient. A step change in the ζ-potential on a channel wall is treated by a pressure source in the compact model. The pressure source is obtained from the pressure Poisson equation and conservation of mass principle. In the proposed compact model, the complex fluidic network is simplified by an electrical circuit. The compact model can predict the flow rate, pressure distribution and other basic characteristics in microfluidic channels quickly with good accuracy when compared to detailed numerical simulation. Using the compact model, fluidic mixing and dispersion control are studied in a complex microfluidic network.

Pure spinors, function superspaces and supergravity theories in ten and eleven dimensions

NASA Astrophysics Data System (ADS)

Howe, P. S.

1991-12-01

The constraints of d = 10 supergravity coupled to super Yang-Mills and d = 11 supergravity are studied from the viewpoint of the differential geometry of certain function superspaces. For d = 10 the appropriate function space is loop superspace, and the presence of Chern-Simons terms in the coupling of supergravity to Yang-Mills is incorporated into the formalism via a central extension of the loop group of the Yang-Mills group. For d = 11 the function superspace is the space of maps from a compact two-manifold to superspace. In both cases the superspaces include additional commuting coordinates which are pure spinors. Permanent address: Department of Mathematics, King's College, London WC2R 2LS, UK.

MERCHANT MARINE SHIP REACTOR

DOEpatents

Mumm, J.F.; North, D.C. Jr.; Rock, H.R.; Geston, D.K.

1961-05-01

A nuclear reactor is described for use in a merchant marine ship. The reactor is of pressurized light water cooled and moderated design in which three passes of the water through the core in successive regions of low, intermediate, and high heat generation and downflow in a fuel region are made. The foregoing design makes a compact reactor construction with extended core life. The core has an egg-crate lattice containing the fuel elements confined between a lower flow baffle and upper grid plate, with the latter serving also as part of a turn- around manifold from which the entire coolant is distributed into the outer fuel elements for the second pass through the core. The inner fuel elements are cooled in the third pass.

Merchant Marine Ship Reactor

DOEpatents

Sankovich, M. F.; Mumm, J. F.; North, Jr, D. C.; Rock, H. R.; Gestson, D. K.

1961-05-01

A nuclear reactor for use in a merchant marine ship is described. The reactor is of pressurized, light water cooled and moderated design in which three passes of the water through the core in successive regions of low, intermediate, and high heat generation and downflow in a fuel region are made. The design makes a compact reactor construction with extended core life. The core has an egg-crate lattice containing the fuel elements that are confined between a lower flow baffle and upper grid plate, with the latter serving also as part of a turn- around manifold from which the entire coolant is distributed into the outer fuel elements for the second pass through the core. The inner fuel elements are cooled in the third pass. (AEC)

Lattice functions, wavelet aliasing, and SO(3) mappings of orthonormal filters

NASA Astrophysics Data System (ADS)

John, Sarah

1998-01-01

A formulation of multiresolution in terms of a family of dyadic lattices {Sj;j∈Z} and filter matrices Mj⊂U(2)⊂GL(2,C) illuminates the role of aliasing in wavelets and provides exact relations between scaling and wavelet filters. By showing the {DN;N∈Z+} collection of compactly supported, orthonormal wavelet filters to be strictly SU(2)⊂U(2), its representation in the Euler angles of the rotation group SO(3) establishes several new results: a 1:1 mapping of the {DN} filters onto a set of orbits on the SO(3) manifold; an equivalence of D∞ to the Shannon filter; and a simple new proof for a criterion ruling out pathologically scaled nonorthonormal filters.

Complexity of the laminar-turbulent boundary in pipe flow

NASA Astrophysics Data System (ADS)

Budanur, Nazmi Burak; Hof, Björn

2018-05-01

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry reduction, which we formulate here for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling-wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.

Sparse array angle estimation using reduced-dimension ESPRIT-MUSIC in MIMO radar.

PubMed

Zhang, Chaozhu; Pang, Yucai

2013-01-01

Sparse linear arrays provide better performance than the filled linear arrays in terms of angle estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. In this paper, both the transmit array and receive array are sparse linear arrays in the bistatic MIMO radar. Firstly, we present an ESPRIT-MUSIC method in which ESPRIT algorithm is used to obtain ambiguous angle estimates. The disambiguation algorithm uses MUSIC-based procedure to identify the true direction cosine estimate from a set of ambiguous candidate estimates. The paired transmit angle and receive angle can be estimated and the manifold ambiguity can be solved. However, the proposed algorithm has high computational complexity due to the requirement of two-dimension search. Further, the Reduced-Dimension ESPRIT-MUSIC (RD-ESPRIT-MUSIC) is proposed to reduce the complexity of the algorithm. And the RD-ESPRIT-MUSIC only demands one-dimension search. Simulation results demonstrate the effectiveness of the method.

Experimental study of flow distribution and pressure loss with circumferential inlet and outlet manifolds

NASA Technical Reports Server (NTRS)

Dittrich, R. T.

1972-01-01

Water flow tests with circumferential inlet and outlet manifolds were conducted to determine factors affecting fluid distribution and pressure losses. Various orifice sizes and manifold geometries were tested over a range of flow velocities. With inlet manifolds, flow distribution was related directly to orifice discharge coefficients. A correlation indicated that nonuniform distribution resulted when the velocity head ratio at the orifice was not in the range of constant discharge coefficient. With outlet manifolds, nonuniform flow was related to static pressure variations along the manifold. Outlet manifolds had appreciably greater pressure losses than comparable inlet manifolds.

Exact ground states for the nearest neighbor quantum XXZ model on the kagome and other lattices with triangular motifs at Jz /Jxy = - 1 / 2

NASA Astrophysics Data System (ADS)

Changlani, Hitesh; Kumar, Krishna; Kochkov, Dmitrii; Fradkin, Eduardo; Clark, Bryan

We report the existence of a quantum macroscopically degenerate ground state manifold on the nearest neighbor XXZ model on the kagome lattice at the point Jz /Jxy = - 1 / 2 . On many lattices with triangular motifs (including the kagome, sawtooth, icosidodecahedron and Shastry-Sutherland lattice for a certain choice of couplings) this Hamiltonian is found to be frustration-free with exact ground states which correspond to three-colorings of these lattices. Several results also generalize to the case of variable couplings and to other motifs (albeit with possibly more complex Hamiltonians). The degenerate manifold on the kagome lattice corresponds to a ''many-body flat band'' of interacting hard-core bosons; and for the one boson case our results also explain the well-known non-interacting flat band. On adding realistic perturbations, state selection in this manifold of quantum many-body states is discussed along with the implications for the phase diagram of the kagome lattice antiferromagnet. supported by DE-FG02-12ER46875, DMR 1408713, DE-FG02-08ER46544.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

NASA Astrophysics Data System (ADS)

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-01

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

PubMed

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-07

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Biventricular non-compaction hypertrophic cardiomyopathy in association with congenital complete heart block and type I mitochondrial complex deficiency.

PubMed

Dhar, Ranjana; Reardon, William; McMahon, Colin J

2015-06-01

We report a baby girl with an antenatal diagnosis of biventricular non-compaction and complete heart block detected at 22 weeks' gestation. Postnatal echocardiography confirmed severe biventricular non-compaction hypertrophic cardiomyopathy, multiple muscular ventricular septal defects, and mild-moderate pulmonary valve stenosis. Skeletal muscle biopsy confirmed complex 1 mitochondrial respiratory chain deficiency. An epicardial VVI pacemaker was implanted on day 3 of life and revised at 7 years of age. She remains stable at 8 years of age following pacing and medical treatment with carvedilol, aspirin, co-enzyme Q10, and carnitine. This represents the first report of biventricular non-compaction hypertrophic phenotype in association with congenital complete heart block and complex 1 mitochondrial respiratory chain deficiency in a child.

Quantitative analysis of dinuclear manganese(II) EPR spectra

NASA Astrophysics Data System (ADS)

Golombek, Adina P.; Hendrich, Michael P.

2003-11-01

A quantitative method for the analysis of EPR spectra from dinuclear Mn(II) complexes is presented. The complex [(Me 3TACN) 2Mn(II) 2(μ-OAc) 3]BPh 4 ( 1) (Me 3TACN= N, N', N''-trimethyl-1,4,7-triazacyclononane; OAc=acetate 1-; BPh 4=tetraphenylborate 1-) was studied with EPR spectroscopy at X- and Q-band frequencies, for both perpendicular and parallel polarizations of the microwave field, and with variable temperature (2-50 K). Complex 1 is an antiferromagnetically coupled dimer which shows signals from all excited spin manifolds, S=1 to 5. The spectra were simulated with diagonalization of the full spin Hamiltonian which includes the Zeeman and zero-field splittings of the individual manganese sites within the dimer, the exchange and dipolar coupling between the two manganese sites of the dimer, and the nuclear hyperfine coupling for each manganese ion. All possible transitions for all spin manifolds were simulated, with the intensities determined from the calculated probability of each transition. In addition, the non-uniform broadening of all resonances was quantitatively predicted using a lineshape model based on D- and r-strain. As the temperature is increased from 2 K, an 11-line hyperfine pattern characteristic of dinuclear Mn(II) is first observed from the S=3 manifold. D- and r-strain are the dominate broadening effects that determine where the hyperfine pattern will be resolved. A single unique parameter set was found to simulate all spectra arising for all temperatures, microwave frequencies, and microwave modes. The simulations are quantitative, allowing for the first time the determination of species concentrations directly from EPR spectra. Thus, this work describes the first method for the quantitative characterization of EPR spectra of dinuclear manganese centers in model complexes and proteins. The exchange coupling parameter J for complex 1 was determined ( J=-1.5±0.3 cm-1; H ex=-2J S1· S2) and found to be in agreement with a previous determination from magnetization. The phenomenon of exchange striction was found to be insignificant for 1.

Formation of a Chern-Simons cylindrical wormhole during evolution of manifolds

NASA Astrophysics Data System (ADS)

Sepehri, Alireza; Ghaffary, Tooraj; Naimi, Yaghoob; Ghaforyan, Hossein; Ebrahimzadeh, Majid

In this paper, the formation of cylindrical wormhole during evolution of manifolds is studied. It is shown that this type of wormholes may be produced at two stages and then disappeared very fast at the third stage. First, one N-dimensional is formed by joining point-like manifolds. Then, this manifold is torn and two child manifolds plus one Chern-Simons manifold appeared. Our universe is born on one of the child manifolds and connected to the other one by Chern-Simons manifold. At the third stage, this Chern-Simons manifold-which plays the role of cylindrical wormhole, dissolves into universes and gives its energy to them and causes inflation. Thus, the Chern-Simons cylindrical wormhole is unstable and dissolves in our four-dimensional universes and another universe very fast.

Dual manifold heat pipe evaporator

DOEpatents

Adkins, Douglas R.; Rawlinson, K. Scott

1994-01-01

An improved evaporator section for a dual manifold heat pipe. Both the upper and lower manifolds can have surfaces exposed to the heat source which evaporate the working fluid. The tubes in the tube bank between the manifolds have openings in their lower extensions into the lower manifold to provide for the transport of evaporated working fluid from the lower manifold into the tubes and from there on into the upper manifold and on to the condenser portion of the heat pipe. A wick structure lining the inner walls of the evaporator tubes extends into both the upper and lower manifolds. At least some of the tubes also have overflow tubes contained within them to carry condensed working fluid from the upper manifold to pass to the lower without spilling down the inside walls of the tubes.

Manifold seal structure for fuel cell stack

DOEpatents

Collins, William P.

1988-01-01

The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.

Dual manifold heat pipe evaporator

DOEpatents

Adkins, D.R.; Rawlinson, K.S.

1994-01-04

An improved evaporator section is described for a dual manifold heat pipe. Both the upper and lower manifolds can have surfaces exposed to the heat source which evaporate the working fluid. The tubes in the tube bank between the manifolds have openings in their lower extensions into the lower manifold to provide for the transport of evaporated working fluid from the lower manifold into the tubes and from there on into the upper manifold and on to the condenser portion of the heat pipe. A wick structure lining the inner walls of the evaporator tubes extends into both the upper and lower manifolds. At least some of the tubes also have overflow tubes contained within them to carry condensed working fluid from the upper manifold to pass to the lower without spilling down the inside walls of the tubes. 1 figure.

Hysteresis in DNA compaction by Dps is described by an Ising model

PubMed Central

Vtyurina, Natalia N.; Dulin, David; Docter, Margreet W.; Meyer, Anne S.; Dekker, Nynke H.; Abbondanzieri, Elio A.

2016-01-01

In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps–DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps–DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states. PMID:27091987

eBits: Compact stream of mesh refinements for remote visualization

DOE PAGES

Sati, Mukul; Lindstrom, Peter; Rossignac, Jarek

2016-05-12

Here, we focus on applications where a remote client needs to visualize or process a complex, manifold triangle mesh, M, but only in a relatively small, user controlled, Region of Interest (RoI) at a time. The client first downloads a coarse base mesh, pre-computed on the server via a series of simplification passes on M, one per Level of Detail (LoD), each pass identifying an independent set of triangles, collapsing them, and, for each collapse, storing, in a Vertex Expansion Record (VER), the information needed to reverse the collapse. On each client initiated RoI modification request, the server pushes tomore » the client a selected subset of these VERs, which, when decoded and applied to refine the mesh locally, ensure that the portion in the RoI is always at full resolution. The eBits approach proposed here offers state of the art compression ratios (using less than 2.5 bits per new full resolution RoI triangle when the RoI has more than 2000 vertices to transmit the connectivity for the selective refinements) and fine-grain control (allowing the user to adjust the RoI by small increments). The effectiveness of eBits results from several novel ideas and novel variations of previous solutions. We represent the VERs using persistent labels so that they can be applied in different orders within a given LoD. The server maintains a shadow copy of the client’s mesh. To avoid sending IDs identifying which vertices should be expanded, we either transmit, for each new vertex, a compact encoding of its death tag–the LoD at which it will be expanded if it lies in the Rol–or transmit vertex masks for the RoI and its neighboring vertices. We also propose a three-step simplification that reduces the overall transmission cost by increasing both the simplification effectiveness and the regularity of the valences in the resulting meshes.« less

eBits: Compact stream of mesh refinements for remote visualization

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

Sati, Mukul; Lindstrom, Peter; Rossignac, Jarek

2016-05-12

Here, we focus on applications where a remote client needs to visualize or process a complex, manifold triangle mesh, M, but only in a relatively small, user controlled, Region of Interest (RoI) at a time. The client first downloads a coarse base mesh, pre-computed on the server via a series of simplification passes on M, one per Level of Detail (LoD), each pass identifying an independent set of triangles, collapsing them, and, for each collapse, storing, in a Vertex Expansion Record (VER), the information needed to reverse the collapse. On each client initiated RoI modification request, the server pushes tomore » the client a selected subset of these VERs, which, when decoded and applied to refine the mesh locally, ensure that the portion in the RoI is always at full resolution. The eBits approach proposed here offers state of the art compression ratios (using less than 2.5 bits per new full resolution RoI triangle when the RoI has more than 2000 vertices to transmit the connectivity for the selective refinements) and fine-grain control (allowing the user to adjust the RoI by small increments). The effectiveness of eBits results from several novel ideas and novel variations of previous solutions. We represent the VERs using persistent labels so that they can be applied in different orders within a given LoD. The server maintains a shadow copy of the client’s mesh. To avoid sending IDs identifying which vertices should be expanded, we either transmit, for each new vertex, a compact encoding of its death tag ​–the LoD at which it will be expanded if it lies in the RoI–or transmit vertex masks for the RoI and its neighboring vertices. We also propose a three-step simplification that reduces the overall transmission cost by increasing both the simplification effectiveness and the regularity of the valences in the resulting meshes.« less

180-GHz Interferometric Imager

NASA Technical Reports Server (NTRS)

Kangaslahti, Pekka P.; Lim, Boon H.; O'Dwyer, Ian J.; Soria, Mary M.; Owen, Heather R.; Gaier, Todd C.; Lambrigtsen, Bjorn, H.; Tanner, Alan B.; Ruf, Christopher

2011-01-01

A 180-GHz interferometric imager uses compact receiver modules, combined high- and low-gain antennas, and ASIC (application specific integrated circuit) correlator technology, enabling continuous, all-weather observations of water vapor with 25-km resolution and 0.3-K noise in 15 minutes of observation for numerical weather forecasting and tropical storm prediction. The GeoSTAR-II prototype instrument is broken down into four major subsystems: the compact, low-noise receivers; sub-array modules; IF signal distribution; and the digitizer/correlator. Instead of the single row of antennas adopted in GeoSTAR, this version has four rows of antennas on a coarser grid. This dramatically improves the sensitivity in the desired field of view. The GeoSTAR-II instrument is a 48-element, synthetic, thinned aperture radiometer operating at 165-183 GHz. The instrument has compact receivers integrated into tiles of 16 elements in a 4x4 arrangement. These tiles become the building block of larger arrays. The tiles contain signal distribution for bias controls, IF signal, and local oscillator signals. The IF signals are digitized and correlated using an ASIC correlator to minimize power consumption. Previous synthetic aperture imagers have used comparatively large multichip modules, whereas this approach uses chip-scale modules mounted on circuit boards, which are in turn mounted on the distribution manifolds. This minimizes the number of connectors and reduces system mass. The use of ASIC technology in the digitizers and correlators leads to a power reduction close to an order of magnitude.

Power module assemblies with staggered coolant channels

DOEpatents

Herron, Nicholas Hayden; Mann, Brooks S; Korich, Mark D

2013-07-16

A manifold is provided for supporting a power module assembly with a plurality of power modules. The manifold includes a first manifold section. The first face of the first manifold section is configured to receive the first power module, and the second face of the first manifold section defines a first cavity with a first baseplate thermally coupled to the first power module. The first face of the second manifold section is configured to receive the second power module, and the second face of the second manifold section defines a second cavity with a second baseplate thermally coupled to the second power module. The second face of the first manifold section and the second face of the second manifold section are coupled together such that the first cavity and the second cavity form a coolant channel. The first cavity is at least partially staggered with respect to second cavity.

Coherent Population Trapping and Optical Ramsey Interference for Compact Rubidium Clock Development

NASA Astrophysics Data System (ADS)

Warren, Zachary Aron

Coherent population trapping (CPT) and optical Ramsey interference provide new avenues for developing compact, high-performance atomic clocks. In this work, I have studied the fundamental aspects of CPT and optical Ramsey interference for Raman clock development. This thesis research is composed of two parts: theoretical and experimental studies. The theoretical component of the research was initially based on pre-existing atomic models of a three-level ?-type system in which the phenomena of CPT and Ramsey interference are formed. This model served as a starting point for studying basic characteristics of CPT and Ramsey interference such as power dependence of CPT, effects of average detuning, and ground-state decoherence on linewidth, which directly impact the performance of the Raman clock. The basic three-level model was also used to model pulsed CPT excitation and measure light shift in Ramsey interference which imposes a fundamental limit on the long-term frequency stability of the Raman clock. The theoretical calculations illustrate reduction (or suppression) of light shift in Ramsey interference as an important advantage over CPT for Raman clock development. To make the model more accurate than an ideal three-level system, I developed a comprehensive atomic model using density-matrix equations including all sixteen Zeeman sublevels in the D1 manifold of 87Rb atoms in a vapor medium. The multi-level atomic model has been used for investigating characteristics of CPT and Ramsey interference under different optical excitation schemes pertaining to the polarization states of the frequency-modulated CPT beam in a Raman clock. It is also used to study the effects of axial and traverse magnetic fields on the contrast of CPT and Ramsey interference. More importantly, the multi-level atomic model is also used to accurately calculate light shift in Ramsey interference in the D1 manifold of 87Rb atoms by taking into account all possible off-resonant excitations and the ground-state decoherence among the Zeeman sublevels. Light shift suppression in Ramsey interference with pulse saturation is also found to be evident in this comprehensive model. In the experimental component of the research, I designed a prototype of the Raman clock using a small (2 cm in length), buffer-gas filled, and isotopically pure 87Rb cell. A fiber-coupled waveguide electro-optic modulator was used to generate the frequency-modulated CPT beam for the experiments. The experimental setup was operated either by continuous excitation or pulsed excitation for experimentally characterizing CPT and Ramsey interference under different experimental conditions and for testing different optical excitation schemes which were investigated theoretically. Several iterations of the clock physics package were developed in order to attain better frequency stability performance in the Raman clock. The experimental work also provided a basis to develop a new repeated-query technique for producing an ultra-narrow linewidth central fringe with a high S/N ratio, and suppressing the side fringes in Ramsey interference. The above described research was carried out keeping in mind compact, high-performance clock development, which relies on technologies that can be miniaturized. Vapor cell based atomic clocks are ideal candidates for compact clock technology. The CPT phenomenon, observed by Raman excitation in a vapor medium, is a promising candidate for compact, high-performance Raman clock development. However, atom-field interaction involved in a vapor medium is often more complex than other media such as cold atom or atomic beam. It is difficult to model this interaction in order to predict its influence on CPT characteristics and, hence, the performance of the Raman clock. This dissertation addresses one such problem by developing a comprehensive atomic model to investigate light shift and modification of light shift in the Raman clock, particularly with pulsed excitation. It demonstrates a clear possibility of reducing (or suppressing) the light shift associated with Ramsey interference in a vapor medium for achieving higher frequency stability in the Raman clock. Additionally, theoretical comparisons of various optical excitation techniques have been calculated to demonstrate the relative strengths and weaknesses of different schemes for Raman clock development. (Abstract shortened by ProQuest.).

Dangerous angular Kaluza-Klein/glueball relics in string theory cosmology

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

Dufaux, J. F.; CITA, University of Toronto, 60 St. George st., Toronto, ON M5S 3H8; Kofman, L.

2008-07-15

The presence of Kaluza-Klein (KK) particles in the universe is a potential manifestation of string theory cosmology. In general, they can be present in the high temperature bath of the early universe. In particular examples, string theory inflation often ends with brane-antibrane annihilation followed by the energy cascading through massive closed string loops to KK modes which then decay into lighter standard model particles. However, massive KK modes in the early universe may become dangerous cosmological relics if the inner manifold contains warped throat(s) with approximate isometries. In the complimentary picture, in the AdS/CFT dual gauge theory with extra isometries,more » massive glueballs of various spins become the dangerous cosmological relics. The decay of these angular KK modes/glueballs, located around the tip of the throat, is caused by isometry breaking which results from gluing the throat to the compact Calabi-Yau (CY) manifold. We address the problem of these angular KK particles/glueballs, studying their interactions and decay channels, from the theory side, and the resulting cosmological constraints on the warped compactification parameters, from the phenomenology side. The abundance and decay time of the long-lived nonrelativistic angular KK modes depend strongly on the parameters of the warped geometry, so that observational constraints rule out a significant fraction of the parameter space. In particular, the coupling of the angular KK particles can be weaker than gravitational.« less

Inhomogeneous anisotropic cosmology

DOE PAGES

Kleban, Matthew; Senatore, Leonardo

2016-10-12

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarilymore » large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.« less

Inhomogeneous anisotropic cosmology

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

Kleban, Matthew; Senatore, Leonardo

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarilymore » large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.« less

Inhomogeneous anisotropic cosmology

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

Kleban, Matthew; Senatore, Leonardo; Kavli Institute for Particle Astrophysics and Cosmology, Stanford University and SLAC,2575 Sand Hill Road, M/S 29, Menlo Park, CA 94025

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with “flat” (including toroidal) and “open” (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuationsmore » and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are “flat” or “open”. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with “flat” or “open” topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.« less

Partial oxidation for improved cold starts in alcohol-fueled engines: Phase 2 topical report

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

NONE

1998-04-01

Alcohol fuels exhibit poor cold-start performance because of their low volatility. Neat alcohol engines become difficult, if not impossible, to start at temperatures close to or below freezing. Improvements in the cold-start performance (both time to start and emissions) are essential to capture the full benefits of alcohols as an alternative transportation fuel. The objective of this project was to develop a neat alcohol partial oxidation (POX) reforming technology to improve an alcohol engine`s ability to start at low temperatures (as low as {minus}30 C) and to reduce its cold-start emissions. The project emphasis was on fuel-grade ethanol (E95) butmore » the technology can be easily extended to other alcohol fuels. Ultimately a compact, on-vehicle, ethanol POX reactor was developed as a fuel system component to produce a hydrogen-rich, fuel-gas mixture for cold starts. The POX reactor is an easily controllable combustion device that allows flexibility during engine startup even in the most extreme conditions. It is a small device that is mounted directly onto the engine intake manifold. The gaseous fuel products (or reformate) from the POX reactor exit the chamber and enter the intake manifold, either replacing or supplementing the standard ethanol fuel consumed during an engine start. The combustion of the reformate during startup can reduce engine start time and tail-pipe emissions.« less

Hyperconifold transitions, mirror symmetry, and string theory

NASA Astrophysics Data System (ADS)

Davies, Rhys

2011-09-01

Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli space) is an isolated singularity which is a finite cyclic quotient of the conifold; these were called hyperconifolds. It was also shown that if the order of the quotient group is even, such singular varieties have projective crepant resolutions, which are therefore smooth Calabi-Yau manifolds. The resulting topological transitions were called hyperconifold transitions, and change the fundamental group as well as the Hodge numbers. Here Batyrev's construction of Calabi-Yau hypersurfaces in toric fourfolds is used to demonstrate that certain compact examples containing the remaining hyperconifolds — the Z and Z cases — also have Calabi-Yau resolutions. The mirrors of the resulting transitions are studied and it is found, surprisingly, that they are ordinary conifold transitions. These are the first examples of conifold transitions with mirrors which are more exotic extremal transitions. The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z or Z. Finally, it is demonstrated that a hyperconifold is a physically sensible background in Type IIB string theory. In analogy to the conifold case, non-perturbative dynamics smooth the physical moduli space, such that hyperconifold transitions correspond to non-singular processes in the full theory.

Modular package for cooling a laser diode array

DOEpatents

Mundinger, David C.; Benett, William J.; Beach, Raymond J.

1992-01-01

A laser diode array is disclosed that includes a plurality of planar packages and active cooling. The laser diode array may be operated in a long duty cycle, or in continuous operation. A laser diode bar and a microchannel heat sink are thermally coupled in a compact, thin planar package having the laser diode bar located proximate to one edge. In an array, a number of such thin planar packages are secured together in a stacked configuration, in close proximity so that the laser diodes are spaced closely. The cooling means includes a microchannel heat sink that is attached proximate to the laser bar so that it absorbs heat generated by laser operation. To provide the coolant to the microchannels, each thin planar package comprises a thin inlet manifold and a thin outlet manifold connected to an inlet corridor and an outlet corridor. The inlet corridor comprises a hole extending through each of the packages in the array, and the outlet corridor comprises a hole extending through each of the packages in the array. The inlet and outlet corridors are connected to a conventional coolant circulation system. The laser diode array with active cooling has application as an optical pump for high power solid state lasers. Further, it can be incorporated in equipment such as communications devices and active sensors, and in military and space applications, and it can be useful in applications having space constraints and energy limitations.

Photophysical properties of ortho-metalated monomeric and dimeric complexes containing rhodium(III) and iridium(III) metal centers

NASA Astrophysics Data System (ADS)

Marshall, Jason Alexander

Photophysical properties of dichloro-bridged dimers and monomeric tris complexes of the type [M(NC)2Cl]2 and M(NC)3, where NC refers to the ortho-metalating ligands 2-phenylpyridine (ppy), benzo[h]quinoline (bzq), or 2-(p-tolyl)pyridine (ptpy) and M is Rh(III) or Ir(III), were investigated. Excited-state emission of Rh(III) complexes are highly structured and independent of temperature from 4--100 K in glassy media, with long lifetimes (102 mus to ms). Emission is not observed from the pale yellow, fluid solutions of Rh(III) complexes at room temperature. Below 7K, decay kinetics are sensitive to temperature and are complicated, requiring multi-exponential fits in 4:1 EtOH/MeOH. The spectroscopic properties are consistent with the assignment of a lowest 3pipi* excited-state manifold perturbed by an admixture of higher-lying states possessing strong spin-orbit interactions. The complicated decays are attributed to spin-relaxation-limited behavior between spin-levels in the 3pipi* manifold. Deep yellow solutions of Ir(III) complexes in 4:1 EtOH/MeOH are observed to emit in both glassy media and in fluid solution, displaying severe changes in spectral shape as the glass softens which are not attributable to rigidochromic shifts. Low-temperature spectra are structured with emission origins in the range 496--520 nm whereas room-temperature emission of complexes in fluid solution are characteristically broad structureless bands with maxima redshifted from spectra measured in rigid media. Both the emission and the excited-state lifetimes display temperature dependence, with lifetimes in the microsecond to tens of microseconds range at 77 K, increasing by more than an order of magnitude as the temperature is decreased to 4 K. Each of these characteristic band shapes arises from separate components of the emission which have been time-resolved from the low-temperature spectrum. A long-lived, structured component of the emission, only observed in rigid media, has been assigned as 3pipi*. The spectroscopic properties of the short-lived component, observed in the time-resolved low-temperature emission spectrum and in the room-temperature fluid-solution emission spectrum, are consistent with a lowest 3MLCT excited state manifold.

A Method for Reducing the Temperature of Exhaust Manifolds

NASA Technical Reports Server (NTRS)

Schey, Oscar W; Young, Alfred W

1931-01-01

This report describes tests conducted at the Langley Memorial Aeronautical Laboratory on an "air-inducting" exhaust manifold for aircraft engines. The exhaust gases from each cylinder port are discharged into the throat of an exhaust pipe which has a frontal bellmouth. Cooling air is drawn into the pipe, where it surrounds and mixes with the exhaust gases. Temperatures of the manifold shell and of the exhaust gases were obtained in flight for both a conventional manifold and the air-inducting manifold. The air-inducting manifold was installed on an engine which was placed on a test stand. Different fuels were sprayed on and into the manifold to determine whether the use of this manifold reduced the fire hazard. The flight tests showed reductions in manifold temperatures of several hundred degrees, to values below the ignition point of aviation gasoline. On the test stand when the engine was run at idling speeds fuels sprayed into the manifold ignited. It is believed that at low engine speeds the fuel remained in the manifold long enough to become thoroughly heated, and was then ignited by the exhaust gas which had not mixed with cooling air. The use of the air-inducting exhaust manifold must reduce the fire hazard by virtue of its lower operating temperature, but it is not a completely satisfactory solution of the problem.

75 FR 901 - Airworthiness Directives; Honeywell International Inc. ALF502 Series and LF507 Series Turbofan...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-07

.... ALF502 series and LF507 series turbofan engines with certain fuel manifold assemblies installed. That AD... of certain part number (P/N) fuel manifold assemblies for cracks, and replacement of cracked fuel manifolds with serviceable manifolds. This AD continues to require inspecting those fuel manifolds for...

Experimental Analysis of Exhaust Manifold with Ceramic Coating for Reduction of Heat Dissipation

NASA Astrophysics Data System (ADS)

Saravanan, J.; Valarmathi, T. N.; Nathc, Rajdeep; Kumar, Prasanth

2017-05-01

Exhaust manifold plays an important role in the exhaust system, the manifold delivers the waste toxic gases to a safe distance and it is used to reduce the sound pollution and air pollution. Exhaust manifold suffers with lot of thermal stress, due to this blow holes occurs in the surface of the exhaust manifold and also more noise is developed. The waste toxic gases from the multiple cylinders are collected into a single pipe by the exhaust manifold. The waste toxic gases can damage the material of the manifold. In this study, to prevent the damage zirconia powder has been coated in the inner surface and alumina (60%) combined with titania (40%) has been used for coating the outer surface of the exhaust manifold. After coating experiments have been performed using a multiple-cylinder four stroke stationary petrol engine. The test results of hardness, emission, corrosion and temperature of the coated and uncoated manifolds have been compared. The result shows that the performance is improved and also emission is reduced in the coated exhaust manifold.

A Search for X-ray Emission in Isolated Compact Triplets

NASA Technical Reports Server (NTRS)

Brown, Beth A.; Williams, Barbara

2006-01-01

We describe preliminary results of an exploratory search for diffuse X-ray emission in a sample of the poorest galaxy groups, i.e., isolated compact triplets of galaxies. These systems represent the simplest forms of galaxy clustering while manifesting all the complexities inherent in other groups. We have selected 20 compact triplets for this initial study. The component galaxies are expected to interact with each other and with the group's intergalactic medium, if present, in complex ways that trigger high-energy processes.

Classical and quantum dynamics in an inverse square potential

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

Guillaumín-España, Elisa, E-mail: ege@correo.azc.uam.mx; Núñez-Yépez, H. N., E-mail: nyhn@xanum.uam.mx; Salas-Brito, A. L., E-mail: asb@correo.azc.uam.mx

2014-10-15

The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence ofmore » bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.« less

Non-naturally reductive Einstein metrics on exceptional Lie groups

NASA Astrophysics Data System (ADS)

Chrysikos, Ioannis; Sakane, Yusuke

2017-06-01

Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Gröbner bases and classify the real solutions of the associated algebraic systems. For the Lie group G2 we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E7 and E8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K) -invariant by different Lie subgroups K.

Cascaded face alignment via intimacy definition feature

NASA Astrophysics Data System (ADS)

Li, Hailiang; Lam, Kin-Man; Chiu, Man-Yau; Wu, Kangheng; Lei, Zhibin

2017-09-01

Recent years have witnessed the emerging popularity of regression-based face aligners, which directly learn mappings between facial appearance and shape-increment manifolds. We propose a random-forest based, cascaded regression model for face alignment by using a locally lightweight feature, namely intimacy definition feature. This feature is more discriminative than the pose-indexed feature, more efficient than the histogram of oriented gradients feature and the scale-invariant feature transform feature, and more compact than the local binary feature (LBF). Experimental validation of our algorithm shows that our approach achieves state-of-the-art performance when testing on some challenging datasets. Compared with the LBF-based algorithm, our method achieves about twice the speed, 20% improvement in terms of alignment accuracy and saves an order of magnitude on memory requirement.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori

NASA Astrophysics Data System (ADS)

Iochum, B.; Masson, T.

2018-07-01

Let P be a Laplace type operator acting on a smooth hermitean vector bundle V of fiber CN over a compact Riemannian manifold given locally by P = - [gμν u(x) ∂μ∂ν +vν(x) ∂ν + w(x) ] where u ,vν , w are MN(C) -valued functions with u(x) positive and invertible. For any a ∈ Γ(End(V)) , we consider the asymptotics Tr(ae-tP) ∼ t↓0+ ∑r=0∞ ar(a , P) t (r - d) / 2 where the coefficients ar(a , P) can be written as an integral of the functions ar(a , P) (x) = tr [ a(x) Rr(x) ] . The computation of R2 is performed opening the opportunity to calculate the modular scalar curvature for noncommutative tori.

The world problem: on the computability of the topology of 4-manifolds

NASA Technical Reports Server (NTRS)

vanMeter, J. R.

2005-01-01

Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.

Fluxonium-Based Artificial Molecule with a Tunable Magnetic Moment

NASA Astrophysics Data System (ADS)

Kou, A.; Smith, W. C.; Vool, U.; Brierley, R. T.; Meier, H.; Frunzio, L.; Girvin, S. M.; Glazman, L. I.; Devoret, M. H.

2017-07-01

Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO®-like nature of superconducting circuits makes them particularly suited for building and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for quantum simulation and protected qubits.

Configurable double-sided modular jet impingement assemblies for electronics cooling

DOEpatents

Zhou, Feng; Dede, Ercan Mehmet

2018-05-22

A modular jet impingement assembly includes an inlet tube fluidly coupled to a fluid inlet, an outlet tube fluidly coupled to a fluid outlet, and a modular manifold having a first distribution recess extending into a first side of the modular manifold, a second distribution recess extending into a second side of the modular manifold, a plurality of inlet connection tubes positioned at an inlet end of the modular manifold, and a plurality of outlet connection tubes positioned at an outlet end of the modular manifold. A first manifold insert is removably positioned within the first distribution recess, a second manifold insert is removably positioned within the second distribution recess, and a first and second heat transfer plate each removably coupled to the modular manifold. The first and second heat transfer plates each comprise an impingement surface.

Bearing Fault Diagnosis Based on Statistical Locally Linear Embedding

PubMed Central

Wang, Xiang; Zheng, Yuan; Zhao, Zhenzhou; Wang, Jinping

2015-01-01

Fault diagnosis is essentially a kind of pattern recognition. The measured signal samples usually distribute on nonlinear low-dimensional manifolds embedded in the high-dimensional signal space, so how to implement feature extraction, dimensionality reduction and improve recognition performance is a crucial task. In this paper a novel machinery fault diagnosis approach based on a statistical locally linear embedding (S-LLE) algorithm which is an extension of LLE by exploiting the fault class label information is proposed. The fault diagnosis approach first extracts the intrinsic manifold features from the high-dimensional feature vectors which are obtained from vibration signals that feature extraction by time-domain, frequency-domain and empirical mode decomposition (EMD), and then translates the complex mode space into a salient low-dimensional feature space by the manifold learning algorithm S-LLE, which outperforms other feature reduction methods such as PCA, LDA and LLE. Finally in the feature reduction space pattern classification and fault diagnosis by classifier are carried out easily and rapidly. Rolling bearing fault signals are used to validate the proposed fault diagnosis approach. The results indicate that the proposed approach obviously improves the classification performance of fault pattern recognition and outperforms the other traditional approaches. PMID:26153771

CFD Analysis and Design of Detailed Target Configurations for an Accelerator-Driven Subcritical System

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

Kraus, Adam; Merzari, Elia; Sofu, Tanju

2016-08-01

High-fidelity analysis has been utilized in the design of beam target options for an accelerator driven subcritical system. Designs featuring stacks of plates with square cross section have been investigated for both tungsten and uranium target materials. The presented work includes the first thermal-hydraulic simulations of the full, detailed target geometry. The innovative target cooling manifold design features many regions with complex flow features, including 90 bends and merging jets, which necessitate three-dimensional fluid simulations. These were performed using the commercial computational fluid dynamics code STAR-CCM+. Conjugate heat transfer was modeled between the plates, cladding, manifold structure, and fluid. Steady-statemore » simulations were performed but lacked good residual convergence. Unsteady simulations were then performed, which converged well and demonstrated that flow instability existed in the lower portion of the manifold. It was established that the flow instability had little effect on the peak plate temperatures, which were well below the melting point. The estimated plate surface temperatures and target region pressure were shown to provide sufficient margin to subcooled boiling for standard operating conditions. This demonstrated the safety of both potential target configurations during normal operation.« less

The functional equation truncation method for approximating slow invariant manifolds: a rapid method for computing intrinsic low-dimensional manifolds.

PubMed

Roussel, Marc R; Tang, Terry

2006-12-07

A slow manifold is a low-dimensional invariant manifold to which trajectories nearby are rapidly attracted on the way to the equilibrium point. The exact computation of the slow manifold simplifies the model without sacrificing accuracy on the slow time scales of the system. The Maas-Pope intrinsic low-dimensional manifold (ILDM) [Combust. Flame 88, 239 (1992)] is frequently used as an approximation to the slow manifold. This approximation is based on a linearized analysis of the differential equations and thus neglects curvature. We present here an efficient way to calculate an approximation equivalent to the ILDM. Our method, called functional equation truncation (FET), first develops a hierarchy of functional equations involving higher derivatives which can then be truncated at second-derivative terms to explicitly neglect the curvature. We prove that the ILDM and FET-approximated (FETA) manifolds are identical for the one-dimensional slow manifold of any planar system. In higher-dimensional spaces, the ILDM and FETA manifolds agree to numerical accuracy almost everywhere. Solution of the FET equations is, however, expected to generally be faster than the ILDM method.

Cycle expansions: From maps to turbulence

NASA Astrophysics Data System (ADS)

Lan, Y.

2010-03-01

We present a derivation, a physical explanation and applications of cycle expansions in different dynamical systems, ranging from simple one-dimensional maps to turbulence in fluids. Cycle expansion is a newly devised powerful tool for computing averages of physical observables in nonlinear chaotic systems which combines many innovative ideas developed in dynamical systems, such as hyperbolicity, invariant manifolds, symbolic dynamics, measure theory and thermodynamic formalism. The concept of cycle expansion has a deep root in theoretical physics, bearing a close analogy to cumulant expansion in statistical physics and effective action functional in quantum field theory, the essence of which is to represent a physical system in a hierarchical way by utilizing certain multiplicative structures such that the dominant parts of physical observables are captured by compact, maneuverable objects while minor detailed variations are described by objects with a larger space and time scale. The technique has been successfully applied to many low-dimensional dynamical systems and much effort has recently been made to extend its use to spatially extended systems. For one-dimensional systems such as the Kuramoto-Sivashinsky equation, the method turns out to be very effective while for more complex real-world systems including the Navier-Stokes equation, the method is only starting to yield its first fruits and much more work is needed to enable practical computations. However, the experience and knowledge accumulated so far is already very useful to a large set of research problems. Several such applications are briefly described in what follows. As more research effort is devoted to the study of complex dynamics of nonlinear systems, cycle expansion will undergo a fast development and find wide applications.

Flexible fuel cell gas manifold system

DOEpatents

Cramer, Michael; Shah, Jagdish; Hayes, Richard P.; Kelley, Dana A.

2005-05-03

A fuel cell stack manifold system in which a flexible manifold body includes a pan having a central area, sidewall extending outward from the periphery of the central area, and at least one compound fold comprising a central area fold connecting adjacent portions of the central area and extending between opposite sides of the central area, and a sidewall fold connecting adjacent portions of the sidewall. The manifold system further includes a rail assembly for attachment to the manifold body and adapted to receive pins by which dielectric insulators are joined to the manifold assembly.

Research on the transfers to Halo orbits from the view of invariant manifolds

NASA Astrophysics Data System (ADS)

Xu, Ming; Tan, Tian; Xu, ShiJie

2012-04-01

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincaré map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust (acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all controlled manifolds are captured because they lie inside the boundary of Earth's gravity trap in the configuration space. The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single- impulse flyby trajectories.

Microchannel heat sink assembly

DOEpatents

Bonde, Wayne L.; Contolini, Robert J.

1992-01-01

The present invention provides a microchannel heat sink with a thermal range from cryogenic temperatures to several hundred degrees centigrade. The heat sink can be used with a variety of fluids, such as cryogenic or corrosive fluids, and can be operated at a high pressure. The heat sink comprises a microchannel layer preferably formed of silicon, and a manifold layer preferably formed of glass. The manifold layer comprises an inlet groove and outlet groove which define an inlet manifold and an outlet manifold. The inlet manifold delivers coolant to the inlet section of the microchannels, and the outlet manifold receives coolant from the outlet section of the microchannels. In one embodiment, the manifold layer comprises an inlet hole extending through the manifold layer to the inlet manifold, and an outlet hole extending through the manifold layer to the outlet manifold. Coolant is supplied to the heat sink through a conduit assembly connected to the heat sink. A resilient seal, such as a gasket or an O-ring, is disposed between the conduit and the hole in the heat sink in order to provide a watetight seal. In other embodiments, the conduit assembly may comprise a metal tube which is connected to the heat sink by a soft solder. In still other embodiments, the heat sink may comprise inlet and outlet nipples. The present invention has application in supercomputers, integrated circuits and other electronic devices, and is suitable for cooling materials to superconducting temperatures.

Manifolds, Tensors, and Forms

NASA Astrophysics Data System (ADS)

Renteln, Paul

2013-11-01

Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.

Fluid delivery manifolds and microfluidic systems

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

Renzi, Ronald F.; Sommer, Gregory J.; Singh, Anup K.

2017-02-28

Embodiments of fluid distribution manifolds, cartridges, and microfluidic systems are described herein. Fluid distribution manifolds may include an insert member and a manifold base and may define a substantially closed channel within the manifold when the insert member is press-fit into the base. Cartridges described herein may allow for simultaneous electrical and fluidic interconnection with an electrical multiplex board and may be held in place using magnetic attraction.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Small covers of graph-associahedra and realization of cycles

NASA Astrophysics Data System (ADS)

Gaifullin, A. A.

2016-11-01

An oriented connected closed manifold M^n is called a URC-manifold if for any oriented connected closed manifold N^n of the same dimension there exists a nonzero-degree mapping of a finite-fold covering \\widehat{M}^n of M^n onto N^n. This condition is equivalent to the following: for any n-dimensional integral homology class of any topological space X, a multiple of it can be realized as the image of the fundamental class of a finite-fold covering \\widehat{M}^n of M^n under a continuous mapping f\\colon \\widehat{M}^n\\to X. In 2007 the author gave a constructive proof of Thom's classical result that a multiple of any integral homology class can be realized as an image of the fundamental class of an oriented smooth manifold. This construction yields the existence of URC-manifolds of all dimensions. For an important class of manifolds, the so-called small covers of graph-associahedra corresponding to connected graphs, we prove that either they or their two-fold orientation coverings are URC-manifolds. In particular, we obtain that the two-fold covering of the small cover of the usual Stasheff associahedron is a URC-manifold. In dimensions 4 and higher, this manifold is simpler than all the previously known URC-manifolds. Bibliography: 39 titles.

Nose-only exposure system

DOEpatents

Cannon, William C.; Bass, Edward W.; Decker, Jr., John R.

1988-01-01

An exposure system for supplying a gaseous material, i.e. an aerosol, gas or a vapor, directly to the noses of experimental animals includes concentric vertical inner and outer manifolds. The outer manifold connects with the necks of a large number of bottles in which the animals are confined with their noses adjacent the bottle necks. Readily detachable small tubes communicate with the inner manifold and extend to the necks of the bottles. The upper end of the outer manifold and the lower end of the inner manifold are closed. Gaseous material is supplied to the upper end of the inner manifold, flows through the small tubes to points adjacent the noses of the individual animals, then is drawn out through the bottom of the outer manifold. The bottles are readily removable and the device can be disassembled, e.g., for cleaning, by removing the bottles, removing the small tubes, and lifting the inner manifold from the outer manifold. The bottles are supported by engagement of their necks with the outer manifold supplemented, if additional support is required, by individual wire cradles. The outer ends of the bottles are closed by plugs, through which pass metal tubes which receive the tails of the animals (usually rodents) and which serve to dissipate body heat. The entire device is mounted for rotation on turntable bearings.

Prediction of high-dimensional states subject to respiratory motion: a manifold learning approach

NASA Astrophysics Data System (ADS)

Liu, Wenyang; Sawant, Amit; Ruan, Dan

2016-07-01

The development of high-dimensional imaging systems in image-guided radiotherapy provides important pathways to the ultimate goal of real-time full volumetric motion monitoring. Effective motion management during radiation treatment usually requires prediction to account for system latency and extra signal/image processing time. It is challenging to predict high-dimensional respiratory motion due to the complexity of the motion pattern combined with the curse of dimensionality. Linear dimension reduction methods such as PCA have been used to construct a linear subspace from the high-dimensional data, followed by efficient predictions on the lower-dimensional subspace. In this study, we extend such rationale to a more general manifold and propose a framework for high-dimensional motion prediction with manifold learning, which allows one to learn more descriptive features compared to linear methods with comparable dimensions. Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where accurate and efficient prediction can be performed. A fixed-point iterative pre-image estimation method is used to recover the predicted value in the original state space. We evaluated and compared the proposed method with a PCA-based approach on level-set surfaces reconstructed from point clouds captured by a 3D photogrammetry system. The prediction accuracy was evaluated in terms of root-mean-squared-error. Our proposed method achieved consistent higher prediction accuracy (sub-millimeter) for both 200 ms and 600 ms lookahead lengths compared to the PCA-based approach, and the performance gain was statistically significant.

Microchannel heat sink assembly

DOEpatents

Bonde, W.L.; Contolini, R.J.

1992-03-24

The present invention provides a microchannel heat sink with a thermal range from cryogenic temperatures to several hundred degrees centigrade. The heat sink can be used with a variety of fluids, such as cryogenic or corrosive fluids, and can be operated at a high pressure. The heat sink comprises a microchannel layer preferably formed of silicon, and a manifold layer preferably formed of glass. The manifold layer comprises an inlet groove and outlet groove which define an inlet manifold and an outlet manifold. The inlet manifold delivers coolant to the inlet section of the microchannels, and the outlet manifold receives coolant from the outlet section of the microchannels. In one embodiment, the manifold layer comprises an inlet hole extending through the manifold layer to the inlet manifold, and an outlet hole extending through the manifold layer to the outlet manifold. Coolant is supplied to the heat sink through a conduit assembly connected to the heat sink. A resilient seal, such as a gasket or an O-ring, is disposed between the conduit and the hole in the heat sink in order to provide a watertight seal. In other embodiments, the conduit assembly may comprise a metal tube which is connected to the heat sink by a soft solder. In still other embodiments, the heat sink may comprise inlet and outlet nipples. The present invention has application in supercomputers, integrated circuits and other electronic devices, and is suitable for cooling materials to superconducting temperatures. 13 figs.

Spectroscopic and Magnetic Investigations of Rhenium(i)chlorine(carbon MONOXIDE)(3)(ALPHA, - Complexes and Group (1B, 8B) Bimetallic Complexes.

NASA Astrophysics Data System (ADS)

Striplin, Durwin Ray

Complexes with the generic formula, Re(I)Cl(CO) _3(alpha,alpha-diimine), where alpha,alpha-diimine = 2,2^'-bipyridine, 1,10 -phenanthroline, or methyl-substituted analogs, were subjected to detailed optical investigations in the 77-4 K range, both in rigid glasses and in PMMA plastics. Excitation spectra, absorption spectra, and decay kinetics of the phosphorescing manifolds were complemented by detailed measurements of polarization ratios to arrive at a coherent picture of the emitting manifolds. Symmetry assignments and energy orderings of the ^3MLCT (metal-to-ligand charge transfer) spin sublevels were made. Analogous assignments for the ^3MLCT spin -sublevels of Ru(alpha, alpha -diimine)_3^{2+} and Os(alpha,alpha-diimine) _{3}^{2+} ions are implied by this analysis. Increases in luminescence decay rates and emission intensities with increasing external magnetic field strength were observed at 4 K. The decay rates were found to be non-quadratic with respect to magnetic field strength. A simple parametric model that includes spin-orbit coupling and a magnetic field perturbation was developed to describe the MLCT excited states. The energies, symmetry assignments, and magnetic field mixing of the ^3MLCT states were rationalized by the model. Fluorescence, phosphorescence, and excitation spectra were measured on a series of mu -bridged bis(diphenylphosphinomethane) homo- and heterobimetallic compounds of Rh(I), Ir(I), Pt(II), and Au(I). These results were augmented with polarization ratios obtained at 77 K and detailed studies of the temperature dependence of the phosphorescence in the 77-4 K range. The triplet manifold is split by spin-orbit coupling into a forbidden state lying lowest in energy followed by a quasi-degenerate pair lying a few wavenumbers higher that decays two orders of magnitude faster. A quadratic dependence of the decay rate on magnetic field strength was recorded at 4 K for ail complexes. The results are consistent with a rm d_{sigma*}to p_sigma orbital promotion, and the direction of charge-transfer for heterobimetallic complexes was unambiguously assigned. Electronic structural models based on D_{rm 4h}, D_{rm 2h}, and C _{rm 2v} micro-symmetries about the axial chromophore were employed to make explicit symmetry assignments of the excited states.

Microwave waveguide manifold and method

DOEpatents

Staehlin, John H.

1987-01-01

A controllably electrically coupled, physically intersecting plural waveguide manifold assembly wherein the intersecting waveguide elements are fabricated in integral unitary relationship from a single piece of metal in order to avoid the inaccuracies and difficult-to-control fabrication steps associated with uniting separate waveguide elements into a unitary structure. An X-band aluminum airborne radar manifold example is disclosed, along with a fabrication sequence for the manifold and the electrical energy communicating apertures joining the manifold elements.

Microwave waveguide manifold and method

DOEpatents

Staehlin, John H.

1987-12-01

A controllably electrically coupled, physically intersecting plural waveguide manifold assembly wherein the intersecting waveguide elements are fabricated in integral unitary relationship from a single piece of metal in order to avoid the inaccuracies and difficult-to-control fabrication steps associated with uniting separate waveguide elements into a unitary structure. An X-band aluminum airborne radar manifold example is disclosed, along with a fabrication sequence for the manifold and the electrical energy communicating apertures joining the manifold elements.

Manifold learning-based subspace distance for machinery damage assessment

NASA Astrophysics Data System (ADS)

Sun, Chuang; Zhang, Zhousuo; He, Zhengjia; Shen, Zhongjie; Chen, Binqiang

2016-03-01

Damage assessment is very meaningful to keep safety and reliability of machinery components, and vibration analysis is an effective way to carry out the damage assessment. In this paper, a damage index is designed by performing manifold distance analysis on vibration signal. To calculate the index, vibration signal is collected firstly, and feature extraction is carried out to obtain statistical features that can capture signal characteristics comprehensively. Then, manifold learning algorithm is utilized to decompose feature matrix to be a subspace, that is, manifold subspace. The manifold learning algorithm seeks to keep local relationship of the feature matrix, which is more meaningful for damage assessment. Finally, Grassmann distance between manifold subspaces is defined as a damage index. The Grassmann distance reflecting manifold structure is a suitable metric to measure distance between subspaces in the manifold. The defined damage index is applied to damage assessment of a rotor and the bearing, and the result validates its effectiveness for damage assessment of machinery component.

Geodesic Monte Carlo on Embedded Manifolds

PubMed Central

Byrne, Simon; Girolami, Mark

2013-01-01

Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

Modular robot

DOEpatents

Ferrante, Todd A.

1997-01-01

A modular robot may comprise a main body having a structure defined by a plurality of stackable modules. The stackable modules may comprise a manifold, a valve module, and a control module. The manifold may comprise a top surface and a bottom surface having a plurality of fluid passages contained therein, at least one of the plurality of fluid passages terminating in a valve port located on the bottom surface of the manifold. The valve module is removably connected to the manifold and selectively fluidically connects the plurality of fluid passages contained in the manifold to a supply of pressurized fluid and to a vent. The control module is removably connected to the valve module and actuates the valve module to selectively control a flow of pressurized fluid through different ones of the plurality of fluid passages in the manifold. The manifold, valve module, and control module are mounted together in a sandwich-like manner and comprise a main body. A plurality of leg assemblies are removably connected to the main body and are removably fluidically connected to the fluid passages in the manifold so that each of the leg assemblies can be selectively actuated by the flow of pressurized fluid in different ones of the plurality of fluid passages in the manifold.

Calculation of flow about posts and powerhead model

NASA Technical Reports Server (NTRS)

1988-01-01

A large number of computational fluid mechanics (CFD) problems were investigated. The primary studies include: the analysis of the turnaround duct/hot gas manifold/transfer tubes (fuel side) of the Space Shuttle Main Engine (SSME); the analysis of the LOX-T manifold (oxidizer side) of the SSME; the analysis of hydrogen accumulation in the Vandeburg flame trench; and modification of the Intel/VT241 systems to accommodate the EADS and PLOT 3D. Some of the analyses were exploratory in nature, using the CONTINUSYS code to provide preliminary information to enhance understanding of the problem, while in other the primary thrust was to acquire design information. In all cases the ability to predict information rapidly in these very complex analyses is seen to be an important demonstration of the power and utility of this mature predictive capability.

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

DOE PAGES

Alexandru, Andrei; Basar, Gokce; Bedaque, Paulo F.; ...

2016-05-10

We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). As a result, we exemplify this approach using amore » simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.« less

Brazing retort manifold design concept may minimize air contamination and enhance uniform gas flow

NASA Technical Reports Server (NTRS)

Ruppe, E. P.

1966-01-01

Brazing retort manifold minimizes air contamination, prevents gas entrapment during purging, and provides uniform gas flow into the retort bell. The manifold is easily cleaned and turbulence within the bell is minimized because all manifold construction lies outside the main enclosure.

Fluid manifold design for a solar energy storage tank

NASA Technical Reports Server (NTRS)

Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.

1975-01-01

A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

New families of interpolating type IIB backgrounds

NASA Astrophysics Data System (ADS)

Minasian, Ruben; Petrini, Michela; Zaffaroni, Alberto

2010-04-01

We construct new families of interpolating two-parameter solutions of type IIB supergravity. These correspond to D3-D5 systems on non-compact six-dimensional manifolds which are mathbb{T}2 fibrations over Eguchi-Hanson and multi-center Taub-NUT spaces, respectively. One end of the interpolation corresponds to a solution with only D5 branes and vanishing NS three-form flux. A topology changing transition occurs at the other end, where the internal space becomes a direct product of the four-dimensional surface and the two-torus and the complexified NS-RR three-form flux becomes imaginary self-dual. Depending on the choice of the connections on the torus fibre, the interpolating family has either mathcal{N}=2 or mathcal{N}=1 supersymmetry. In the mathcal{N}=2 case it can be shown that the solutions are regular.

21 CFR 870.4290 - Cardiopulmonary bypass adaptor, stopcock, manifold, or fitting.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Cardiopulmonary bypass adaptor, stopcock, manifold... Devices § 870.4290 Cardiopulmonary bypass adaptor, stopcock, manifold, or fitting. (a) Identification. A cardiopulmonary bypass adaptor, stopcock, manifold, or fitting is a device used in cardiovascular diagnostic...

21 CFR 870.4290 - Cardiopulmonary bypass adaptor, stopcock, manifold, or fitting.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Cardiopulmonary bypass adaptor, stopcock, manifold... Devices § 870.4290 Cardiopulmonary bypass adaptor, stopcock, manifold, or fitting. (a) Identification. A cardiopulmonary bypass adaptor, stopcock, manifold, or fitting is a device used in cardiovascular diagnostic...

Geometry of quantum state manifolds generated by the Lie algebra operators

NASA Astrophysics Data System (ADS)

Kuzmak, A. R.

2018-03-01

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results, we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

Dual manifold system and method for fluid transfer

DOEpatents

Doktycz, Mitchel J [Knoxville, TN; Bryan, William Louis [Knoxville, TN; Kress, Reid [Oak Ridge, TN

2003-05-27

A dual-manifold assembly is provided for the rapid, parallel transfer of liquid reagents from a microtiter plate to a solid state microelectronic device having biological sensors integrated thereon. The assembly includes aspiration and dispense manifolds connected by a plurality of conduits. In operation, the aspiration manifold is actuated such that the aspiration manifold is seated onto an array of reagent-filled wells of the microtiter plate. The wells are pressurized to force reagent through conduits toward the dispense manifold. A pressure pulse provided by a standard ink-jet printhead ejects nanoliter-to-picoliter droplets of reagent through an array of printhead orifices and onto test sites on the surface of the microelectronic device.

Dual manifold system and method for fluid transfer

DOEpatents

Doktycz, Mitchel J.; Bryan, William Louis; Kress, Reid

2003-09-30

A dual-manifold assembly is provided for the rapid, parallel transfer of liquid reagents from a microtiter plate to a solid state microelectronic device having biological sensors integrated thereon. The assembly includes aspiration and dispense manifolds connected by a plurality of conduits. In operation, the aspiration manifold is actuated such that the aspiration manifold is seated onto an array of reagent-filled wells of the microtiter plate. The wells are pressurized to force reagent through conduits toward the dispense manifold. A pressure pulse provided by a standard ink-jet printhead ejects nanoliter-to-picoliter droplets of reagent through an array of printhead orifices and onto test sites on the surface of the microelectronic device.

Monopolar fuel cell stack coupled together without use of top or bottom cover plates or tie rods

NASA Technical Reports Server (NTRS)

Narayanan, Sekharipuram R. (Inventor); Valdez, Thomas I. (Inventor)

2009-01-01

A monopolar fuel cell stack comprises a plurality of sealed unit cells coupled together. Each unit cell comprises two outer cathodes adjacent to corresponding membrane electrode assemblies and a center anode plate. An inlet and outlet manifold are coupled to the anode plate and communicate with a channel therein. Fuel flows from the inlet manifold through the channel in contact with the anode plate and flows out through the outlet manifold. The inlet and outlet manifolds are arranged to couple to the inlet and outlet manifolds respectively of an adjacent one of the plurality of unit cells to permit fuel flow in common into all of the inlet manifolds of the plurality of the unit cells when coupled together in a stack and out of all of the outlet manifolds of the plurality of unit cells when coupled together in a stack.

Towards a double field theory on para-Hermitian manifolds

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

Vaisman, Izu

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action ofmore » the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.« less

Active contours on statistical manifolds and texture segmentation

Treesearch

Sang-Mook Lee; A. Lynn Abbott; Neil A. Clark; Philip A. Araman

2005-01-01

A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2- dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto a set of probability density functions. In this novel framework, color or texture features are measured at each image point and their statistical...

Multipoint Fuel Injection Arrangements

NASA Technical Reports Server (NTRS)

Prociw, Lev Alexander (Inventor)

2017-01-01

A multipoint fuel injection system includes a plurality of fuel manifolds. Each manifold is in fluid communication with a plurality of injectors arranged circumferentially about a longitudinal axis for multipoint fuel injection. The injectors of separate respective manifolds are spaced radially apart from one another for separate radial staging of fuel flow to each respective manifold.

Active contours on statistical manifolds and texture segmentaiton

Treesearch

Sang-Mook Lee; A. Lynn Abbott; Neil A. Clark; Philip A. Araman

2005-01-01

A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2- dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto-a set of probability density functions. In this novel framework, color or texture features are measured at each Image point and their statistical...

Optimal transfers between unstable periodic orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.; Anderson, Rodney L.; Scheeres, Daniel J.; Born, George H.

2011-03-01

This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between unstable periodic orbits in the Sun-Earth, Earth-Moon, and Jupiter-Europa three-body systems. Multiple solutions are found between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost is accompanied by an increase in transfer time of flight.

Modular robot

DOEpatents

Ferrante, T.A.

1997-11-11

A modular robot may comprise a main body having a structure defined by a plurality of stackable modules. The stackable modules may comprise a manifold, a valve module, and a control module. The manifold may comprise a top surface and a bottom surface having a plurality of fluid passages contained therein, at least one of the plurality of fluid passages terminating in a valve port located on the bottom surface of the manifold. The valve module is removably connected to the manifold and selectively fluidically connects the plurality of fluid passages contained in the manifold to a supply of pressurized fluid and to a vent. The control module is removably connected to the valve module and actuates the valve module to selectively control a flow of pressurized fluid through different ones of the plurality of fluid passages in the manifold. The manifold, valve module, and control module are mounted together in a sandwich-like manner and comprise a main body. A plurality of leg assemblies are removably connected to the main body and are removably fluidically connected to the fluid passages in the manifold so that each of the leg assemblies can be selectively actuated by the flow of pressurized fluid in different ones of the plurality of fluid passages in the manifold. 12 figs.

Arrhythmia Mechanism and Scaling Effect on the Spectral Properties of Electroanatomical Maps With Manifold Harmonics.

PubMed

Sanroman-Junquera, Margarita; Mora-Jimenez, Inmaculada; Garcia-Alberola, Arcadio; Caamano, Antonio J; Trenor, Beatriz; Rojo-Alvarez, Jose L

2018-04-01

Spatial and temporal processing of intracardiac electrograms provides relevant information to support the arrhythmia ablation during electrophysiological studies. Current cardiac navigation systems (CNS) and electrocardiographic imaging (ECGI) build detailed 3-D electroanatomical maps (EAM), which represent the spatial anatomical distribution of bioelectrical features, such as activation time or voltage. We present a principled methodology for spectral analysis of both EAM geometry and bioelectrical feature in CNS or ECGI, including their spectral representation, cutoff frequency, or spatial sampling rate (SSR). Existing manifold harmonic techniques for spectral mesh analysis are adapted to account for a fourth dimension, corresponding to the EAM bioelectrical feature. Appropriate scaling is required to address different magnitudes and units. With our approach, simulated and real EAM showed strong SSR dependence on both the arrhythmia mechanism and the cardiac anatomical shape. For instance, high frequencies increased significantly the SSR because of the "early-meets-late" in flutter EAM, compared with the sinus rhythm. Besides, higher frequency components were obtained for the left atrium (more complex anatomy) than for the right atrium in sinus rhythm. The proposed manifold harmonics methodology opens the field toward new signal processing tools for principled EAM spatiofeature analysis in CNS and ECGI, and to an improved knowledge on arrhythmia mechanisms.

Manifold optimization-based analysis dictionary learning with an ℓ1∕2-norm regularizer.

PubMed

Li, Zhenni; Ding, Shuxue; Li, Yujie; Yang, Zuyuan; Xie, Shengli; Chen, Wuhui

2018-02-01

Recently there has been increasing attention towards analysis dictionary learning. In analysis dictionary learning, it is an open problem to obtain the strong sparsity-promoting solutions efficiently while simultaneously avoiding the trivial solutions of the dictionary. In this paper, to obtain the strong sparsity-promoting solutions, we employ the ℓ 1∕2 norm as a regularizer. The very recent study on ℓ 1∕2 norm regularization theory in compressive sensing shows that its solutions can give sparser results than using the ℓ 1 norm. We transform a complex nonconvex optimization into a number of one-dimensional minimization problems. Then the closed-form solutions can be obtained efficiently. To avoid trivial solutions, we apply manifold optimization to update the dictionary directly on the manifold satisfying the orthonormality constraint, so that the dictionary can avoid the trivial solutions well while simultaneously capturing the intrinsic properties of the dictionary. The experiments with synthetic and real-world data verify that the proposed algorithm for analysis dictionary learning can not only obtain strong sparsity-promoting solutions efficiently, but also learn more accurate dictionary in terms of dictionary recovery and image processing than the state-of-the-art algorithms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Locally optimal transfer trajectories between libration point orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.

2009-12-01

Techniques from dynamical systems theory and primer vector theory have been applied to the construction of locally optimal transfer trajectories between libration point orbits. When two libration point orbits have different energies, it has been found that the unstable manifold of the first orbit can be connected to the stable manifold of the second orbit with a bridging trajectory. A bounding sphere centered on the secondary, with a radius less than the radius of the sphere of influence of the secondary, was used to study the stable and unstable manifold trajectories. It was numerically demonstrated that within the bounding sphere, the two-body parameters of the unstable and stable manifold trajectories could be analyzed to locate low transfer costs. It was shown that as the two-body parameters of an unstable manifold trajectory more closely matched the two-body parameters of a stable manifold trajectory, the total DeltaV necessary to complete the transfer decreased. Primer vector theory was successfully applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connected the unstable manifold of the first orbit to the stable manifold of the second orbit. Transfer trajectories were constructed between halo orbits in the Sun-Earth and Earth-Moon three-body systems. Multiple solutions were found between the same initial and final orbits, where certain solutions retraced interior portions of the trajectory. All of the trajectories created satisfied the conditions for optimality. The costs of transfers constructed using invariant manifolds were compared to the costs of transfers constructed without the use of invariant manifolds, when data was available. In all cases, the total cost of the transfers were significantly lower when invariant manifolds were used in the transfer construction. In many cases, the transfers that employed invariant manifolds were three to four times more efficient, in terms of fuel expenditure, than the transfer that did not. The decrease in transfer cost was accompanied by an increase in transfer time of flight. Transfers constructed in the Earth-Moon system were shown to be particularly viable for lunar navigation and communication constellations, as excellent coverage of the lunar surface can be achieved during the transfer.

Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields

NASA Astrophysics Data System (ADS)

Díaz-Marín, Homero G.

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.

A New Theory of Trajectory Design and NASA's Vision

NASA Technical Reports Server (NTRS)

Folta, David

2006-01-01

This new theory is defined as the use of chaos to design trajectories and orbits that can be used to meet complex mission goals. The benefits are; a) minimizes fuel costs; b) optimizes trajectory profiles; c) provides non-standard and new orbit designs; and d) mitigates operational risks. Other synonymous terms include dynamical systems, invariant manifolds, capture orbits and ballistic orbits.

Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams

PubMed Central

Beims, Marcus W.; Gallas, Jason A. C.

2016-01-01

Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems. PMID:26732416

Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams

NASA Astrophysics Data System (ADS)

Beims, Marcus W.; Gallas, Jason A. C.

2016-01-01

Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems.

A light writable microfluidic "flash memory": optically addressed actuator array with latched operation for microfluidic applications.

PubMed

Hua, Zhishan; Pal, Rohit; Srivannavit, Onnop; Burns, Mark A; Gulari, Erdogan

2008-03-01

This paper presents a novel optically addressed microactuator array (microfluidic "flash memory") with latched operation. Analogous to the address-data bus mediated memory address protocol in electronics, the microactuator array consists of individual phase-change based actuators addressed by localized heating through focused light patterns (address bus), which can be provided by a modified projector or high power laser pointer. A common pressure manifold (data bus) for the entire array is used to generate large deflections of the phase change actuators in the molten phase. The use of phase change material as the working media enables latched operation of the actuator array. After the initial light "writing" during which the phase is temporarily changed to molten, the actuated status is self-maintained by the solid phase of the actuator without power and pressure inputs. The microfluidic flash memory can be re-configured by a new light illumination pattern and common pressure signal. The proposed approach can achieve actuation of arbitrary units in a large-scale array without the need for complex external equipment such as solenoid valves and electrical modules, which leads to significantly simplified system implementation and compact system size. The proposed work therefore provides a flexible, energy-efficient, and low cost multiplexing solution for microfluidic applications based on physical displacements. As an example, the use of the latched microactuator array as "normally closed" or "normally open" microvalves is demonstrated. The phase-change wax is fully encapsulated and thus immune from contamination issues in fluidic environments.

Engine Air Intake Manifold Having Built In Intercooler

DOEpatents

Freese, V, Charles E.

2000-09-12

A turbocharged V type engine can be equipped with an exhaust gas recirculation cooler integrated into the intake manifold, so as to achieve efficiency, cost reductions and space economization improvements. The cooler can take the form of a tube-shell heat exchanger that utilizes a cylindrical chamber in the air intake manifold as the heat exchanger housing. The intake manifold depends into the central space formed by the two banks of cylinders on the V type engine, such that the central space is effectively utilized for containing the manifold and cooler.

Data-driven non-linear elasticity: constitutive manifold construction and problem discretization

NASA Astrophysics Data System (ADS)

Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco

2017-11-01

The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.

Physics from geometry: Non-Kahler compactifications, black rings anddS/CFT

NASA Astrophysics Data System (ADS)

Cyrier, Michelle

The spectrum that arises in four dimensions from compactification of ten dimensional string theory onto six dimensional manifolds is determined entirely by the geometry of the compactification manifold. The massless spectrum for compactifications on Calabi-Yau threefolds, which are Kahler and have complex structure, is well understood. In chapter 2 of this thesis, We study the compactification of heterotic string theory on manifolds that are non-Kahler. Such manifolds arise as a solution for compactifications of heterotic string theory with nonzero H-flux. We begin the study of the massless spectrum arising from compactification using this construction by counting zero modes of the linearized equations of motion for the gaugino in the supergravity approximation. We rephrase the question in terms of a cohomology problem and show that for a trivial gauge bundle, this cohomology reduces to the Dolbeault cohomology of the 3-fold, which we then compute. Another check of string theory is to study the entropy of black holes made in string theory. In Chapter 3, We review the microstate counting of four dimensional black holes made from M theory. We then describe a new solution in five dimensions, the supersymmetric black ring, and describe its microscopic entropy using a similar counting. These agree with the semi-classical Bekenstein-Hawking entropy for these black holes. Finally, one powerful tool for quantum gravity is the holographic duality of string theory in an Anti de Sitter background and a theory living on its conformal boundary. Strominger conjectured a similar duality between quantum gravity in a de Sitter background and the corresponding theory on its boundary. In chapter 4 we examine issues with different representations of the conformal field theory on the boundary for a massive quantum field theory living in the bulk and try to write down a sensible CFT.

Complexity and chaos control in a discrete-time prey-predator model

NASA Astrophysics Data System (ADS)

Din, Qamar

2017-08-01

We investigate the complex behavior and chaos control in a discrete-time prey-predator model. Taking into account the Leslie-Gower prey-predator model, we propose a discrete-time prey-predator system with predator partially dependent on prey and investigate the boundedness, existence and uniqueness of positive equilibrium and bifurcation analysis of the system by using center manifold theorem and bifurcation theory. Various feedback control strategies are implemented for controlling the bifurcation and chaos in the system. Numerical simulations are provided to illustrate theoretical discussion.

COMBINED DELAY AND GRAPH EMBEDDING OF EPILEPTIC DISCHARGES IN EEG REVEALS COMPLEX AND RECURRENT NONLINEAR DYNAMICS.

PubMed

Erem, B; Hyde, D E; Peters, J M; Duffy, F H; Brooks, D H; Warfield, S K

2015-04-01

The dynamical structure of the brain's electrical signals contains valuable information about its physiology. Here we combine techniques for nonlinear dynamical analysis and manifold identification to reveal complex and recurrent dynamics in interictal epileptiform discharges (IEDs). Our results suggest that recurrent IEDs exhibit some consistent dynamics, which may only last briefly, and so individual IED dynamics may need to be considered in order to understand their genesis. This could potentially serve to constrain the dynamics of the inverse source localization problem.

The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

NASA Astrophysics Data System (ADS)

Abe, Mitsuko

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein-Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some bar ∂ -torsions. bar ∂ -torsion is the extension of R-torsion for the de Rham complex to that for the bar ∂ -complex of a complex analytic manifold.

Elegant Gaussian beams for enhanced optical manipulation

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

Alpmann, Christina, E-mail: c.alpmann@uni-muenster.de; Schöler, Christoph; Denz, Cornelia

2015-06-15

Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread functionmore » is relevant.« less

Homological Order in Three and Four dimensions: Wilson Algebra, Entanglement Entropy and Twist Defects

NASA Astrophysics Data System (ADS)

Roy, Abhishek; Chen, Xiao; Teo, Jeffrey

2013-03-01

We investigate homological orders in two, three and four dimensions by studying Zk toric code models on simplicial, cellular or in general differential complexes. The ground state degeneracy is obtained from Wilson loop and surface operators, and the homological intersection form. We compute these for a series of closed 3 and 4 dimensional manifolds and study the projective representations of mapping class groups (modular transformations). Braiding statistics between point and string excitations in (3+1)-dimensions or between dual string excitations in (4+1)-dimensions are topologically determined by the higher dimensional linking number, and can be understood by an effective topological field theory. An algorithm for calculating entanglemnent entropy of any bipartition of closed manifolds is presented, and its topological signature is completely characterized homologically. Extrinsic twist defects (or disclinations) are studied in 2,3 and 4 dimensions and are shown to carry exotic fusion and braiding properties. Simons Fellowship

The Infinitesimal Moduli Space of Heterotic G 2 Systems

NASA Astrophysics Data System (ADS)

de la Ossa, Xenia; Larfors, Magdalena; Svanes, Eirik E.

2018-06-01

Heterotic string compactifications on integrable G 2 structure manifolds Y with instanton bundles {(V,A), (TY,\\tilde{θ})} yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative D and show that it is equivalent to a heterotic G 2 system encoding the geometry of the heterotic string compactifications. This operator D acts on a bundle Q}=T^*Y \\oplus End(V) \\oplus End(TY)} and satisfies a nilpotency condition \\check{{D^2=0} , for an appropriate projection of D. Furthermore, we determine the infinitesimal moduli space of these systems and show that it corresponds to the finite-dimensional cohomology group H^1_{D}(Q). We comment on the similarities and differences of our result with Atiyah's well-known analysis of deformations of holomorphic vector bundles over complex manifolds. Our analysis leads to results that are of relevance to all orders in the {α'} expansion.

Bifurcation study of phase oscillator systems with attractive and repulsive interaction.

PubMed

Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman

2014-08-01

We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.

Bifurcation study of phase oscillator systems with attractive and repulsive interaction

NASA Astrophysics Data System (ADS)

Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman

2014-08-01

We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.

Mapping the Complete Reaction Path of a Complex Photochemical Reaction.

PubMed

Smith, Adam D; Warne, Emily M; Bellshaw, Darren; Horke, Daniel A; Tudorovskya, Maria; Springate, Emma; Jones, Alfred J H; Cacho, Cephise; Chapman, Richard T; Kirrander, Adam; Minns, Russell S

2018-05-04

We probe the dynamics of dissociating CS_{2} molecules across the entire reaction pathway upon excitation. Photoelectron spectroscopy measurements using laboratory-generated femtosecond extreme ultraviolet pulses monitor the competing dissociation, internal conversion, and intersystem crossing dynamics. Dissociation occurs either in the initially excited singlet manifold or, via intersystem crossing, in the triplet manifold. Both product channels are monitored and show that, despite being more rapid, the singlet dissociation is the minor product and that triplet state products dominate the final yield. We explain this by a consideration of accurate potential energy curves for both the singlet and triplet states. We propose that rapid internal conversion stabilizes the singlet population dynamically, allowing for singlet-triplet relaxation via intersystem crossing and the efficient formation of spin-forbidden dissociation products on longer timescales. The study demonstrates the importance of measuring the full reaction pathway for defining accurate reaction mechanisms.

Mapping the Complete Reaction Path of a Complex Photochemical Reaction

NASA Astrophysics Data System (ADS)

Smith, Adam D.; Warne, Emily M.; Bellshaw, Darren; Horke, Daniel A.; Tudorovskya, Maria; Springate, Emma; Jones, Alfred J. H.; Cacho, Cephise; Chapman, Richard T.; Kirrander, Adam; Minns, Russell S.

2018-05-01

We probe the dynamics of dissociating CS2 molecules across the entire reaction pathway upon excitation. Photoelectron spectroscopy measurements using laboratory-generated femtosecond extreme ultraviolet pulses monitor the competing dissociation, internal conversion, and intersystem crossing dynamics. Dissociation occurs either in the initially excited singlet manifold or, via intersystem crossing, in the triplet manifold. Both product channels are monitored and show that, despite being more rapid, the singlet dissociation is the minor product and that triplet state products dominate the final yield. We explain this by a consideration of accurate potential energy curves for both the singlet and triplet states. We propose that rapid internal conversion stabilizes the singlet population dynamically, allowing for singlet-triplet relaxation via intersystem crossing and the efficient formation of spin-forbidden dissociation products on longer timescales. The study demonstrates the importance of measuring the full reaction pathway for defining accurate reaction mechanisms.

Cohomological rigidity of manifolds defined by 3-dimensional polytopes

NASA Astrophysics Data System (ADS)

Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.

2017-04-01

A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.

Wave equations on anti self dual (ASD) manifolds

NASA Astrophysics Data System (ADS)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

Manifold gasket accommodating differential movement of fuel cell stack

DOEpatents

Kelley, Dana A.; Farooque, Mohammad

2007-11-13

A gasket for use in a fuel cell system having at least one externally manifolded fuel cell stack, for sealing the manifold edge and the stack face. In accordance with the present invention, the gasket accommodates differential movement between the stack and manifold by promoting slippage at interfaces between the gasket and the dielectric and between the gasket and the stack face.

Scalable microreactors and methods for using same

DOEpatents

Lawal, Adeniyi; Qian, Dongying

2010-03-02

The present invention provides a scalable microreactor comprising a multilayered reaction block having alternating reaction plates and heat exchanger plates that have a plurality of microchannels; a multilaminated reactor input manifold, a collecting reactor output manifold, a heat exchange input manifold and a heat exchange output manifold. The present invention also provides methods of using the microreactor for multiphase chemical reactions.

Masking Strategies for Image Manifolds.

PubMed

Dadkhahi, Hamid; Duarte, Marco F

2016-07-07

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the datadependent masking process, even for modest mask sizes.

Simultaneous high-speed gas property measurements at the exhaust gas recirculation cooler exit and at the turbocharger inlet of a multicylinder diesel engine using diode-laser-absorption spectroscopy.

PubMed

Jatana, Gurneesh S; Magee, Mark; Fain, David; Naik, Sameer V; Shaver, Gregory M; Lucht, Robert P

2015-02-10

A diode-laser-absorption-spectroscopy-based sensor system was used to perform high-speed (100 Hz to 5 kHz) measurements of gas properties (temperature, pressure, and H(2)O vapor concentration) at the turbocharger inlet and at the exhaust gas recirculation (EGR) cooler exit of a diesel engine. An earlier version of this system was previously used for high-speed measurements of gas temperature and H(2)O vapor concentration in the intake manifold of the diesel engine. A 1387.2 N m tunable distributed feedback diode laser was used to scan across multiple H(2)O absorption transitions, and the direct absorption signal was recorded using a high-speed data acquisition system. Compact optical connectors were designed to conduct simultaneous measurements in the intake manifold, the EGR cooler exit, and the turbocharger inlet of the engine. For measurements at the turbocharger inlet, these custom optical connectors survived gas temperatures as high as 800 K using a simple and passive arrangement in which the temperature-sensitive components were protected from high temperatures using ceramic insulators. This arrangement reduced system cost and complexity by eliminating the need for any active water or oil cooling. Diode-laser measurements performed during steady-state engine operation were within 5% of the thermocouple and pressure sensor measurements, and within 10% of the H(2)O concentration values derived from the CO(2) gas analyzer measurements. Measurements were also performed in the engine during transient events. In one such transient event, where a step change in fueling was introduced, the diode-laser sensor was able to capture the 30 ms change in the gas properties; the thermocouple, on the other hand, required 7.4 s to accurately reflect the change in gas conditions, while the gas analyzer required nearly 600 ms. To the best of our knowledge, this is the first implementation of such a simple and passive arrangement of high-temperature optical connectors as well as the first documented application of diode-laser absorption for high-speed gas dynamics measurements in the turbocharger inlet and EGR cooler exit of a diesel engine.

BFV-Complex and Higher Homotopy Structures

NASA Astrophysics Data System (ADS)

Schätz, Florian

2009-03-01

We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are L ∞ quasi-isomorphic and control the same formal deformation problem. However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instead.

Heterotic model building: 16 special manifolds

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Lee, Seung-Joo; Lukas, Andre; Sun, Chuang

2014-06-01

We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded from http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.

Heat shield manifold system for a midframe case of a gas turbine engine

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

Mayer, Clinton A.; Eng, Jesse; Schopf, Cheryl A.

A heat shield manifold system for an inner casing between a compressor and turbine assembly is disclosed. The heat shield manifold system protects the outer case from high temperature compressor discharge air, thereby enabling the outer case extending between a compressor and a turbine assembly to be formed from less expensive materials than otherwise would be required. In addition, the heat shield manifold system may be configured such that compressor bleed air is passed from the compressor into the heat shield manifold system without passing through a conventional flange to flange joint that is susceptible to leakage.

A comparative study of two prediction models for brain tumor progression

NASA Astrophysics Data System (ADS)

Zhou, Deqi; Tran, Loc; Wang, Jihong; Li, Jiang

2015-03-01

MR diffusion tensor imaging (DTI) technique together with traditional T1 or T2 weighted MRI scans supplies rich information sources for brain cancer diagnoses. These images form large-scale, high-dimensional data sets. Due to the fact that significant correlations exist among these images, we assume low-dimensional geometry data structures (manifolds) are embedded in the high-dimensional space. Those manifolds might be hidden from radiologists because it is challenging for human experts to interpret high-dimensional data. Identification of the manifold is a critical step for successfully analyzing multimodal MR images. We have developed various manifold learning algorithms (Tran et al. 2011; Tran et al. 2013) for medical image analysis. This paper presents a comparative study of an incremental manifold learning scheme (Tran. et al. 2013) versus the deep learning model (Hinton et al. 2006) in the application of brain tumor progression prediction. The incremental manifold learning is a variant of manifold learning algorithm to handle large-scale datasets in which a representative subset of original data is sampled first to construct a manifold skeleton and remaining data points are then inserted into the skeleton by following their local geometry. The incremental manifold learning algorithm aims at mitigating the computational burden associated with traditional manifold learning methods for large-scale datasets. Deep learning is a recently developed multilayer perceptron model that has achieved start-of-the-art performances in many applications. A recent technique named "Dropout" can further boost the deep model by preventing weight coadaptation to avoid over-fitting (Hinton et al. 2012). We applied the two models on multiple MRI scans from four brain tumor patients to predict tumor progression and compared the performances of the two models in terms of average prediction accuracy, sensitivity, specificity and precision. The quantitative performance metrics were calculated as average over the four patients. Experimental results show that both the manifold learning and deep neural network models produced better results compared to using raw data and principle component analysis (PCA), and the deep learning model is a better method than manifold learning on this data set. The averaged sensitivity and specificity by deep learning are comparable with these by the manifold learning approach while its precision is considerably higher. This means that the predicted abnormal points by deep learning are more likely to correspond to the actual progression region.

Manifold seal for fuel cell stack assembly

DOEpatents

Schmitten, Phillip F.; Wright, Maynard K.

1989-01-01

An assembly for sealing a manifold to a stack of fuel cells includes a first resilient member for providing a first sealing barrier between the manifold and the stack. A second resilient member provides a second sealing barrier between the manifold and the stack. The first and second resilient members are retained in such a manner as to define an area therebetween adapted for retaining a sealing composition.

Explorations in fuzzy physics and non-commutative geometry

NASA Astrophysics Data System (ADS)

Kurkcuoglu, Seckin

Fuzzy spaces arise as discrete approximations to continuum manifolds. They are usually obtained through quantizing coadjoint orbits of compact Lie groups and they can be described in terms of finite-dimensional matrix algebras, which for large matrix sizes approximate the algebra of functions of the limiting continuum manifold. Their ability to exactly preserve the symmetries of their parent manifolds is especially appealing for physical applications. Quantum Field Theories are built over them as finite-dimensional matrix models preserving almost all the symmetries of their respective continuum models. In this dissertation, we first focus our attention to the study of fuzzy supersymmetric spaces. In this regard, we obtain the fuzzy supersphere S2,2F through quantizing the supersphere, and demonstrate that it has exact supersymmetry. We derive a finite series formula for the *-product of functions over S2,2F and analyze the differential geometric information encoded in this formula. Subsequently, we show that quantum field theories on S2,2F are realized as finite-dimensional supermatrix models, and in particular we obtain the non-linear sigma model over the fuzzy supersphere by constructing the fuzzy supersymmetric extensions of a certain class of projectors. We show that this model too, is realized as a finite-dimensional supermatrix model with exact supersymmetry. Next, we show that fuzzy spaces have a generalized Hopf algebra structure. By focusing on the fuzzy sphere, we establish that there is a *-homomorphism from the group algebra SU(2)* of SU(2) to the fuzzy sphere. Using this and the canonical Hopf algebra structure of SU(2)* we show that both the fuzzy sphere and their direct sum are Hopf algebras. Using these results, we discuss processes in which a fuzzy sphere with angular momenta J splits into fuzzy spheres with angular momenta K and L. Finally, we study the formulation of Chern-Simons (CS) theory on an infinite strip of the non-commutative plane. We develop a finite-dimensional matrix model, whose large size limit approximates the CS theory on the infinite strip, and show that there are edge observables in this model obeying a finite-dimensional Lie algebra, that resembles the Kac-Moody algebra.

Failure Investigation of an Intra-Manifold Explosion in a Horizontally-Mounted 870 lbf Reaction Control Thruster

NASA Technical Reports Server (NTRS)

Durning, Joseph G., III; Westover, Shayne C.; Cone, Darren M.

2011-01-01

In June 2010, an 870 lbf Space Shuttle Orbiter Reaction Control System Primary Thruster experienced an unintended shutdown during a test being performed at the NASA White Sands Test Facility. Subsequent removal and inspection of the thruster revealed permanent deformation and misalignment of the thruster valve mounting plate. Destructive evaluation determined that after three nominal firing sequences, the thruster had experienced an energetic event within the fuel (monomethylhydrazine) manifold at the start of the fourth firing sequence. The current understanding of the phenomenon of intra-manifold explosions in hypergolic bipropellant thrusters is documented in literature where it is colloquially referred to as a ZOT. The typical ZOT scenario involves operation of a thruster in a gravitational field with environmental pressures above the triple point pressure of the propellants. Post-firing, when the thruster valves are commanded closed, there remains a residual quantity of propellant in both the fuel and oxidizer (nitrogen tetroxide) injector manifolds known as the "dribble volume". In an ambient ground test configuration, these propellant volumes will drain from the injector manifolds but are impeded by the local atmospheric pressure. The evacuation of propellants from the thruster injector manifolds relies on the fluids vapor pressure to expel the liquid. The higher vapor pressure oxidizer will evacuate from the manifold before the lower vapor pressure fuel. The localized cooling resulting from the oxidizer boiling during manifold draining can result in fuel vapor migration and condensation in the oxidizer passage. The liquid fuel will then react with the oxidizer that enters the manifold during the next firing and may produce a localized high pressure reaction or explosion within the confines of the oxidizer injector manifold. The typical ZOT scenario was considered during this failure investigation, but was ultimately ruled out as a cause of the explosion. Converse to the typical ZOT failure mechanism, the failure of this particular thruster was determined to be the result of liquid oxidizer being present within the fuel manifold.

Improved repetition rate mixed isotope CO2 TEA laser

NASA Astrophysics Data System (ADS)

Cohn, D. B.

2014-09-01

A compact CO2 TEA laser has been developed for remote chemical detection that operates at a repetition rate of 250 Hz. It emits 700 mJ/pulse at 10.6 μm in a multimode beam with the 12C16O2 isotope. With mixed 12C16O2 plus 13C16O2 isotopes it emits multiple lines in both isotope manifolds to improve detection of a broad range of chemicals. In particular, output pulse energies are 110 mJ/pulse at 9.77 μm, 250 mJ/pulse at 10 μm, and 550 mJ/pulse at 11.15 μm, useful for detection of the chemical agents Sarin, Tabun, and VX. Related work shows capability for long term sealed operation with a catalyst and an agile tuner at a wavelength shift rate of 200 Hz.

Propulsion simulation test technique for V/STOL configurations

NASA Technical Reports Server (NTRS)

Bailey, R. O.; Smith, S. C.; Bustie, J. B.

1983-01-01

Ames Research Center is developing the technology for turbine-powered jet engine simulators so that airframe/propulsion system interactions on V/STOL fighter aircraft and other highly integrated configurations can be studied. This paper describes the status of the compact multimission aircraft propulsion simulator (CMAPS) technology. Three CMAPS units have accumulated a total of 340 hr during approximately 1-1/2 yr of static and wind-tunnel testing. A wind-tunnel test of a twin-engine CMAPS-equipped close-coupled canard-wing V/STOL model configuration with nonaxisymmetric nozzles was recently completed. During this test approximately 140 total hours were logged on two CMAPS units, indicating that the rotating machinery is reliable and that the CMAPS and associated control system provide a usable test tool. However, additional development is required to correct a drive manifold O-ring problem that limits the engine-pressure-ratio (EPR) to approximately 3.5.

Bipropellant propulsion with reciprocating pumps

NASA Astrophysics Data System (ADS)

Whitehead, John C.

1993-06-01

A pressure regulated gas generator rocket cycle with alternately pressurized pairs of reciprocating pumps offers thrust-on-demand operation with significantly lower inert mass than conventional spacecraft liquid propulsion systems. The operation of bipropellant feed systems with reciprocating pumps is explained, with consideration for both short and long term missions. There are several methods for startup and shutdown of this self-starting pump-fed system, with preference determined by thrust duty cycle and mission duration. Progress to date includes extensive development testing of components unique to this type of system, and several live tests with monopropellant hydrazine. Pneumatic pump control valves which render pistons and bellows automatically responsive to downstream liquid demand are significantly simpler than those described previously. A compact pumpset mounted to central liquid manifolds has a pair of oxidizer pumps pneumatically slaved to a pair of fuel pumps to reduce vibration. A warm gas pressure reducer for tank expulsion can eliminate any remaining need for inert gas storage.

A reconstruction theorem for Connes-Landi deformations of commutative spectral triples

NASA Astrophysics Data System (ADS)

Ćaćić, Branimir

2015-12-01

We formulate and prove an extension of Connes's reconstruction theorem for commutative spectral triples to so-called Connes-Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G, also known as toric noncommutative manifolds. In particular, we propose an abstract definition for such spectral triples, where noncommutativity is entirely governed by a deformation parameter sitting in the second group cohomology of the Pontryagin dual of G, and then show that such spectral triples are well-behaved under further Connes-Landi deformation, thereby allowing for both quantisation from and dequantisation to G-equivariant abstract commutative spectral triples. We then use a refinement of the Connes-Dubois-Violette splitting homomorphism to conclude that suitable Connes-Landi deformations of commutative spectral triples by a rational deformation parameter are almost-commutative in the general, topologically non-trivial sense.

Extrema of mass, first law of black hole mechanics, and a staticity theorem in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

1998-08-01

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derive the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial data for the manifold with an interior boundary we get the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and a compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion-electric fields on static slices.

ER = EPR and non-perturbative action integrals for quantum gravity

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina

In this paper, we construct and calculate non-perturbative path integrals in a multiply-connected spacetime. This is done by summing over homotopy classes of paths. The topology of the spacetime is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of quantum foam described by virtual black holes. As these “bubbles” are entangled, they are connected by Planckian ERBs because of the ER = EPR conjecture. Hence, the spacetime will possess a large first Betti number B1. For any compact 2-surface in the spacetime, the topology (in particular the homotopy) of that surface is non-trivial due to the large number of Planckian ERBs that define homotopy through this surface. The quantization of spacetime with this topology — along with the proper choice of the 2-surfaces — is conjectured to allow non-perturbative path integrals of quantum gravity theory over the spacetime manifold.

Aging and rejuvenation of active matter under topological constraints.

PubMed

Janssen, Liesbeth M C; Kaiser, Andreas; Löwen, Hartmut

2017-07-18

The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these non-equilibrium processes, and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. Our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.

Communication: Broad manifold of excitonic states in light-harvesting complex 1 promotes efficient unidirectional energy transfer in vivo

NASA Astrophysics Data System (ADS)

Sohail, Sara H.; Dahlberg, Peter D.; Allodi, Marco A.; Massey, Sara C.; Ting, Po-Chieh; Martin, Elizabeth C.; Hunter, C. Neil; Engel, Gregory S.

2017-10-01

In photosynthetic organisms, the pigment-protein complexes that comprise the light-harvesting antenna exhibit complex electronic structures and ultrafast dynamics due to the coupling among the chromophores. Here, we present absorptive two-dimensional (2D) electronic spectra from living cultures of the purple bacterium, Rhodobacter sphaeroides, acquired using gradient assisted photon echo spectroscopy. Diagonal slices through the 2D lineshape of the LH1 stimulated emission/ground state bleach feature reveal a resolvable higher energy population within the B875 manifold. The waiting time evolution of diagonal, horizontal, and vertical slices through the 2D lineshape shows a sub-100 fs intra-complex relaxation as this higher energy population red shifts. The absorption (855 nm) of this higher lying sub-population of B875 before it has red shifted optimizes spectral overlap between the LH1 B875 band and the B850 band of LH2. Access to an energetically broad distribution of excitonic states within B875 offers a mechanism for efficient energy transfer from LH2 to LH1 during photosynthesis while limiting back transfer. Two-dimensional lineshapes reveal a rapid decay in the ground-state bleach/stimulated emission of B875. This signal, identified as a decrease in the dipole strength of a strong transition in LH1 on the red side of the B875 band, is assigned to the rapid localization of an initially delocalized exciton state, a dephasing process that frustrates back transfer from LH1 to LH2.

Fuel cell manifold sealing system

DOEpatents

Grevstad, Paul E.; Johnson, Carl K.; Mientek, Anthony P.

1980-01-01

A manifold-to-stack seal and sealing method for fuel cell stacks. This seal system solves the problem of maintaining a low leak rate manifold seal as the fuel cell stack undergoes compressive creep. The seal system eliminates the problem of the manifold-to-stack seal sliding against the rough stack surface as the stack becomes shorter because of cell creep, which relative motion destroys the seal. The seal system described herein utilizes a polymer seal frame firmly clamped between the manifold and the stack such that the seal frame moves with the stack. Thus, as the stack creeps, the seal frame creeps with it, and there is no sliding at the rough, tough to seal, stack-to-seal frame interface. Here the sliding is on a smooth easy to seal location between the seal frame and the manifold.

Method for producing a fuel cell manifold seal

DOEpatents

Grevstad, Paul E.; Johnson, Carl K.; Mientek, Anthony P.

1982-01-01

A manifold-to-stack seal and sealing method for fuel cell stacks. This seal system solves the problem of maintaining a low leak rate manifold seal as the fuel cell stack undergoes compressive creep. The seal system eliminates the problem of the manifold-to-stack seal sliding against the rough stack surface as the stack becomes shorter because of cell creep, which relative motion destroys the seal. The seal system described herein utilizes a polymer seal frame firmly clamped between the manifold and the stack such that the seal frame moves with the stack. Thus, as the stack creeps, the seal frame creeps with it, and there is no sliding at the rough, tough to seal, stack-to-seal frame interface. Here the sliding is on a smooth easy to seal location between the seal frame and the manifold.

Robustness analysis of superpixel algorithms to image blur, additive Gaussian noise, and impulse noise

NASA Astrophysics Data System (ADS)

Brekhna, Brekhna; Mahmood, Arif; Zhou, Yuanfeng; Zhang, Caiming

2017-11-01

Superpixels have gradually become popular in computer vision and image processing applications. However, no comprehensive study has been performed to evaluate the robustness of superpixel algorithms in regard to common forms of noise in natural images. We evaluated the robustness of 11 recently proposed algorithms to different types of noise. The images were corrupted with various degrees of Gaussian blur, additive white Gaussian noise, and impulse noise that either made the object boundaries weak or added extra information to it. We performed a robustness analysis of simple linear iterative clustering (SLIC), Voronoi Cells (VCells), flooding-based superpixel generation (FCCS), bilateral geodesic distance (Bilateral-G), superpixel via geodesic distance (SSS-G), manifold SLIC (M-SLIC), Turbopixels, superpixels extracted via energy-driven sampling (SEEDS), lazy random walk (LRW), real-time superpixel segmentation by DBSCAN clustering, and video supervoxels using partially absorbing random walks (PARW) algorithms. The evaluation process was carried out both qualitatively and quantitatively. For quantitative performance comparison, we used achievable segmentation accuracy (ASA), compactness, under-segmentation error (USE), and boundary recall (BR) on the Berkeley image database. The results demonstrated that all algorithms suffered performance degradation due to noise. For Gaussian blur, Bilateral-G exhibited optimal results for ASA and USE measures, SLIC yielded optimal compactness, whereas FCCS and DBSCAN remained optimal for BR. For the case of additive Gaussian and impulse noises, FCCS exhibited optimal results for ASA, USE, and BR, whereas Bilateral-G remained a close competitor in ASA and USE for Gaussian noise only. Additionally, Turbopixel demonstrated optimal performance for compactness for both types of noise. Thus, no single algorithm was able to yield optimal results for all three types of noise across all performance measures. Conclusively, to solve real-world problems effectively, more robust superpixel algorithms must be developed.

Quantification, Distribution, and Possible Source of Bacterial Biofilm in Mouse Automated Watering Systems

PubMed Central

Meier, Thomas R; Maute, Carrie J; Cadillac, Joan M; Lee, Ji Young; Righter, Daniel J; Hugunin, Kelly MS; Deininger, Rolf A; Dysko, Robert C

2008-01-01

The use of automated watering systems for providing drinking water to rodents has become commonplace in the research setting. Little is known regarding bacterial biofilm growth within the water piping attached to the racks (manifolds). The purposes of this project were to determine whether the mouse oral flora contributed to the aerobic bacterial component of the rack biofilm, quantify bacterial growth in rack manifolds over 6 mo, assess our rack sanitation practices, and quantify bacterial biofilm development within sections of the manifold. By using standard methods of bacterial identification, the aerobic oral flora of 8 strains and stocks of mice were determined on their arrival at our animal facility. Ten rack manifolds were sampled before, during, and after sanitation and monthly for 6 mo. Manifolds were evaluated for aerobic bacterial growth by culture on R2A and trypticase soy agar, in addition to bacterial ATP quantification by bioluminescence. In addition, 6 racks were sampled at 32 accessible sites for evaluation of biofilm distribution within the watering manifold. The identified aerobic bacteria in the oral flora were inconsistent with the bacteria from the manifold, suggesting that the mice do not contribute to the biofilm bacteria. Bacterial growth in manifolds increased while they were in service, with exponential growth of the biofilm from months 3 to 6 and a significant decrease after sanitization. Bacterial biofilm distribution was not significantly different across location quartiles of the rack manifold, but bacterial levels differed between the shelf pipe and connecting elbow pipes. PMID:18351724

Quantification, distribution, and possible source of bacterial biofilm in mouse automated watering systems.

PubMed

Meier, Thomas R; Maute, Carrie J; Cadillac, Joan M; Lee, Ji Young; Righter, Daniel J; Hugunin, Kelly M S; Deininger, Rolf A; Dysko, Robert C

2008-03-01

The use of automated watering systems for providing drinking water to rodents has become commonplace in the research setting. Little is known regarding bacterial biofilm growth within the water piping attached to the racks (manifolds). The purposes of this project were to determine whether the mouse oral flora contributed to the aerobic bacterial component of the rack biofilm, quantify bacterial growth in rack manifolds over 6 mo, assess our rack sanitation practices, and quantify bacterial biofilm development within sections of the manifold. By using standard methods of bacterial identification, the aerobic oral flora of 8 strains and stocks of mice were determined on their arrival at our animal facility. Ten rack manifolds were sampled before, during, and after sanitation and monthly for 6 mo. Manifolds were evaluated for aerobic bacterial growth by culture on R2A and trypticase soy agar, in addition to bacterial ATP quantification by bioluminescence. In addition, 6 racks were sampled at 32 accessible sites for evaluation of biofilm distribution within the watering manifold. The identified aerobic bacteria in the oral flora were inconsistent with the bacteria from the manifold, suggesting that the mice do not contribute to the biofilm bacteria. Bacterial growth in manifolds increased while they were in service, with exponential growth of the biofilm from months 3 to 6 and a significant decrease after sanitization. Bacterial biofilm distribution was not significantly different across location quartiles of the rack manifold, but bacterial levels differed between the shelf pipe and connecting elbow pipes.

Discriminative clustering on manifold for adaptive transductive classification.

PubMed

Zhang, Zhao; Jia, Lei; Zhang, Min; Li, Bing; Zhang, Li; Li, Fanzhang

2017-10-01

In this paper, we mainly propose a novel adaptive transductive label propagation approach by joint discriminative clustering on manifolds for representing and classifying high-dimensional data. Our framework seamlessly combines the unsupervised manifold learning, discriminative clustering and adaptive classification into a unified model. Also, our method incorporates the adaptive graph weight construction with label propagation. Specifically, our method is capable of propagating label information using adaptive weights over low-dimensional manifold features, which is different from most existing studies that usually predict the labels and construct the weights in the original Euclidean space. For transductive classification by our formulation, we first perform the joint discriminative K-means clustering and manifold learning to capture the low-dimensional nonlinear manifolds. Then, we construct the adaptive weights over the learnt manifold features, where the adaptive weights are calculated through performing the joint minimization of the reconstruction errors over features and soft labels so that the graph weights can be joint-optimal for data representation and classification. Using the adaptive weights, we can easily estimate the unknown labels of samples. After that, our method returns the updated weights for further updating the manifold features. Extensive simulations on image classification and segmentation show that our proposed algorithm can deliver the state-of-the-art performance on several public datasets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Guzzo, Massimiliano; Lega, Elena

2018-06-01

The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.

Learning an intrinsic-variable preserving manifold for dynamic visual tracking.

PubMed

Qiao, Hong; Zhang, Peng; Zhang, Bo; Zheng, Suiwu

2010-06-01

Manifold learning is a hot topic in the field of computer science, particularly since nonlinear dimensionality reduction based on manifold learning was proposed in Science in 2000. The work has achieved great success. The main purpose of current manifold-learning approaches is to search for independent intrinsic variables underlying high dimensional inputs which lie on a low dimensional manifold. In this paper, a new manifold is built up in the training step of the process, on which the input training samples are set to be close to each other if the values of their intrinsic variables are close to each other. Then, the process of dimensionality reduction is transformed into a procedure of preserving the continuity of the intrinsic variables. By utilizing the new manifold, the dynamic tracking of a human who can move and rotate freely is achieved. From the theoretical point of view, it is the first approach to transfer the manifold-learning framework to dynamic tracking. From the application point of view, a new and low dimensional feature for visual tracking is obtained and successfully applied to the real-time tracking of a free-moving object from a dynamic vision system. Experimental results from a dynamic tracking system which is mounted on a dynamic robot validate the effectiveness of the new algorithm.

A general Kastler-Kalau-Walze type theorem for manifolds with boundary

NASA Astrophysics Data System (ADS)

Wang, Jian; Wang, Yong

2016-11-01

In this paper, we establish a general Kastler-Kalau-Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38-42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.

LCK rank of locally conformally Kähler manifolds with potential

NASA Astrophysics Data System (ADS)

Ornea, Liviu; Verbitsky, Misha

2016-09-01

An LCK manifold with potential is a quotient of a Kähler manifold X equipped with a positive Kähler potential f, such that the monodromy group acts on X by holomorphic homotheties and multiplies f by a character. The LCK rank is the rank of the image of this character, considered as a function from the monodromy group to real numbers. We prove that an LCK manifold with potential can have any rank between 1 and b1(M) . Moreover, LCK manifolds with proper potential (ones with rank 1) are dense. Two errata to our previous work are given in the last section.

Conical diffuser for fuel cells

NASA Technical Reports Server (NTRS)

Craft, D. W.

1976-01-01

Diffuser is inserted into inlet manifold, producing smooth transition of flow from pipe diameter to manifold diameter. Expected pressure gradient and resulting cell-to-cell temperature gradient are reduced. Outlet manifold has nozzle insert that reduces exit losses.

On the Influence of Material Parameters in a Complex Material Model for Powder Compaction

NASA Astrophysics Data System (ADS)

Staf, Hjalmar; Lindskog, Per; Andersson, Daniel C.; Larsson, Per-Lennart

2016-10-01

Parameters in a complex material model for powder compaction, based on a continuum mechanics approach, are evaluated using real insert geometries. The parameter sensitivity with respect to density and stress after compaction, pertinent to a wide range of geometries, is studied in order to investigate completeness and limitations of the material model. Finite element simulations with varied material parameters are used to build surrogate models for the sensitivity study. The conclusion from this analysis is that a simplification of the material model is relevant, especially for simple insert geometries. Parameters linked to anisotropy and the plastic strain evolution angle have a small impact on the final result.

Modular jet impingement assemblies with passive and active flow control for electronics cooling

DOEpatents

Zhou, Feng; Dede, Ercan Mehmet; Joshi, Shailesh

2016-09-13

Power electronics modules having modular jet impingement assembly utilized to cool heat generating devices are disclosed. The modular jet impingement assemblies include a modular manifold having a distribution recess, one or more angled inlet connection tubes positioned at an inlet end of the modular manifold that fluidly couple the inlet tube to the distribution recess and one or more outlet connection tubes positioned at an outlet end of the modular manifold that fluidly coupling the outlet tube to the distribution recess. The modular jet impingement assemblies include a manifold insert removably positioned within the distribution recess and include one or more inlet branch channels each including an impinging slot and one or more outlet branch channels each including a collecting slot. Further a heat transfer plate coupled to the modular manifold, the heat transfer plate comprising an impingement surface including an array of fins that extend toward the manifold insert.

Distributed coupling and multi-frequency microwave accelerators

DOEpatents

Tantawi, Sami G.; Li, Zenghai; Borchard, Philipp

2016-07-05

A microwave circuit for a linear accelerator has multiple metallic cell sections, a pair of distribution waveguide manifolds, and a sequence of feed arms connecting the manifolds to the cell sections. The distribution waveguide manifolds are connected to the cell sections so that alternating pairs of cell sections are connected to opposite distribution waveguide manifolds. The distribution waveguide manifolds have concave modifications of their walls opposite the feed arms, and the feed arms have portions of two distinct widths. In some embodiments, the distribution waveguide manifolds are connected to the cell sections by two different types of junctions adapted to allow two frequency operation. The microwave circuit may be manufactured by making two quasi-identical parts, and joining the two parts to form the microwave circuit, thereby allowing for many manufacturing techniques including electron beam welding, and thereby allowing the use of un-annealled copper alloys, and hence greater tolerance to high gradient operation.

Halo orbit transfer trajectory design using invariant manifold in the Sun-Earth system accounting radiation pressure and oblateness

NASA Astrophysics Data System (ADS)

Srivastava, Vineet K.; Kumar, Jai; Kushvah, Badam Singh

2018-01-01

In this paper, we study the invariant manifold and its application in transfer trajectory problem from a low Earth parking orbit to the Sun-Earth L1 and L2-halo orbits with the inclusion of radiation pressure and oblateness. Invariant manifold of the halo orbit provides a natural entrance to travel the spacecraft in the solar system along some specific paths due to its strong hyperbolic character. In this regard, the halo orbits near both collinear Lagrangian points are computed first. The manifold's approximation near the nominal halo orbit is computed using the eigenvectors of the monodromy matrix. The obtained local approximation provides globalization of the manifold by applying backward time propagation to the governing equations of motion. The desired transfer trajectory well suited for the transfer is explored by looking at a possible intersection between the Earth's parking orbit of the spacecraft and the manifold.

Extrinsic local regression on manifold-valued data

PubMed Central

Lin, Lizhen; St Thomas, Brian; Zhu, Hongtu; Dunson, David B.

2017-01-01

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach. PMID:29225385

Edge compression manifold apparatus

DOEpatents

Renzi, Ronald F.

2004-12-21

A manifold for connecting external capillaries to the inlet and/or outlet ports of a microfluidic device for high pressure applications is provided. The fluid connector for coupling at least one fluid conduit to a corresponding port of a substrate that includes: (i) a manifold comprising one or more channels extending therethrough wherein each channel is at least partially threaded, (ii) one or more threaded ferrules each defining a bore extending therethrough with each ferrule supporting a fluid conduit wherein each ferrule is threaded into a channel of the manifold, (iii) a substrate having one or more ports on its upper surface wherein the substrate is positioned below the manifold so that the one or more ports is aligned with the one or more channels of the manifold, and (iv) device to apply an axial compressive force to the substrate to couple the one or more ports of the substrate to a corresponding proximal end of a fluid conduit.

Edge compression manifold apparatus

DOEpatents

Renzi, Ronald F [Tracy, CA

2007-02-27

A manifold for connecting external capillaries to the inlet and/or outlet ports of a microfluidic device for high pressure applications is provided. The fluid connector for coupling at least one fluid conduit to a corresponding port of a substrate that includes: (i) a manifold comprising one or more channels extending therethrough wherein each channel is at least partially threaded, (ii) one or more threaded ferrules each defining a bore extending therethrough with each ferrule supporting a fluid conduit wherein each ferrule is threaded into a channel of the manifold, (iii) a substrate having one or more ports on its upper surface wherein the substrate is positioned below the manifold so that the one or more ports is aligned with the one or more channels of the manifold, and (iv) device to apply an axial compressive force to the substrate to couple the one or more ports of the substrate to a corresponding proximal end of a fluid conduit.

One-dimensional super Calabi-Yau manifolds and their mirrors

NASA Astrophysics Data System (ADS)

Noja, S.; Cacciatori, S. L.; Piazza, F. Dalla; Marrani, A.; Re, R.

2017-04-01

We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to P^1, namely the projective super space P^{.1|2} and the weighted projective super space W{P}_{(2)}^{.1|1} . Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces {P}^{.n|m} . We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of {P}^{.1|2} , whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of {P}^{.1|m} , discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that {P}^{.1|2} is self-mirror, whereas W{P}_{(2)}^{.1|1} has a zero dimensional mirror. Also, the mirror map for {P}^{.1|2} naturally endows it with a structure of N = 2 super Riemann surface.

Bifurcation Analysis Using Rigorous Branch and Bound Methods

NASA Technical Reports Server (NTRS)

Smith, Andrew P.; Crespo, Luis G.; Munoz, Cesar A.; Lowenberg, Mark H.

2014-01-01

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Prize to a Faculty Member for Research in an Undergraduate: Chaotic mixing and front propagation

NASA Astrophysics Data System (ADS)

Solomon, Tom

2014-03-01

We present results from a series of experiments - all done with undergraduate students - on chaotic fluid mixing and the effects of fluid flows on the behavior of reaction systems. Simple, well-ordered laminar fluid flows can give rise to fluid mixing with complexity far beyond that of the underlying flow, with tracers that separate exponentially in time and invariant manifolds that act as barriers to transport. Recently, we have studied how fluid mixing affects the propagation of reaction fronts in a flow. This is an issue with applications to a wide range of systems including microfluidic chemical reactors, blooms of phytoplankton in the oceans, and the spreading of a disease in a moving population. To analyze and predict the behavior of the fronts, we generalize tools developed to describe passive mixing. In particular, the concept of an invariant manifold is expanded to account for reactive burning. ``Burning invariant manifolds'' (BIMs) are predicted and measured experimentally as structures in the flow that act as one-way barriers that block the motion of reaction fronts. We test these ideas experimentally in three fluid flows: (a) and chain of alternating vortices; (b) an extended, spatially-random pattern of vortices; and (c) a time-independent, three-dimensional, nested vortex flow. The reaction fronts are produced chemically with variations of the well-known Belousov-Zhabotinsky reaction. Supported by Research Corporation and the National Science Foundation.

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.

Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions

NASA Astrophysics Data System (ADS)

Holmes, Philip J.

1981-06-01

We study the instabilities known to aeronautical engineers as flutter and divergence. Mathematically, these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation. Making use of the center manifold and normal form theorems, we concentrate on the situation in which flutter and divergence become coupled, and show that there are essentially two ways in which this is likely to occur. In the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator. This system, which may be analyzed by conventional phase-plane techniques, captures all the qualitative features of the full system. We discuss the reduction and show how the nonlinear terms may be simplified and put into normal form. Invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics. Repeating the approach in the second case, we show that the essential model is now three dimensional and that far more complex behavior is possible, including nonperiodic and ‘chaotic’ motions. Throughout, we take a two degree of freedom system as an example, but the general methods are applicable to multi- and even infinite degree of freedom problems.

Deep Compaction Control of Sandy Soils

NASA Astrophysics Data System (ADS)

Bałachowski, Lech; Kurek, Norbert

2015-02-01

Vibroflotation, vibratory compaction, micro-blasting or heavy tamping are typical improvement methods for the cohesionless deposits of high thickness. The complex mechanism of deep soil compaction is related to void ratio decrease with grain rearrangements, lateral stress increase, prestressing effect of certain number of load cycles, water pressure dissipation, aging and other effects. Calibration chamber based interpretation of CPTU/DMT can be used to take into account vertical and horizontal stress and void ratio effects. Some examples of interpretation of soundings in pre-treated and compacted sands are given. Some acceptance criteria for compaction control are discussed. The improvement factors are analysed including the normalised approach based on the soil behaviour type index.

Modeling multivariate time series on manifolds with skew radial basis functions.

PubMed

Jamshidi, Arta A; Kirby, Michael J

2011-01-01

We present an approach for constructing nonlinear empirical mappings from high-dimensional domains to multivariate ranges. We employ radial basis functions and skew radial basis functions for constructing a model using data that are potentially scattered or sparse. The algorithm progresses iteratively, adding a new function at each step to refine the model. The placement of the functions is driven by a statistical hypothesis test that accounts for correlation in the multivariate range variables. The test is applied on training and validation data and reveals nonstatistical or geometric structure when it fails. At each step, the added function is fit to data contained in a spatiotemporally defined local region to determine the parameters--in particular, the scale of the local model. The scale of the function is determined by the zero crossings of the autocorrelation function of the residuals. The model parameters and the number of basis functions are determined automatically from the given data, and there is no need to initialize any ad hoc parameters save for the selection of the skew radial basis functions. Compactly supported skew radial basis functions are employed to improve model accuracy, order, and convergence properties. The extension of the algorithm to higher-dimensional ranges produces reduced-order models by exploiting the existence of correlation in the range variable data. Structure is tested not just in a single time series but between all pairs of time series. We illustrate the new methodologies using several illustrative problems, including modeling data on manifolds and the prediction of chaotic time series.

Quantifying networks complexity from information geometry viewpoint

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

Felice, Domenico, E-mail: domenico.felice@unicam.it; Mancini, Stefano; INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy onmore » simplexes and find that it monotonically increases with their dimension.« less

Feasibility and Testing of Additive Manufactured Components

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

Dehoff, Ryan R.; Hummelt, Ed; Solovyeva, Lyudmila

2016-09-01

This project focused on demonstrating the ability to fabricate two parts with different geometry: an arc flash interrupter and a hydraulic manifold. Eaton Corporation provided ORNL solid models, information related to tolerances and sensitive parameters of the parts and provided testing and evaluation. ORNL successfully manufactured both components, provided cost models of the manufacturing (materials, labor, time and post processing) and delivered test components for Eaton evaluation. The arc flash suppressor was fabricated using the Renishaw laser powder bed technology in CoCrMo while the manifold was produced from Ti-6Al-4V using the Arcam electron beam melting technology. These manufacturing techniques weremore » selected based on the design and geometrical tolerances required. A full-scale manifold was produced on the Arcam A2 system (nearly 12 inches tall). A portion of the manifold was also produced in the Arcam Q10 system. Although a full scale manifold could not be produced in the system, a full scale manifold is expected to have similar material properties, geometric accuracy, and surface finish as could be fabricated on an Arcam Q20 system that is capable of producing four full scale manifolds in a production environment. In addition to the manifold, mechanical test specimens, geometric tolerance artifacts, and microstructure samples were produced alongside the manifold. The development and demonstration of these two key components helped Eaton understand the impact additive manufacturing can have on many of their existing products. By working within the MDF and leveraging ORNL’s manufacturing and characterization capabilities, the work will ensure the rapid insertion and commercialization of this technology.« less

Combustor with two stage primary fuel assembly

DOEpatents

Sharifi, Mehran; Zolyomi, Wendel; Whidden, Graydon Lane

2000-01-01

A combustor for a gas turbine having first and second passages for pre-mixing primary fuel and air supplied to a primary combustion zone. The flow of fuel to the first and second pre-mixing passages is separately regulated using a single annular fuel distribution ring having first and second row of fuel discharge ports. The interior portion of the fuel distribution ring is divided by a baffle into first and second fuel distribution manifolds and is located upstream of the inlets to the two pre-mixing passages. The annular fuel distribution ring is supplied with fuel by an annular fuel supply manifold, the interior portion of which is divided by a baffle into first and second fuel supply manifolds. A first flow of fuel is regulated by a first control valve and directed to the first fuel supply manifold, from which the fuel is distributed to first fuel supply tubes that direct it to the first fuel distribution manifold. From the first fuel distribution manifold, the first flow of fuel is distributed to the first row of fuel discharge ports, which direct it into the first pre-mixing passage. A second flow of fuel is regulated by a second control valve and directed to the second fuel supply manifold, from which the fuel is distributed to second fuel supply tubes that direct it to the second fuel distribution manifold. From the second fuel distribution manifold, the second flow of fuel is distributed to the second row of fuel discharge ports, which direct it into the second pre-mixing passage.

Engine Cylinder Temperature Control

DOEpatents

Kilkenny, Jonathan Patrick; Duffy, Kevin Patrick

2005-09-27

A method and apparatus for controlling a temperature in a combustion cylinder in an internal combustion engine. The cylinder is fluidly connected to an intake manifold and an exhaust manifold. The method and apparatus includes increasing a back pressure associated with the exhaust manifold to a level sufficient to maintain a desired quantity of residual exhaust gas in the cylinder, and varying operation of an intake valve located between the intake manifold and the cylinder to an open duration sufficient to maintain a desired quantity of fresh air from the intake manifold to the cylinder, wherein controlling the quantities of residual exhaust gas and fresh air are performed to maintain the temperature in the cylinder at a desired level.

Conjugate Heat Transfer Analyses on the Manifold for Ramjet Fuel Injectors

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen J.

2006-01-01

Three-dimensional conjugate heat transfer analyses on the manifold located upstream of the ramjet fuel injector are performed using CFdesign, a finite-element computational fluid dynamics (CFD) software. The flow field of the hot fuel (JP-7) flowing through the manifold is simulated and the wall temperature of the manifold is computed. The three-dimensional numerical results of the fuel temperature are compared with those obtained using a one-dimensional analysis based on empirical equations, and they showed a good agreement. The numerical results revealed that it takes around 30 to 40 sec to reach the equilibrium where the fuel temperature has dropped about 3 F from the inlet to the exit of the manifold.

The role of invariant manifolds in lowthrust trajectory design (part III)

NASA Technical Reports Server (NTRS)

Lo, Martin W.; Anderson, Rodney L.; Lam, Try; Whiffen, Greg

2006-01-01

This paper is the third in a series to explore the role of invariant manifolds in the design of low thrust trajectories. In previous papers, we analyzed an impulsive thrust resonant gravity assist flyby trajectory to capture into Europa orbit using the invariant manifolds of unstable resonant periodic orbits and libration orbits. The energy savings provided by the gravity assist may be interpreted dynamically as the result of a finite number of intersecting invariant manifolds. In this paper we demonstrate that the same dynamics is at work for low thrust trajectories with resonant flybys and low energy capture. However, in this case, the flybys and capture are effected by continuous families of intersecting invariant manifolds.

Ceramic matrix composite article and process of fabricating a ceramic matrix composite article

DOEpatents

Cairo, Ronald Robert; DiMascio, Paul Stephen; Parolini, Jason Robert

2016-01-12

A ceramic matrix composite article and a process of fabricating a ceramic matrix composite are disclosed. The ceramic matrix composite article includes a matrix distribution pattern formed by a manifold and ceramic matrix composite plies laid up on the matrix distribution pattern, includes the manifold, or a combination thereof. The manifold includes one or more matrix distribution channels operably connected to a delivery interface, the delivery interface configured for providing matrix material to one or more of the ceramic matrix composite plies. The process includes providing the manifold, forming the matrix distribution pattern by transporting the matrix material through the manifold, and contacting the ceramic matrix composite plies with the matrix material.

Manifold and method of batch measurement of Hg-196 concentration using a mass spectrometer

DOEpatents

Grossman, Mark W.; Evans, Roger

1991-01-01

A sample manifold and method of its use has been developed so that milligram quantities of mercury can be analyzed mass spectroscopically to determine the .sup.196 Hg concentration to less than 0.02 atomic percent. Using natural mercury as a standard, accuracy of .+-.0.002 atomic percent can be obtained. The mass spectrometer preferably used is a commercially available GC/MS manufactured by Hewlett Packard. A novel sample manifold is contained within an oven allowing flow rate control of Hg into the MS. Another part of the manifold connects to an auxiliary pumping system which facilitates rapid clean up of residual Hg in the manifold. Sample cycle time is about 1 hour.

Equation-free and variable free modeling for complex/multiscale systems. Coarse-grained computation in science and engineering using fine-grained models

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

Kevrekidis, Ioannis G.

The work explored the linking of modern developing machine learning techniques (manifold learning and in particular diffusion maps) with traditional PDE modeling/discretization/scientific computation techniques via the equation-free methodology developed by the PI. The result (in addition to several PhD degrees, two of them by CSGF Fellows) was a sequence of strong developments - in part on the algorithmic side, linking data mining with scientific computing, and in part on applications, ranging from PDE discretizations to molecular dynamics and complex network dynamics.

Atomizing nozzle and process

DOEpatents

Anderson, I.E.; Figliola, R.S.; Molnar, H.M.

1993-07-20

High pressure atomizing nozzle includes a high pressure gas manifold having a divergent expansion chamber between a gas inlet and arcuate manifold segment to minimize standing shock wave patterns in the manifold and thereby improve filling of the manifold with high pressure gas for improved melt atomization. The atomizing nozzle is especially useful in atomizing rare earth-transition metal alloys to form fine powder particles wherein a majority of the powder particles exhibit particle sizes having near-optimum magnetic properties.

Atomizing nozzle and process

DOEpatents

Anderson, Iver E.; Figliola, Richard S.; Molnar, Holly M.

1992-06-30

High pressure atomizing nozzle includes a high pressure gas manifold having a divergent expansion chamber between a gas inlet and arcuate manifold segment to minimize standing shock wave patterns in the manifold and thereby improve filling of the manifold with high pressure gas for improved melt atomization. The atomizing nozzle is especially useful in atomizing rare earth-transition metal alloys to form fine powder particles wherein a majority of the powder particles exhibit particle sizes having near-optimum magnetic properties.

Dynamics of cosmic strings with higher-dimensional windings

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

Yamauchi, Daisuke; Lake, Matthew J.; Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400

2015-06-11

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around S{sup 1} subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string lengthmore » lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.« less

Dynamics of cosmic strings with higher-dimensional windings

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

Yamauchi, Daisuke; Lake, Matthew J., E-mail: yamauchi@resceu.s.u-tokyo.ac.jp, E-mail: matthewj@nu.ac.th

2015-06-01

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around S{sup 1} subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string lengthmore » lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.« less

Improved Critical Eigenfunction Restriction Estimates on Riemannian Surfaces with Nonpositive Curvature

NASA Astrophysics Data System (ADS)

Xi, Yakun; Zhang, Cheng

2017-03-01

We show that one can obtain improved L 4 geodesic restriction estimates for eigenfunctions on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting Sogge's strategy in (Improved critical eigenfunction estimates on manifolds of nonpositive curvature, Preprint). We first combine the improved L 2 restriction estimate of Blair and Sogge (Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint) and the classical improved {L^∞} estimate of Bérard to obtain an improved weak-type L 4 restriction estimate. We then upgrade this weak estimate to a strong one by using the improved Lorentz space estimate of Bak and Seeger (Math Res Lett 18(4):767-781, 2011). This estimate improves the L 4 restriction estimate of Burq et al. (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009) by a power of {(log logλ)^{-1}}. Moreover, in the case of compact hyperbolic surfaces, we obtain further improvements in terms of {(logλ)^{-1}} by applying the ideas from (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) and (Blair and Sogge, Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint). We are able to compute various constants that appeared in (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) explicitly, by proving detailed oscillatory integral estimates and lifting calculations to the universal cover H^2.

Covariant balance laws in continua with microstructure

NASA Astrophysics Data System (ADS)

Yavari, Arash; Marsden, Jerrold E.

2009-02-01

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas. We model a structured continuum as a triplet of Riemannian manifolds: a material manifold, the ambient space manifold of material particles and a director field manifold. The Green-Naghdi-Rivlin theorem and its extensions for structured continua are critically reviewed. We show that when the ambient space is Euclidean and when the microstructure manifold is the tangent space of the ambient space manifold, postulating a single balance of energy law and its invariance under time-dependent isometries of the ambient space, one obtains conservation of mass, balances of linear and angular momenta but not a separate balance of linear momentum. We develop a covariant elasticity theory for structured continua by postulating that energy balance is invariant under time-dependent spatial diffeomorphisms of the ambient space, which in this case is the product of two Riemannian manifolds. We then introduce two types of constrained continua in which microstructure manifold is linked to the reference and ambient space manifolds. In the case when at every material point, the microstructure manifold is the tangent space of the ambient space manifold at the image of the material point, we show that the assumption of covariance leads to balances of linear and angular momenta with contributions from both forces and micro-forces along with two Doyle-Ericksen formulas. We show that generalized covariance leads to two balances of linear momentum and a single coupled balance of angular momentum. Using this theory, we covariantly obtain the balance laws for two specific examples, namely elastic solids with distributed voids and mixtures. Finally, the Lagrangian field theory of structured elasticity is revisited and a connection is made between covariance and Noether's theorem.

A manifold learning approach to target detection in high-resolution hyperspectral imagery

NASA Astrophysics Data System (ADS)

Ziemann, Amanda K.

Imagery collected from airborne platforms and satellites provide an important medium for remotely analyzing the content in a scene. In particular, the ability to detect a specific material within a scene is of high importance to both civilian and defense applications. This may include identifying "targets" such as vehicles, buildings, or boats. Sensors that process hyperspectral images provide the high-dimensional spectral information necessary to perform such analyses. However, for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m << d. In the remote sensing community, this has led to a recent increase in the use of manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data; this is particularly true when implementing traditional target detection approaches, and the limitations of these models are well-documented. With manifold learning based approaches, the only assumption is that the data reside on an underlying manifold that can be discretely modeled by a graph. The research presented here focuses on the use of graph theory and manifold learning in hyperspectral imagery. Early work explored various graph-building techniques with application to the background model of the Topological Anomaly Detection (TAD) algorithm, which is a graph theory based approach to anomaly detection. This led towards a focus on target detection, and in the development of a specific graph-based model of the data and subsequent dimensionality reduction using manifold learning. An adaptive graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation; the artificial target manifold helps to guide the separation of the target data from the background data in the new, lower-dimensional manifold coordinates. Then, target detection is performed in the manifold space.

All (4,0): Sigma models with (4,0) off-shell supersymmetry

NASA Astrophysics Data System (ADS)

Hull, Chris; Lindström, Ulf

2017-08-01

Off-shell (4, 0) supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.

Single-stranded DNA condensed with poly-L-lysine results in nanometric particles that are significantly smaller, more stable in physiological ionic strength fluids and afford higher efficiency of gene delivery than their double-stranded counterparts.

PubMed

Molas, M; Bartrons, R; Perales, J C

2002-08-15

Nonviral gene transfer vectors have been actively studied in the past years in order to obtain structural entities with minimum size and defined shape. The final size of a gene transfer vector, which is compacted into unimolecular complexes, is directly proportional to the mass of the nucleic acid to be compacted. Thus, the purpose of this study was to assess the possibility of producing ssDNA vectors and their biophysical and biological characterization. We have obtained ssDNA/poly-L-lysine complexes that are significantly smaller than their double-stranded counterparts. We have also identified a lesser aggregative behavior of compacted single-stranded vs. double-stranded DNA vectors in the presence of physiological NaCl concentrations. Expression of compacted ssDNA is observed in hepatoma cell lines. Moreover, we have successfully delivered galactosylated ssDNA complexes into cells that express the asialoglycoprotein receptor via receptor-mediated endocytosis. The reduced size and biophysical behavior of ssDNA vectors may provide an advantage for transfection of eukaryotic cells.

Physical Factors Affecting Plasmid DNA Compaction in Stearylamine-Containing Nanoemulsions Intended for Gene Delivery

PubMed Central

Silva, André Leandro; Júnior, Francisco Alexandrino; Verissimo, Lourena Mafra; Agnez-Lima, Lucymara Fassarella; Egito, Lucila Carmem Monte; de Oliveira, Anselmo Gomes; do Egito, Eryvaldo Socrates Tabosa

2012-01-01

Cationic lipids have been used in the development of non-viral gene delivery systems as lipoplexes. Stearylamine, a cationic lipid that presents a primary amine group when in solution, is able to compact genetic material by electrostatic interactions. In dispersed systems such as nanoemulsions this lipid anchors on the oil/water interface confering a positive charge to them. The aim of this work was to evaluate factors that influence DNA compaction in cationic nanoemulsions containing stearylamine. The influence of the stearylamine incorporation phase (water or oil), time of complexation, and different incubation temperatures were studied. The complexation rate was assessed by electrophoresis migration on agarose gel 0.7%, and nanoemulsion and lipoplex characterization was done by Dynamic Light Scattering (DLS). The results demonstrate that the best DNA compaction process occurs after 120 min of complexation, at low temperature (4 ± 1 °C), and after incorporation of the cationic lipid into the aqueous phase. Although the zeta potential of lipoplexes was lower than the results found for basic nanoemulsions, the granulometry did not change. Moreover, it was demonstrated that lipoplexes are suitable vehicles for gene delivery. PMID:24281666

Scaling Up Graph-Based Semisupervised Learning via Prototype Vector Machines

PubMed Central

Zhang, Kai; Lan, Liang; Kwok, James T.; Vucetic, Slobodan; Parvin, Bahram

2014-01-01

When the amount of labeled data are limited, semi-supervised learning can improve the learner's performance by also using the often easily available unlabeled data. In particular, a popular approach requires the learned function to be smooth on the underlying data manifold. By approximating this manifold as a weighted graph, such graph-based techniques can often achieve state-of-the-art performance. However, their high time and space complexities make them less attractive on large data sets. In this paper, we propose to scale up graph-based semisupervised learning using a set of sparse prototypes derived from the data. These prototypes serve as a small set of data representatives, which can be used to approximate the graph-based regularizer and to control model complexity. Consequently, both training and testing become much more efficient. Moreover, when the Gaussian kernel is used to define the graph affinity, a simple and principled method to select the prototypes can be obtained. Experiments on a number of real-world data sets demonstrate encouraging performance and scaling properties of the proposed approach. It also compares favorably with models learned via ℓ1-regularization at the same level of model sparsity. These results demonstrate the efficacy of the proposed approach in producing highly parsimonious and accurate models for semisupervised learning. PMID:25720002

Integrated high pressure manifold for thermoplastic microfluidic devices

NASA Astrophysics Data System (ADS)

Aghvami, S. Ali; Fraden, Seth

2017-11-01

We introduce an integrated tubing manifold for thermoplastic microfluidic chips that tolerates high pressure. In contrast to easy tubing in PDMS microfluidic devices, tube connection has been challenging for plastic microfluidics. Our integrated manifold connection tolerates 360 psi while conventional PDMS connections fail at 50 psi. Important design considerations are incorporation of a quick-connect, leak-free and high-pressure manifold for the inlets and outlets on the lid and registration marks that allow the precise alignment of the inlets and outlets. In our method, devices are comprised of two molded pieces joined together to create a sealed device. The first piece contains the microfluidic features and the second contains the inlet and outlet manifold, a frame for rigidity and a viewing window. The mold for the lid with integrated manifold is CNC milled from aluminium. A cone shape PDMS component which acts as an O-ring, seals the connection between molded manifold and tubing. The lid piece with integrated inlet and outlets will be a standard piece and can be used for different chips and designs. Sealing the thermoplastic device is accomplished by timed immersion of the lid in a mixture of volatile and non-volatile solvents followed by application of heat and pressure.

Manifold learning of brain MRIs by deep learning.

PubMed

Brosch, Tom; Tam, Roger

2013-01-01

Manifold learning of medical images plays a potentially important role for modeling anatomical variability within a population with pplications that include segmentation, registration, and prediction of clinical parameters. This paper describes a novel method for learning the manifold of 3D brain images that, unlike most existing manifold learning methods, does not require the manifold space to be locally linear, and does not require a predefined similarity measure or a prebuilt proximity graph. Our manifold learning method is based on deep learning, a machine learning approach that uses layered networks (called deep belief networks, or DBNs) and has received much attention recently in the computer vision field due to their success in object recognition tasks. DBNs have traditionally been too computationally expensive for application to 3D images due to the large number of trainable parameters. Our primary contributions are (1) a much more computationally efficient training method for DBNs that makes training on 3D medical images with a resolution of up to 128 x 128 x 128 practical, and (2) the demonstration that DBNs can learn a low-dimensional manifold of brain volumes that detects modes of variations that correlate to demographic and disease parameters.

Semiautomated solid-phase extraction manifold with a solvent-level sensor.

PubMed

Orlando, R M; Rath, S; Rohwedder, J J R

2013-11-15

A semiautomated solid-phase extraction manifold for multiple extractions is presented. The manifold utilizes commercial solid-phase syringe cartridges and automatically introduces and elutes all the solvents during the extraction, reducing the typical workload and stress of the analyst. The manifold consists of a peristaltic pump with solenoid valves in a flow circuit that contains transmissive photomicrosensors. The photomicrosensors were used to control the solvent dispenser and the solvent level inside the cartridge. As solvent-level sensors, the photomicrosensors determined the exact time the solvent reached the top frit to avoid sorbent drying and accurately perform the solvent exchange. The repeatability of the manifold to introduce a particular volume of solvent into the cartridges was measured, and the precisions were between 0.05 and 2.89% (RSD). To evaluate the manifold, the amount of two fluoroquinolones in a fortified blank milk sample was determined. The results of the intra- and inter-day precision of multiple extractions from the fortified milk samples resulted in precisions better than 9.0% (RSD) and confirmed that the arrangement of the semiautomated manifold could adequately be used in solid-phase extraction with commercial cartridges. Copyright © 2013 Elsevier B.V. All rights reserved.

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

PubMed

Sun, Shiliang; Xie, Xijiong

2016-09-01

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

Synthesis and characterization of para-pyridine linked NHC palladium complexes and their studies for the Heck-Mizoroki coupling reaction.

PubMed

Liu, Ya-Ming; Lin, Yi-Chun; Chen, Wen-Ching; Cheng, Jen-Hao; Chen, Yi-Lin; Yap, Glenn P A; Sun, Shih-Sheng; Ong, Tiow-Gan

2012-06-28

This paper describes the synthesis of 1-(pyridine-4-ylmethyl) NHC and their Pd(II) and Ag(I) complexes, which are fully characterized. Interestingly, we have also synthesized a Pd complex 3a-CO(3) using a more direct treatment of K(2)CO(3) with PdCl(2). 3a-CO(3) represents the first reported solid structure of a Pd η(2)-carbonato complex stabilized by an NHC framework. 3a-CO(3) can be easily converted to a PdCl(2) derivative by treating it with chloroform. We have found these palladium complexes mediate the Heck-Mizoroki coupling with a low catalyst loading. Furthermore, we also expand such catalytic manifold toward constructing fused polyaromatic substrates, a highly useful class of compounds in optoelectronic chemistry.

Trisections in Three and Four Dimensions

NASA Astrophysics Data System (ADS)

Koenig, Dale R.

Every closed orientable three dimensional manifold has a Heegaard splitting, a decomposition into two handlebodies. Any two Heegaard splittings of the same manifold can be made isotopic after a finite number of stabilization operations. The notion of trisections, developed by Gay and Kirby, provided an analogue in four dimensions. They showed that any closed smooth orientable four dimensional manifold can be broken into three four dimensional handlebodies, with "niceness" conditions on their intersections, and showed that any two trisections are isotopic after stabilizations. In this thesis we investigate the notion of trisections in both three and four dimensions. In dimension three we define trisections of 3-manifolds and stabilization on these trisections. We use this to define the trisection genus of a 3-manifold. We then present several examples, showing among other things that the trisection genus is not additive under connect sum. We prove a stable equivalence theorem for trisections of 3-manifolds, showing that any two trisections of the same three-manifold can be made isotopic after stabilizations. We also show that trisections of S3 can be very complicated, so there is no analogue of Waldhausen's theorem for trisections of three manifolds. We then move on to trisections in four dimensions. We first show that if there exist four manifolds with unbalanced trisection genus lower than their balanced trisection genus, then trisection genus as defined by Gay and Kirby is not additive under connect sum. We produce several new classes of trisections, including several likely such examples. We include a class of examples that are provably minimal genus. We provide trisection diagrams for many of these trisections, and summarize some methods for quickly checking that these diagrams produce valid trisections.

Constructive methods of invariant manifolds for kinetic problems

NASA Astrophysics Data System (ADS)

Gorban, Alexander N.; Karlin, Iliya V.; Zinovyev, Andrei Yu.

2004-06-01

The concept of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space ( the invariance equation). The equation of motion for immersed manifolds is obtained ( the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed. The systematic use of thermodynamics structures and of the quasi-chemical representation allow to construct approximations which are in concordance with physical restrictions. The following examples of applications are presented: nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn∼1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; model reduction in chemical kinetics; derivation and numerical implementation of constitutive equations for polymeric fluids; the limits of macroscopic description for polymer molecules, etc.

Pattern formation and geometry of the manifold

NASA Astrophysics Data System (ADS)

Haji, Amir Hossein; Mahzoon, Mojtaba; Javadpour, Sirus

2011-03-01

The objective of the present work is to investigate how pattern formation in the Cahn-Hilliard system can be influenced by geometry of the manifold. This is in contrast to control methods in which the physical field is modified and the pattern formation of the original system changes in response to control inputs. The idea begins with the cylindrical manifold symmetry leading to circumferential rolls while the torus manifold can be used to produce and control helical rolls. The next step is to search for a weaker restriction on the geometry of the manifold in order to reduce its dimension. In particular a short amplitude sinusoidal modulation on a flat surface is studied. At the final step a sequential pattern formation is presented.

Manifold and method of batch measurement of Hg-196 concentration using a mass spectrometer

DOEpatents

Grossman, M.W.; Evans, R.

1991-11-26

A sample manifold and method of its use has been developed so that milligram quantities of mercury can be analyzed mass spectroscopically to determine the [sup 196]Hg concentration to less than 0.02 atomic percent. Using natural mercury as a standard, accuracy of [+-]0.002 atomic percent can be obtained. The mass spectrometer preferably used is a commercially available GC/MS manufactured by Hewlett Packard. A novel sample manifold is contained within an oven allowing flow rate control of Hg into the MS. Another part of the manifold connects to an auxiliary pumping system which facilitates rapid clean up of residual Hg in the manifold. Sample cycle time is about 1 hour. 8 figures.

Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux

NASA Astrophysics Data System (ADS)

Balasuriya, Sanjeeva

2016-12-01

State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses destroy the smooth invariant manifolds, necessitating new definitions for stable and unstable pseudo-manifolds. Their time-evolution is characterised by solving a Volterra integral equation of the second kind with discontinuous inhomogeniety. A criteria for heteroclinic trajectory persistence in this impulsive context is developed, as is a quantification of an instantaneous flux across broken heteroclinic manifolds. Several examples, including a kicked Duffing oscillator and an underwater explosion in the vicinity of an eddy, are used to illustrate the theory.

Inelastic Compaction in High-Porosity Limestone Monitored Using Acoustic Emissions

NASA Astrophysics Data System (ADS)

Baud, Patrick; Schubnel, Alexandre; Heap, Michael; Rolland, Alexandra

2017-12-01

We performed a systematic investigation of mechanical compaction and strain localization in Saint-Maximin limestone, a quartz-rich, high-porosity (37%) limestone from France. Our new data show that the presence of a significant proportion of secondary mineral (i.e., quartz) did not impact the mechanical strength of the limestone in both the brittle faulting and cataclastic flow regimes, but that the presence of water exerted a significant weakening effect. In contrast to previously published studies on deformation in limestones, inelastic compaction in Saint-Maximin limestone was accompanied by abundant acoustic emission (AE) activity. The location of AE hypocenters during triaxial experiments revealed the presence of compaction localization. Two failure modes were identified in agreement with microstructural analysis and X-ray computed tomography imaging: compactive shear bands developed at low confinement and complex diffuse compaction bands formed at higher confinement. Microstructural observations on deformed samples suggest that the recorded AE activity associated with inelastic compaction, unusual for a porous limestone, could have been due to microcracking at the quartz grain interfaces. Similar to published data on high-porosity macroporous limestones, the crushing of calcite grains was the dominant micromechanism of inelastic compaction in Saint-Maximin limestone. New P wave velocity data show that the effect of microcracking was dominant near the yield point and resulted in a decrease in P wave velocity, while porosity reduction resulted in a significant increase in P wave velocity beyond a few percent of plastic volumetric strain. These new data highlight the complex interplay between mineralogy, rock microstructure, and strain localization in porous rocks.

77 FR 49386 - Airworthiness Directives; Airbus Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-16

... prompted by reports of silicon particles inside the oxygen generator manifolds, which had chafed from the... the part number and serial number of each passenger oxygen container, replacing the oxygen generator manifold of the affected oxygen container with a serviceable manifold, and performing an operational check...

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

Stability of Kinesthetic Perception in Efferent-Afferent Spaces: The Concept of Iso-perceptual Manifold.

PubMed

Latash, Mark L

2018-02-21

The main goal of this paper is to introduce the concept of iso-perceptual manifold for perception of body configuration and related variables (kinesthetic perception) and to discuss its relation to the equilibrium-point hypothesis and the concepts of reference coordinate and uncontrolled manifold. Hierarchical control of action is postulated with abundant transformations between sets of spatial reference coordinates for salient effectors at different levels. Iso-perceptual manifold is defined in the combined space of afferent and efferent variables as the subspace corresponding to a stable percept. Examples of motion along an iso-perceptual manifold (perceptually equivalent motion) are considered during various natural actions. Some combinations of afferent and efferent signals, in particular those implying a violation of body's integrity, give rise to variable percepts by artificial projection onto iso-perceptual manifolds. This framework is used to interpret unusual features of vibration-induced kinesthetic illusions and to predict new illusions not yet reported in the literature. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

Unsupervised image matching based on manifold alignment.

PubMed

Pei, Yuru; Huang, Fengchun; Shi, Fuhao; Zha, Hongbin

2012-08-01

This paper challenges the issue of automatic matching between two image sets with similar intrinsic structures and different appearances, especially when there is no prior correspondence. An unsupervised manifold alignment framework is proposed to establish correspondence between data sets by a mapping function in the mutual embedding space. We introduce a local similarity metric based on parameterized distance curves to represent the connection of one point with the rest of the manifold. A small set of valid feature pairs can be found without manual interactions by matching the distance curve of one manifold with the curve cluster of the other manifold. To avoid potential confusions in image matching, we propose an extended affine transformation to solve the nonrigid alignment in the embedding space. The comparatively tight alignments and the structure preservation can be obtained simultaneously. The point pairs with the minimum distance after alignment are viewed as the matchings. We apply manifold alignment to image set matching problems. The correspondence between image sets of different poses, illuminations, and identities can be established effectively by our approach.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Toward a Definition of Complexity for Quantum Field Theory States.

PubMed

Chapman, Shira; Heller, Michal P; Marrochio, Hugo; Pastawski, Fernando

2018-03-23

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum-preserving quadratic generators which form su(1,1) algebras. On the manifold of Gaussian states generated by these operations, the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and those of holographic complexity proposals.

Toward a Definition of Complexity for Quantum Field Theory States

NASA Astrophysics Data System (ADS)

Chapman, Shira; Heller, Michal P.; Marrochio, Hugo; Pastawski, Fernando

2018-03-01

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum-preserving quadratic generators which form s u (1 ,1 ) algebras. On the manifold of Gaussian states generated by these operations, the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and those of holographic complexity proposals.

Tiny, Dusty, Galactic HI Clouds: The GALFA-HI Compact Cloud Catalog

NASA Astrophysics Data System (ADS)

Saul, Destry R.; Putman, M. E.; Peek, J. G.

2013-01-01

The recently published GALFA-HI Compact Cloud Catalog contains 2000 nearby neutral hydrogen clouds under 20' in angular size detected with a machine-vision algorithm in the Galactic Arecibo L-Band Feed Array HI survey (GALFA-HI). At a distance of 1kpc, the compact clouds would typically be 1 solar mass and 1pc in size. We observe that nearly all of the compact clouds that are classified as high velocity (> 90 km/s) are near previously-identified high velocity complexes. We separate the compact clouds into populations based on velocity, linewidth, and position. We have begun to search for evidence of dust in these clouds using IRIS and have detections in several populations.

Manifold Coal-Slurry Transport System

NASA Technical Reports Server (NTRS)

Liddle, S. G.; Estus, J. M.; Lavin, M. L.

1986-01-01

Feeding several slurry pipes into main pipeline reduces congestion in coal mines. System based on manifold concept: feeder pipelines from each working entry joined to main pipeline that carries coal slurry out of panel and onto surface. Manifold concept makes coal-slurry haulage much simpler than existing slurry systems.

40 CFR 86.884-8 - Dynamometer and engine equipment.

Code of Federal Regulations, 2014 CFR

2014-07-01

... appropriate type of smokemeter placed no more than 32 feet from the exhaust manifold(s), turbocharger outlet(s..., turbocharger outlet, or exhaust aftertreatment device, whichever is farthest downstream. (3) For engines with... 10 to 32 feet downstream from the exhaust manifold, turbocharger outlet, or exhaust aftertreatment...

Becchi-Rouet-Stora-Tyutin formalism and zero locus reduction

NASA Astrophysics Data System (ADS)

Grigoriev, M. A.; Semikhatov, A. M.; Tipunin, I. Yu.

2001-08-01

In the Becchi-Rouet-Stora-Tyutin (BRST) quantization of gauge theories, the zero locus ZQ of the BRST differential Q carries an (anti)bracket whose parity is opposite to that of the fundamental bracket. Observables of the BRST theory are in a 1:1 correspondence with Casimir functions of the bracket on ZQ. For any constrained dynamical system with the phase space N0 and the constraint surface Σ, we prove its equivalence to the constrained system on the BFV-extended phase space with the constraint surface given by ZQ. Reduction to the zero locus of the differential gives rise to relations between bracket operations and differentials arising in different complexes (the Gerstenhaber, Schouten, Berezin-Kirillov, and Sklyanin brackets); the equation ensuring the existence of a nilpotent vector field on the reduced manifold can be the classical Yang-Baxter equation. We also generalize our constructions to the bi-QP manifolds which from the BRST theory viewpoint correspond to the BRST-anti-BRST-symmetric quantization.

Multimodal Medical Image Fusion by Adaptive Manifold Filter.

PubMed

Geng, Peng; Liu, Shuaiqi; Zhuang, Shanna

2015-01-01

Medical image fusion plays an important role in diagnosis and treatment of diseases such as image-guided radiotherapy and surgery. The modified local contrast information is proposed to fuse multimodal medical images. Firstly, the adaptive manifold filter is introduced into filtering source images as the low-frequency part in the modified local contrast. Secondly, the modified spatial frequency of the source images is adopted as the high-frequency part in the modified local contrast. Finally, the pixel with larger modified local contrast is selected into the fused image. The presented scheme outperforms the guided filter method in spatial domain, the dual-tree complex wavelet transform-based method, nonsubsampled contourlet transform-based method, and four classic fusion methods in terms of visual quality. Furthermore, the mutual information values by the presented method are averagely 55%, 41%, and 62% higher than the three methods and those values of edge based similarity measure by the presented method are averagely 13%, 33%, and 14% higher than the three methods for the six pairs of source images.

46 CFR 153.285 - Valving for cargo pump manifolds.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 5 2010-10-01 2010-10-01 false Valving for cargo pump manifolds. 153.285 Section 153... SHIPS CARRYING BULK LIQUID, LIQUEFIED GAS, OR COMPRESSED GAS HAZARDOUS MATERIALS Design and Equipment Piping Systems and Cargo Handling Equipment § 153.285 Valving for cargo pump manifolds. (a) When cargo...

30 CFR 250.444 - What are the choke manifold requirements?

Code of Federal Regulations, 2014 CFR

2014-07-01

... THE INTERIOR OFFSHORE OIL AND GAS AND SULPHUR OPERATIONS IN THE OUTER CONTINENTAL SHELF Oil and Gas Drilling Operations Blowout Preventer (bop) System Requirements § 250.444 What are the choke manifold..., and abrasiveness of drilling fluids and well fluids that you may encounter. (b) Choke manifold...

30 CFR 250.444 - What are the choke manifold requirements?

Code of Federal Regulations, 2013 CFR

2013-07-01

... THE INTERIOR OFFSHORE OIL AND GAS AND SULPHUR OPERATIONS IN THE OUTER CONTINENTAL SHELF Oil and Gas Drilling Operations Blowout Preventer (bop) System Requirements § 250.444 What are the choke manifold..., and abrasiveness of drilling fluids and well fluids that you may encounter. (b) Choke manifold...

30 CFR 250.444 - What are the choke manifold requirements?

Code of Federal Regulations, 2012 CFR

2012-07-01

... THE INTERIOR OFFSHORE OIL AND GAS AND SULPHUR OPERATIONS IN THE OUTER CONTINENTAL SHELF Oil and Gas Drilling Operations Blowout Preventer (bop) System Requirements § 250.444 What are the choke manifold..., and abrasiveness of drilling fluids and well fluids that you may encounter. (b) Choke manifold...

LIFE CYCLE DESIGN OF AIR INTAKE MANIFOLDS; PHASE I: 2.0 L FORD CONTOUR AIR INTAKE MANIFOLD

EPA Science Inventory

The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...

Manifold to uniformly distribute a solid-liquid slurry

DOEpatents

Kern, Kenneth C.

1983-01-01

This invention features a manifold that divides a stream of coal particles and liquid into several smaller streams maintaining equal or nearly equal mass compositions. The manifold consists of a horizontal, variable area header having sharp-edged, right-angled take-offs which are oriented on the bottom of the header.

Long Time Quantum Evolution of Observables on Cusp Manifolds

NASA Astrophysics Data System (ADS)

Bonthonneau, Yannick

2016-04-01

The Eisenstein functions {E(s)} are some generalized eigenfunctions of the Laplacian on manifolds with cusps. We give a version of Quantum Unique Ergodicity for them, for {|{I}s| to ∞} and {R}s to d/2} with {{R}s - d/2 ≥ log log |{I}s| / log |{I}s|}. For the purpose of the proof, we build a semi-classical quantization procedure for finite volume manifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We also prove an Egorov Lemma until Ehrenfest times on such manifolds.

Fuel cell system including a unit for electrical isolation of a fuel cell stack from a manifold assembly and method therefor

DOEpatents

Kelley; Dana A. , Farooque; Mohammad , Davis; Keith

2007-10-02

A fuel cell system with improved electrical isolation having a fuel cell stack with a positive potential end and a negative potential, a manifold for use in coupling gases to and from a face of the fuel cell stack, an electrical isolating assembly for electrically isolating the manifold from the stack, and a unit for adjusting an electrical potential of the manifold such as to impede the flow of electrolyte from the stack across the isolating assembly.

Adjustable flow rate controller for polymer solutions

DOEpatents

Jackson, Kenneth M.

1981-01-01

An adjustable device for controlling the flow rate of polymer solutions which results in only little shearing of the polymer molecules, said device comprising an inlet manifold, an outlet manifold, a plurality of tubes capable of providing communication between said inlet and outlet manifolds, said tubes each having an internal diameter that is smaller than that of the inlet manifold and large enough to insure that viscosity of the polymer solution passing through each said tube will not be reduced more than about 25 percent, and a valve associated with each tube, said valve being capable of opening or closing communication in that tube between the inlet and outlet manifolds, each said valve when fully open having a diameter that is substantially at least as great as that of the tube with which it is associated.

High specific power, direct methanol fuel cell stack

DOEpatents

Ramsey, John C [Los Alamos, NM; Wilson, Mahlon S [Los Alamos, NM

2007-05-08

The present invention is a fuel cell stack including at least one direct methanol fuel cell. A cathode manifold is used to convey ambient air to each fuel cell, and an anode manifold is used to convey liquid methanol fuel to each fuel cell. Tie-bolt penetrations and tie-bolts are spaced evenly around the perimeter to hold the fuel cell stack together. Each fuel cell uses two graphite-based plates. One plate includes a cathode active area that is defined by serpentine channels connecting the inlet manifold with an integral flow restrictor to the outlet manifold. The other plate includes an anode active area defined by serpentine channels connecting the inlet and outlet of the anode manifold. Located between the two plates is the fuel cell active region.

Second order sliding mode control for a quadrotor UAV.

PubMed

Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang

2014-07-01

A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Battery Vent Mechanism And Method

DOEpatents

Ching, Larry K. W.

2000-02-15

Disclosed herein is a venting mechanism for a battery. The venting mechanism includes a battery vent structure which is located on the battery cover and may be integrally formed therewith. The venting mechanism includes an opening extending through the battery cover such that the opening communicates with a plurality of battery cells located within the battery case. The venting mechanism also includes a vent manifold which attaches to the battery vent structure. The vent manifold includes a first opening which communicates with the battery vent structure opening and second and third openings which allow the vent manifold to be connected to two separate conduits. In this manner, a plurality of batteries may be interconnected for venting purposes, thus eliminating the need to provide separate vent lines for each battery. The vent manifold may be attached to the battery vent structure by a spin-welding technique. To facilitate this technique, the vent manifold may be provided with a flange portion which fits into a corresponding groove portion on the battery vent structure. The vent manifold includes an internal chamber which is large enough to completely house a conventional battery flame arrester and overpressure safety valve. In this manner, the vent manifold, when installed, lessens the likelihood of tampering with the flame arrester and safety valve.

Battery venting system and method

DOEpatents

Casale, T.J.; Ching, L.K.W.; Baer, J.T.; Swan, D.H.

1999-01-05

Disclosed herein is a venting mechanism for a battery. The venting mechanism includes a battery vent structure which is located on the battery cover and may be integrally formed therewith. The venting mechanism includes an opening extending through the battery cover such that the opening communicates with a plurality of battery cells located within the battery case. The venting mechanism also includes a vent manifold which attaches to the battery vent structure. The vent manifold includes a first opening which communicates with the battery vent structure opening and second and third openings which allow the vent manifold to be connected to two separate conduits. In this manner, a plurality of batteries may be interconnected for venting purposes, thus eliminating the need to provide separate vent lines for each battery. The vent manifold may be attached to the battery vent structure by a spin-welding technique. To facilitate this technique, the vent manifold may be provided with a flange portion which fits into a corresponding groove portion on the battery vent structure. The vent manifold includes an internal chamber which is large enough to completely house a conventional battery flame arrester and overpressure safety valve. In this manner, the vent manifold, when installed, lessens the likelihood of tampering with the flame arrester and safety valve. 8 figs.

Battery venting system and method

DOEpatents

Casale, Thomas J.; Ching, Larry K. W.; Baer, Jose T.; Swan, David H.

1999-01-05

Disclosed herein is a venting mechanism for a battery. The venting mechanism includes a battery vent structure which is located on the battery cover and may be integrally formed therewith. The venting mechanism includes an opening extending through the battery cover such that the opening communicates with a plurality of battery cells located within the battery case. The venting mechanism also includes a vent manifold which attaches to the battery vent structure. The vent manifold includes a first opening which communicates with the battery vent structure opening and second and third openings which allow the vent manifold to be connected to two separate conduits. In this manner, a plurality of batteries may be interconnected for venting purposes, thus eliminating the need to provide separate vent lines for each battery. The vent manifold may be attached to the battery vent structure by a spin-welding technique. To facilitate this technique, the vent manifold may be provided with a flange portion which fits into a corresponding groove portion on the battery vent structure. The vent manifold includes an internal chamber which is large enough to completely house a conventional battery flame arrester and overpressure safety valve. In this manner, the vent manifold, when installed, lessens the likelihood of tampering with the flame arrester and safety valve.

Compact continuum brain model for human electroencephalogram

NASA Astrophysics Data System (ADS)

Kim, J. W.; Shin, H.-B.; Robinson, P. A.

2007-12-01

A low-dimensional, compact brain model has recently been developed based on physiologically based mean-field continuum formulation of electric activity of the brain. The essential feature of the new compact model is a second order time-delayed differential equation that has physiologically plausible terms, such as rapid corticocortical feedback and delayed feedback via extracortical pathways. Due to its compact form, the model facilitates insight into complex brain dynamics via standard linear and nonlinear techniques. The model successfully reproduces many features of previous models and experiments. For example, experimentally observed typical rhythms of electroencephalogram (EEG) signals are reproduced in a physiologically plausible parameter region. In the nonlinear regime, onsets of seizures, which often develop into limit cycles, are illustrated by modulating model parameters. It is also shown that a hysteresis can occur when the system has multiple attractors. As a further illustration of this approach, power spectra of the model are fitted to those of sleep EEGs of two subjects (one with apnea, the other with narcolepsy). The model parameters obtained from the fittings show good matches with previous literature. Our results suggest that the compact model can provide a theoretical basis for analyzing complex EEG signals.

An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics

PubMed Central

Fu, Chunjiang; Suzuki, Yasuyuki; Kiyono, Ken; Morasso, Pietro; Nomura, Taishin

2014-01-01

Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics. PMID:25339687

An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics.

PubMed

Fu, Chunjiang; Suzuki, Yasuyuki; Kiyono, Ken; Morasso, Pietro; Nomura, Taishin

2014-12-06

Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.

Complex pectin metabolism by gut bacteria reveals novel catalytic functions

PubMed Central

Baslé, Arnaud; Gray, Joseph; Venditto, Immacolata; Briggs, Jonathon; Zhang, Xiaoyang; Labourel, Aurore; Terrapon, Nicolas; Buffetto, Fanny; Nepogodiev, Sergey; Xiao, Yao; Field, Robert A.; Zhu, Yanping; O’Neil, Malcolm A.; Urbanowicz, Breeana R.; York, William S.; Davies, Gideon J.; Abbott, D. Wade; Ralet, Marie-Christine; Martens, Eric C.; Henrissat, Bernard; Gilbert, Harry J.

2017-01-01

Carbohydrate polymers drive microbial diversity in the human gut microbiota. It is unclear, however, whether bacterial consortia or single organisms are required to depolymerize highly complex glycans. Here we show that the gut bacterium Bacteroides thetaiotaomicron utilizes the most structurally complex glycan known; the plant pectic polysaccharide rhamnogalacturonan-II, cleaving all but one of its 21 distinct glycosidic linkages. We show that rhamnogalacturonan-II side-chain and backbone deconstruction are coordinated, to overcome steric constraints, and that degradation reveals previously undiscovered enzyme families and novel catalytic activities. The degradome informs revision of the current structural model of RG-II and highlights how individual gut bacteria orchestrate manifold enzymes to metabolize the most challenging glycans in the human diet. PMID:28329766

Complete waveform model for compact binaries on eccentric orbits

NASA Astrophysics Data System (ADS)

Huerta, E. A.; Kumar, Prayush; Agarwal, Bhanu; George, Daniel; Schive, Hsi-Yu; Pfeiffer, Harald P.; Haas, Roland; Ren, Wei; Chu, Tony; Boyle, Michael; Hemberger, Daniel A.; Kidder, Lawrence E.; Scheel, Mark A.; Szilagyi, Bela

2017-01-01

We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are nonspinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third-order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to nonlinear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero-eccentricity limit. To improve phase accuracy, we also incorporate higher-order post-Newtonian corrections for the energy flux of quasicircular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a catalog of numerical relativity simulations. We show that this inspiral-merger-ringdown waveform model reproduces the effective-one-body model of Ref. [Y. Pan et al., Phys. Rev. D 89, 061501 (2014)., 10.1103/PhysRevD.89.061501] for quasicircular black hole binaries with mass ratios between 1 to 15 in the zero-eccentricity limit over a wide range of the parameter space under consideration. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our new eccentric model reproduces the true features of eccentric compact binary coalescence throughout merger. We use this model to show that the gravitational-wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasicircular, spin-aligned waveforms if the eccentricity e0 of these systems when they enter the aLIGO band at a gravitational-wave frequency of 14 Hz satisfies e0GW 150914≤0.15 and e0GW 151226≤0.1 . We also find that varying the spin combinations of the quasicircular, spin-aligned template waveforms does not improve the recovery of nonspinning, eccentric signals when e0≥0.1 . This suggests that these two signal manifolds are predominantly orthogonal.

Development and Experimental Evaluation of Passive Fuel Cell Thermal Control

NASA Technical Reports Server (NTRS)

Colozza, Anthony J.; Jakupca, Ian J.; Castle, Charles H.; Burke, Kenneth A.

2014-01-01

To provide uniform cooling for a fuel cell stack, a cooling plate concept was evaluated. This concept utilized thin cooling plates to extract heat from the interior of a fuel cell stack and move this heat to a cooling manifold where it can be transferred to an external cooling fluid. The advantages of this cooling approach include a reduced number of ancillary components and the ability to directly utilize an external cooling fluid loop for cooling the fuel cell stack. A number of different types of cooling plates and manifolds were developed. The cooling plates consisted of two main types; a plate based on thermopyrolytic graphite (TPG) and a planar (or flat plate) heat pipe. The plates, along with solid metal control samples, were tested for both thermal and electrical conductivity. To transfer heat from the cooling plates to the cooling fluid, a number of manifold designs utilizing various materials were devised, constructed, and tested. A key aspect of the manifold was that it had to be electrically nonconductive so it would not short out the fuel cell stack during operation. Different manifold and cooling plate configurations were tested in a vacuum chamber to minimize convective heat losses. Cooling plates were placed in the grooves within the manifolds and heated with surface-mounted electric pad heaters. The plate temperature and its thermal distribution were recorded for all tested combinations of manifold cooling flow rates and heater power loads. This testing simulated the performance of the cooling plates and manifold within an operational fuel cell stack. Different types of control valves and control schemes were tested and evaluated based on their ability to maintain a constant temperature of the cooling plates. The control valves regulated the cooling fluid flow through the manifold, thereby controlling the heat flow to the cooling fluid. Through this work, a cooling plate and manifold system was developed that could maintain the cooling plates within a minimal temperature band with negligible thermal gradients over power profiles that would be experienced within an operating fuel cell stack.

Final Report. Analysis and Reduction of Complex Networks Under Uncertainty

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

Marzouk, Youssef M.; Coles, T.; Spantini, A.

2013-09-30

The project was a collaborative effort among MIT, Sandia National Laboratories (local PI Dr. Habib Najm), the University of Southern California (local PI Prof. Roger Ghanem), and The Johns Hopkins University (local PI Prof. Omar Knio, now at Duke University). Our focus was the analysis and reduction of large-scale dynamical systems emerging from networks of interacting components. Such networks underlie myriad natural and engineered systems. Examples important to DOE include chemical models of energy conversion processes, and elements of national infrastructure—e.g., electric power grids. Time scales in chemical systems span orders of magnitude, while infrastructure networks feature both local andmore » long-distance connectivity, with associated clusters of time scales. These systems also blend continuous and discrete behavior; examples include saturation phenomena in surface chemistry and catalysis, and switching in electrical networks. Reducing size and stiffness is essential to tractable and predictive simulation of these systems. Computational singular perturbation (CSP) has been effectively used to identify and decouple dynamics at disparate time scales in chemical systems, allowing reduction of model complexity and stiffness. In realistic settings, however, model reduction must contend with uncertainties, which are often greatest in large-scale systems most in need of reduction. Uncertainty is not limited to parameters; one must also address structural uncertainties—e.g., whether a link is present in a network—and the impact of random perturbations, e.g., fluctuating loads or sources. Research under this project developed new methods for the analysis and reduction of complex multiscale networks under uncertainty, by combining computational singular perturbation (CSP) with probabilistic uncertainty quantification. CSP yields asymptotic approximations of reduceddimensionality “slow manifolds” on which a multiscale dynamical system evolves. Introducing uncertainty in this context raised fundamentally new issues, e.g., how is the topology of slow manifolds transformed by parametric uncertainty? How to construct dynamical models on these uncertain manifolds? To address these questions, we used stochastic spectral polynomial chaos (PC) methods to reformulate uncertain network models and analyzed them using CSP in probabilistic terms. Finding uncertain manifolds involved the solution of stochastic eigenvalue problems, facilitated by projection onto PC bases. These problems motivated us to explore the spectral properties stochastic Galerkin systems. We also introduced novel methods for rank-reduction in stochastic eigensystems—transformations of a uncertain dynamical system that lead to lower storage and solution complexity. These technical accomplishments are detailed below. This report focuses on the MIT portion of the joint project.« less

System light-loading technology for mHealth: Manifold-learning-based medical data cleansing and clinical trials in WE-CARE Project.

PubMed

Huang, Anpeng; Xu, Wenyao; Li, Zhinan; Xie, Linzhen; Sarrafzadeh, Majid; Li, Xiaoming; Cong, Jason

2014-09-01

Cardiovascular disease (CVD) is a major issue to public health. It contributes 41% to the Chinese death rate each year. This huge loss encouraged us to develop a Wearable Efficient teleCARdiology systEm (WE-CARE) for early warning and prevention of CVD risks in real time. WE-CARE is expected to work 24/7 online for mobile health (mHealth) applications. Unfortunately, this purpose is often disrupted in system experiments and clinical trials, even if related enabling technologies work properly. This phenomenon is rooted in the overload issue of complex Electrocardiogram (ECG) data in terms of system integration. In this study, our main objective is to get a system light-loading technology to enable mHealth with a benchmarked ECG anomaly recognition rate. To achieve this objective, we propose an approach to purify clinical features from ECG raw data based on manifold learning, called the Manifold-based ECG-feature Purification algorithm. Our clinical trials verify that our proposal can detect anomalies with a recognition rate of up to 94% which is highly valuable in daily public health-risk alert applications based on clinical criteria. Most importantly, the experiment results demonstrate that the WE-CARE system enabled by our proposal can enhance system reliability by at least two times and reduce false negative rates to 0.76%, and extend the battery life by 40.54%, in the system integration level.

77 FR 72200 - Airworthiness Directives; The Boeing Company Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-05

... correctly on the engine fuel feed manifold couplings. This AD also requires inspecting the assembly of the engine fuel feed manifold rigid and full flexible couplings. This AD was prompted by reports of fuel leaks due to improperly assembled engine fuel feed manifold couplings. We are issuing this AD to detect...

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

Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow

NASA Astrophysics Data System (ADS)

Kajigaya, Toru; Kunikawa, Keita

2018-06-01

In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a Lagrangian submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized Lagrangian mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial Lagrangian submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable Lagrangian submanifold, then the generalized MCF converges exponentially fast to an f-minimal Lagrangian submanifold.

Effectiveness of Rack Sanitation Procedures for Elimination of Bacteria from Automatic Watering Manifolds.

PubMed

Costello, Terry; Watkins, Linda; Straign, Mike; Bean, William; Toth, Linda; Rehg, Jerold

1998-03-01

An important responsibility of animal care programs is to protect research animals from exposure to potentially pathogenic microorganisms. To validate the need for steam sterilization of rodent automatic watering racks, we evaluate the post-sanitation microbial contamination of experimentally inoculated racks and of racks that had been used to house conventional mice. We tested three sanitation protocols: rack-washer sanitation without manifold flush, sanitation that included manifold flush, and sanitation that included manifold flush followed by autoclaving. Rack sanitation, with or without manifold flush, did not reliably eliminate microbial flora from the lixits or manifold drainage water. A total of 43% of all non-autoclaved racks were positive for bacterial contamination after sanitation, and racks that had been used for conventional animal housing were more frequently positive than were experimentally inoculated racks (79% vs 18%). These data indicate that steam sterilization is necessary for eliminating bacteria from automatic watering systems. These observations are particularly important in light of increasing numbers of immune-impaired rodents that may be inadvertently and unnecessarily exposed to microbial pathogens via the automatic watering system.

Access to Mars from Earth-Moon Libration Point Orbits:. [Manifold and Direct Options

NASA Technical Reports Server (NTRS)

Kakoi, Masaki; Howell, Kathleen C.; Folta, David

2014-01-01

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.

On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature

NASA Astrophysics Data System (ADS)

Hu, Xue

2018-06-01

In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove that the trace-free part of the mass aspect tensor of an APE 4-manifold with harmonic curvature and normalized Einstein conformal infinity is zero. As to the rigidity, we first show that a complete noncompact Riemannian 4-manifold with harmonic curvature and positive Yamabe constant as well as a L2-pinching condition is Einstein. As an application, we then obtain that an APE 4-manifold with harmonic curvature and positive Yamabe constant is isometric to the hyperbolic space provided that the L2-norm of the traceless Ricci tensor or the Weyl tensor is small enough and the conformal infinity is a standard round 3-sphere.

Fixed points, stable manifolds, weather regimes, and their predictability

DOE PAGES

Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael

2009-10-27

In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemblemore » forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.« less

Mirror symmetry in emergent gravity

NASA Astrophysics Data System (ADS)

Yang, Hyun Seok

2017-09-01

Given a six-dimensional symplectic manifold (M , B), a nondegenerate, co-closed four-form C introduces a dual symplectic structure B ˜ = * C independent of B via the Hodge duality *. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of noncommutative U (1) gauge fields by considering the Seiberg-Witten map for each symplectic structure. As a result, emergent gravity suggests a beautiful picture that the variety of six-dimensional manifolds emergent from noncommutative U (1) gauge fields is doubled. In particular, the doubling for the variety of emergent Calabi-Yau manifolds allows us to arrange a pair of Calabi-Yau manifolds such that they are mirror to each other. Therefore, we argue that the mirror symmetry of Calabi-Yau manifolds is the Hodge theory for the deformation of symplectic and dual symplectic structures.

Polynomial chaos representation of databases on manifolds

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

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. Themore » method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.« less

Fixed points, stable manifolds, weather regimes, and their predictability.

PubMed

Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael

2009-12-01

In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model's fixed points in phase space. The model dynamics is characterized by the coexistence of multiple "weather regimes." To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, "bred vectors" and singular vectors. These results are then verified in the framework of ensemble forecasts issued from "clouds" (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.

A novel manifold-manifold distance index applied to looseness state assessment of viscoelastic sandwich structures

NASA Astrophysics Data System (ADS)

Sun, Chuang; Zhang, Zhousuo; Guo, Ting; Luo, Xue; Qu, Jinxiu; Zhang, Chenxuan; Cheng, Wei; Li, Bing

2014-06-01

Viscoelastic sandwich structures (VSS) are widely used in mechanical equipment; their state assessment is necessary to detect structural states and to keep equipment running with high reliability. This paper proposes a novel manifold-manifold distance-based assessment (M2DBA) method for assessing the looseness state in VSSs. In the M2DBA method, a manifold-manifold distance is viewed as a health index. To design the index, response signals from the structure are firstly acquired by condition monitoring technology and a Hankel matrix is constructed by using the response signals to describe state patterns of the VSS. Thereafter, a subspace analysis method, that is, principal component analysis (PCA), is performed to extract the condition subspace hidden in the Hankel matrix. From the subspace, pattern changes in dynamic structural properties are characterized. Further, a Grassmann manifold (GM) is formed by organizing a set of subspaces. The manifold is mapped to a reproducing kernel Hilbert space (RKHS), where support vector data description (SVDD) is used to model the manifold as a hypersphere. Finally, a health index is defined as the cosine of the angle between the hypersphere centers corresponding to the structural baseline state and the looseness state. The defined health index contains similarity information existing in the two structural states, so structural looseness states can be effectively identified. Moreover, the health index is derived by analysis of the global properties of subspace sets, which is different from traditional subspace analysis methods. The effectiveness of the health index for state assessment is validated by test data collected from a VSS subjected to different degrees of looseness. The results show that the health index is a very effective metric for detecting the occurrence and extension of structural looseness. Comparison results indicate that the defined index outperforms some existing state-of-the-art ones.

Complete integrability of geodesics in toric Sasaki-Einstein spaces

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-01-01

We describe a method for constructing Killing-Yano tensors on toric Sasaki- Einstein manifolds using their geometrical properties. We take advantage of the fact that the metric cones of these spaces are Calabi-Yau manifolds. The complete list of special Killing forms can be extracted making use of the description of the Calabi-Yau manifolds in terms of toric data. This general procedure for toric Sasaki-Einstein manifolds is exemplified in the case of the 5-dimensional spaces Yp,q and T1,1. Finally we discuss the integrability of geodesic motion in these spaces.

Protein–protein docking by fast generalized Fourier transforms on 5D rotational manifolds

PubMed Central

Padhorny, Dzmitry; Kazennov, Andrey; Zerbe, Brandon S.; Porter, Kathryn A.; Xia, Bing; Mottarella, Scott E.; Kholodov, Yaroslav; Ritchie, David W.; Vajda, Sandor; Kozakov, Dima

2016-01-01

Energy evaluation using fast Fourier transforms (FFTs) enables sampling billions of putative complex structures and hence revolutionized rigid protein–protein docking. However, in current methods, efficient acceleration is achieved only in either the translational or the rotational subspace. Developing an efficient and accurate docking method that expands FFT-based sampling to five rotational coordinates is an extensively studied but still unsolved problem. The algorithm presented here retains the accuracy of earlier methods but yields at least 10-fold speedup. The improvement is due to two innovations. First, the search space is treated as the product manifold SO(3)×(SO(3)∖S1), where SO(3) is the rotation group representing the space of the rotating ligand, and (SO(3)∖S1) is the space spanned by the two Euler angles that define the orientation of the vector from the center of the fixed receptor toward the center of the ligand. This representation enables the use of efficient FFT methods developed for SO(3). Second, we select the centers of highly populated clusters of docked structures, rather than the lowest energy conformations, as predictions of the complex, and hence there is no need for very high accuracy in energy evaluation. Therefore, it is sufficient to use a limited number of spherical basis functions in the Fourier space, which increases the efficiency of sampling while retaining the accuracy of docking results. A major advantage of the method is that, in contrast to classical approaches, increasing the number of correlation function terms is computationally inexpensive, which enables using complex energy functions for scoring. PMID:27412858

Manifold learning for automatically predicting articular cartilage morphology in the knee with data from the osteoarthritis initiative (OAI)

NASA Astrophysics Data System (ADS)

Donoghue, C.; Rao, A.; Bull, A. M. J.; Rueckert, D.

2011-03-01

Osteoarthritis (OA) is a degenerative, debilitating disease with a large socio-economic impact. This study looks to manifold learning as an automatic approach to harness the plethora of data provided by the Osteoarthritis Initiative (OAI). We construct several Laplacian Eigenmap embeddings of articular cartilage appearance from MR images of the knee using multiple MR sequences. A region of interest (ROI) defined as the weight bearing medial femur is automatically located in all images through non-rigid registration. A pairwise intensity based similarity measure is computed between all images, resulting in a fully connected graph, where each vertex represents an image and the weight of edges is the similarity measure. Spectral analysis is then applied to these pairwise similarities, which acts to reduce the dimensionality non-linearly and embeds these images in a manifold representation. In the manifold space, images that are close to each other are considered to be more "similar" than those far away. In the experiment presented here we use manifold learning to automatically predict the morphological changes in the articular cartilage by using the co-ordinates of the images in the manifold as independent variables for multiple linear regression. In the study presented here five manifolds are generated from five sequences of 390 distinct knees. We find statistically significant correlations (up to R2 = 0.75), between our predictors and the results presented in the literature.

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

Oegetbil, O.

After reviewing the existing results we give an extensive analysis of the critical points of the potentials of the gauged N=2 Yang-Mills/Einstein supergravity theories coupled to tensor multiplets and hypermultiplets. Our analysis includes all the possible gaugings of all N=2 Maxwell-Einstein supergravity theories whose scalar manifolds are symmetric spaces. In general, the scalar potential gets contributions from R-symmetry gauging, tensor couplings, and hypercouplings. We show that the coupling of a hypermultiplet into a theory whose potential has a nonzero value at its critical point, and gauging a compact subgroup of the hyperscalar isometry group will only rescale the value ofmore » the potential at the critical point by a positive factor, and therefore will not change the nature of an existing critical point. However this is not the case for noncompact SO(1,1) gaugings. An SO(1,1) gauging of the hyperisometry will generally lead to de Sitter vacua, which is analogous to the ground states found by simultaneously gauging SO(1,1) symmetry of the real scalar manifold with U(1){sub R} in earlier literature. SO(m,1) gaugings with m>1, which give contributions to the scalar potential only in the magical Jordan family theories, on the other hand, do not lead to de Sitter vacua. Anti-de Sitter vacua are generically obtained when the U(1){sub R} symmetry is gauged. We also show that it is possible to embed certain generic Jordan family theories into the magical Jordan family preserving the nature of the ground states. However the magical Jordan family theories have additional ground states which are not found in the generic Jordan family theories.« less

Variable volume combustor with nested fuel manifold system

DOEpatents

McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael

2016-09-13

The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.

Compressed gas manifold

DOEpatents

Hildebrand, Richard J.; Wozniak, John J.

2001-01-01

A compressed gas storage cell interconnecting manifold including a thermally activated pressure relief device, a manual safety shut-off valve, and a port for connecting the compressed gas storage cells to a motor vehicle power source and to a refueling adapter. The manifold is mechanically and pneumatically connected to a compressed gas storage cell by a bolt including a gas passage therein.

LCD OF AIR INTAKE MANIFOLDS PHASE 2: FORD F250 AIR INTAKE MANIFOLD

EPA Science Inventory

The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...

Monitoring the performance of a storm water separating manifold with distributed temperature sensing.

PubMed

Langeveld, J G; de Haan, C; Klootwijk, M; Schilperoort, R P S

2012-01-01

Storm water separating manifolds in house connections have been introduced as a cost effective solution to disconnect impervious areas from combined sewers. Such manifolds have been applied by the municipality of Breda, the Netherlands. In order to investigate the performance of the manifolds, a monitoring technique (distributed temperature sensing or DTS) using fiber optic cables has been applied in the sewer system of Breda. This paper describes the application of DTS as a research tool in sewer systems. DTS proves to be a powerful tool to monitor the performance of (parts of) a sewer system in time and space. The research project showed that DTS is capable of monitoring the performance of house connections and identifying locations of inflow of both sewage and storm runoff. The research results show that the performance of storm water separating manifolds varies over time, thus making them unreliable.

Natural differential operations on manifolds: an algebraic approach

NASA Astrophysics Data System (ADS)

Katsylo, P. I.; Timashev, D. A.

2008-10-01

Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles \\mathscr{V},\\mathscr{W}\\to M all the natural differential operations D\\colon\\Gamma(\\mathscr{V})\\to\\Gamma(\\mathscr{W}) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds.Bibliography: 21 titles.

Capillary interconnect device

DOEpatents

Renzi, Ronald F.

2007-12-25

A manifold for connecting external capillaries to the inlet and/or outlet ports of a microfluidic device for high pressure applications is provided. The fluid connector for coupling at least one fluid conduit to a corresponding port of a substrate that includes: (i) a manifold comprising one or more channels extending therethrough wherein each channel is at least partially threaded, (ii) one or more threaded ferrules each defining a bore extending therethrough with each ferrule supporting a fluid conduit wherein each ferrule is threaded into a channel of the manifold, (iii) a substrate having one or more ports on its upper surface wherein the substrate is positioned below the manifold so that the one or more ports is aligned with the one or more channels of the manifold, and (iv) means for applying an axial compressive force to the substrate to couple the one or more ports of the substrate to a corresponding proximal end of a fluid conduit.

Swimming invariant manifolds and the motion of bacteria in a fluid flow

NASA Astrophysics Data System (ADS)

Yoest, Helena; Mitchell, Kevin; Solomon, Tom

2017-11-01

We present experiments on the motion of both wild-type and smooth-swimming bacillus subtilis in a hyperbolic, microfluidic fluid flow. Passive invariant manifolds crossing the fixed point in the flow act as barriers that block inert tracers in the flow. Self-propelled tracers can cross these passive manifolds, but are blocked by and attracted to swimming invariant manifolds (SWIMs) that split from the passive manifolds with larger and larger non-dimensional swimming speed v0 ≡V0 / U , where V0 is the swimming speed in the absence of a flow and U is a characteristic flos speed. We present the theory that predicts these SWIMs for smooth-swimming tracers, along with experiments that we are conducting to test these theories. We also discuss potential effects of rheotaxis and chemotaxis on the phenomena. Supported by NSF Grant DMR-1361881.

Salient object detection: manifold-based similarity adaptation approach

NASA Astrophysics Data System (ADS)

Zhou, Jingbo; Ren, Yongfeng; Yan, Yunyang; Gao, Shangbing

2014-11-01

A saliency detection algorithm based on manifold-based similarity adaptation is proposed. The proposed algorithm is divided into three steps. First, we segment an input image into superpixels, which are represented as the nodes in a graph. Second, a new similarity measurement is used in the proposed algorithm. The weight matrix of the graph, which indicates the similarities between the nodes, uses a similarity-based method. It also captures the manifold structure of the image patches, in which the graph edges are determined in a data adaptive manner in terms of both similarity and manifold structure. Then, we use local reconstruction method as a diffusion method to obtain the saliency maps. The objective function in the proposed method is based on local reconstruction, with which estimated weights capture the manifold structure. Experiments on four bench-mark databases demonstrate the accuracy and robustness of the proposed method.

Remtech SSME nozzle design TPS

NASA Technical Reports Server (NTRS)

Bancroft, Steven A.; Engel, Carl D.; Pond, John E.

1990-01-01

Thermal damage to the Space Shuttle Main Engine (SSME) aft manifold Thermal Protection System (TPS) has been observed for flights STS-8 through STS-13. This damaged area is located on the ME2 and ME3 and extends over a region of approximately one square foot. Total failure or burn-through of the TPS could lead to severe thermal damage of the SSME manifold and loss of an engine nozzle necessitating nozzle replacement causing significant schedule delays and cost increases. Thermal damage to the manifold can be defined as a situation where the manifold temperature becomes greater than 1300 F; thereby causing loss of heat treatment in the nozzle. Results of Orbiter/nozzle wind tunnel tests and Hot Gas Facility tests of the TPS are presented. Aerothermal and thermal analysis models for the SSME aft manifold are discussed along with the flight predictions, design trajectory and design environment. Finally, the TPS design concept and TPS thermal response are addressed.

[Management of the new first aid service at enterprises and construction sites].

PubMed

Prandi, E; Cantoni, S; Mosconi, G

2006-01-01

First aid at work organization and management represents a complex and critical aspect of the manifold problems of hygiene and security at work; nevertheless, even in relatively well organized productions, these themes are often neglected, if not completely ignored. In this work the authors analize the laws which regulate the correct first aid at work organization and management and an approach to the problem based on the preliminary risk assessment is suggested.

An adaptive proper orthogonal decomposition method for model order reduction of multi-disc rotor system

NASA Astrophysics Data System (ADS)

Jin, Yulin; Lu, Kuan; Hou, Lei; Chen, Yushu

2017-12-01

The proper orthogonal decomposition (POD) method is a main and efficient tool for order reduction of high-dimensional complex systems in many research fields. However, the robustness problem of this method is always unsolved, although there are some modified POD methods which were proposed to solve this problem. In this paper, a new adaptive POD method called the interpolation Grassmann manifold (IGM) method is proposed to address the weakness of local property of the interpolation tangent-space of Grassmann manifold (ITGM) method in a wider parametric region. This method is demonstrated here by a nonlinear rotor system of 33-degrees of freedom (DOFs) with a pair of liquid-film bearings and a pedestal looseness fault. The motion region of the rotor system is divided into two parts: simple motion region and complex motion region. The adaptive POD method is compared with the ITGM method for the large and small spans of parameter in the two parametric regions to present the advantage of this method and disadvantage of the ITGM method. The comparisons of the responses are applied to verify the accuracy and robustness of the adaptive POD method, as well as the computational efficiency is also analyzed. As a result, the new adaptive POD method has a strong robustness and high computational efficiency and accuracy in a wide scope of parameter.

Multilinear Graph Embedding: Representation and Regularization for Images.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting

2014-02-01

Given a set of images, finding a compact and discriminative representation is still a big challenge especially when multiple latent factors are hidden in the way of data generation. To represent multifactor images, although multilinear models are widely used to parameterize the data, most methods are based on high-order singular value decomposition (HOSVD), which preserves global statistics but interprets local variations inadequately. To this end, we propose a novel method, called multilinear graph embedding (MGE), as well as its kernelization MKGE to leverage the manifold learning techniques into multilinear models. Our method theoretically links the linear, nonlinear, and multilinear dimensionality reduction. We also show that the supervised MGE encodes informative image priors for image regularization, provided that an image is represented as a high-order tensor. From our experiments on face and gait recognition, the superior performance demonstrates that MGE better represents multifactor images than classic methods, including HOSVD and its variants. In addition, the significant improvement in image (or tensor) completion validates the potential of MGE for image regularization.

Automatic Suppression of Intense Monochromatic Light in Electro-Optical Sensors

PubMed Central

Ritt, Gunnar; Eberle, Bernd

2012-01-01

Electro-optical imaging sensors are widely distributed and used for many different tasks. Due to technical improvements, their pixel size has been steadily decreasing, resulting in a reduced saturation capacity. As a consequence, this progress makes them susceptible to intense point light sources. Developments in laser technology have led to very compact and powerful laser sources of any wavelength in the visible and near infrared spectral region, offered as laser pointers. The manifold of wavelengths makes it difficult to encounter sensor saturation over the complete operating waveband by conventional measures like absorption or interference filters. We present a concept for electro-optical sensors to suppress overexposure in the visible spectral region. The key element of the concept is a spatial light modulator in combination with wavelength multiplexing. This approach allows spectral filtering within a localized area in the field of view of the sensor. The system offers the possibility of automatic reduction of overexposure by monochromatic laser radiation. PMID:23202039

Aging and rejuvenation of active matter under topological constraints

DOE PAGES

Janssen, Liesbeth M. C.; Kaiser, Andreas; Lowen, Hartmut

2017-07-18

The coupling of active, self-motile particles to topological constraints can give rise to novel nonequilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these nonequilibrium processes,more » and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. In conclusion, our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.« less

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

Law, P.R.

In Matsushita (J. Math. Phys. {bold 22}, 979--982 (1981), {ital ibid}. {bold 24}, 36--40 (1983)), for curvature endomorphisms for the pseudo-Euclidean space {ital R}{sup 2,2}, an analog of the Petrov classification as a basis for applications to neutral Einstein metrics on compact, orientable, four-dimensional manifolds is provided. This paper points out flaws in Matsushita's classification and, moreover, that an error in Chern's ( Pseudo-Riemannian geometry and the Gauss--Bonnet formula,'' Acad. Brasileira Ciencias {bold 35}, 17--26 (1963) and {ital Shiing}-{ital Shen} {ital Chern}: {ital Selected} {ital Papers} (Springer-Verlag, New York, 1978)) Gauss--Bonnet formula for pseudo-Riemannian geometry was incorporated in Matsushita's subsequentmore » analysis. A self-contained account of the subject of the title is presented to correct these errors, including a discussion of the validity of an appropriate analog of the Thorpe--Hitchin inequality of the Riemannian case. When the inequality obtains in the neutral case, the Euler characteristic is nonpositive, in contradistinction to Matsushita's deductions.« less

High speed exhaust gas recirculation valve

DOEpatents

Fensom, Rod; Kidder, David J.

2005-01-18

In order to minimize pollutants such as Nox, internal combustion engines typically include an exhaust gas recirculation (EGR) valve that can be used to redirect a portion of exhaust gases to an intake conduit, such as an intake manifold, so that the redirected exhaust gases will be recycled. It is desirable to have an EGR valve with fast-acting capabilities, and it is also desirable to have the EGR valve take up as little space as possible. An exhaust gas recirculation valve is provided that includes an exhaust passage tube, a valve element pivotally mounted within the exhaust passage tube, a linear actuator; and a gear train. The gear train includes a rack gear operatively connected to the linear actuator, and at least one rotatable gear meshing with the rack gear and operatively connected to the valve element to cause rotation of the valve element upon actuation of the linear actuator. The apparatus provides a highly compact package having a high-speed valve actuation capability.

Improved repetition rate mixed isotope CO{sub 2} TEA laser

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

Cohn, D. B., E-mail: dbctechnology@earthlink.net

2014-09-15

A compact CO{sub 2} TEA laser has been developed for remote chemical detection that operates at a repetition rate of 250 Hz. It emits 700 mJ/pulse at 10.6 μm in a multimode beam with the {sup 12}C{sup 16}O{sub 2} isotope. With mixed {sup 12}C{sup 16}O{sub 2} plus {sup 13}C{sup 16}O{sub 2} isotopes it emits multiple lines in both isotope manifolds to improve detection of a broad range of chemicals. In particular, output pulse energies are 110 mJ/pulse at 9.77 μm, 250 mJ/pulse at 10 μm, and 550 mJ/pulse at 11.15 μm, useful for detection of the chemical agents Sarin, Tabun, and VX. Relatedmore » work shows capability for long term sealed operation with a catalyst and an agile tuner at a wavelength shift rate of 200 Hz.« less

Aging and rejuvenation of active matter under topological constraints

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

Janssen, Liesbeth M. C.; Kaiser, Andreas; Lowen, Hartmut

The coupling of active, self-motile particles to topological constraints can give rise to novel nonequilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these nonequilibrium processes,more » and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. In conclusion, our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.« less

Non-topological cycloops

NASA Astrophysics Data System (ADS)

Lake, Matthew; Thomas, Steven; Ward, John

2010-01-01

We propose a mechanism for the creation of cosmic string loops with dynamically stabilised windings in the internal space. Assuming a velocity correlations regime in the post-inflationary epoch, such windings are seen to arise naturally in string networks prior to loop formation. The angular momentum of the string in the compact space may then be sufficient to ensure that the windings remain stable after the loop chops off from the network, even if the internal manifold is simply connected. For concreteness we embed our model in the Klebanov-Strassler geometry, which provides a natural mechanism for brane inflation, as well a being one of the best understood compactification schemes in type IIB string theory. We see that the interaction of angular momentum with the string tension causes the loop to oscillate between phases of expansion and contraction. This, in principle, should give rise to a distinct gravitational wave signature, the future detection of which could provide indirect evidence for the existence of extra dimensions.

Time dependence of triplet-singlet excitation transfer from compact poly rA to bound dye at 77 K.

PubMed Central

Pearlstein, R M; Van Nostrand, F; Nairn, J A

1979-01-01

The nonexponential phosphorescence decay of a highly folded form of poly-riboadenylic acid (poly rA) with noncovalently bound dye is explained by a novel application of a well-known theory of electronic excitation transfer based on the Förster mechanism. This theory, originally used to describe singlet-singlet energy transfer from donor molecules to an acceptor in a solution, is here applied to the transfer of triplet excitation from the adenine (in poly rA) to the singlet manifold of either of the bound dyes, ethidium bromide or proflavine. New experimental data are presented that allow straight-forward theoretical interpretation. These data fit the form predicted by the theory, U(t) exp(-Bt1/2), where U(t) is the decay of the poly rA phosphorescence in the absence of dye, for a range of relative concentrations of either dye. The self-consistency of these theoretical fits is demonstrated by the proportionality of B to the square root of the Förster triplet-singlet overlap integrals for transfer from poly rA to each of the dyes, as demanded by the theory. From these self-consistent values of B, the theory enables one to deduce the mean packing density of nucleotides in this folded poly rA, which we estimate to be approximately 1 nm-3. We conclude that some variations of the method described here may be useful for deducing packing densities of nucleotides in other compact nucleic acid structures. PMID:262411

Interference evaluation between manifold and wet Christmas tree CP systems

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

Brasil, S.L.D.C.; Baptista, W.

2000-05-01

Offshore production wells are controlled by valves installed in the marine soil, called wet Christmas trees (WCTs). A manifold receives the production of several wells and transports it to the platform. The manifold is cathodically protected by Al anodes and the WCT by Zn anodes. A computer simulation was carried out to evaluate the interference between the equipment cathodic protection systems.

Noncommutative gauge theory for Poisson manifolds

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Wess, Julius

2000-09-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Classical BV Theories on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai

2014-12-01

In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.

On a program manifold's stability of one contour automatic control systems

NASA Astrophysics Data System (ADS)

Zumatov, S. S.

2017-12-01

Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold's absolute stability of one contour automatic control systems are obtained. The Hurwitz's angle of absolute stability was determined. The sufficient conditions of program manifold's absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov's second method.

Mechanical systems with closed orbits on manifolds of revolution

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

Kudryavtseva, E A; Fedoseev, D A

We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles.

Scientific data interpolation with low dimensional manifold model

NASA Astrophysics Data System (ADS)

Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley

2018-01-01

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Encoding quantum information in a stabilized manifold of a superconducting cavity

NASA Astrophysics Data System (ADS)

Touzard, S.; Leghtas, Z.; Mundhada, S. O.; Axline, C.; Reagor, M.; Chou, K.; Blumoff, J.; Sliwa, K. M.; Shankar, S.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.

In a superconducting Josephson circuit architecture, we activate a multi-photon process between two modes by applying microwave drives at specific frequencies. This creates a pairwise exchange of photons between a high-Q cavity and the environment. The resulting open dynamical system develops a two-dimensional quasi-energy ground state manifold. Can we encode, protect and manipulate quantum information in this manifold? We experimentally investigate the convergence and escape rates in and out of this confined subspace. Finally, using quantum Zeno dynamics, we aim to perform gates which maintain the state in the protected manifold at all times. Work supported by: ARO, ONR, AFOSR and YINQE.

Pluripotential theory on quaternionic manifolds

NASA Astrophysics Data System (ADS)

Alesker, Semyon

2012-05-01

On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003) [1] for the flat quaternionic space Hn and in Alesker and Verbitsky (2006) [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.

Analysis on singular spaces: Lie manifolds and operator algebras

NASA Astrophysics Data System (ADS)

Nistor, Victor

2016-07-01

We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called ;Lie manifolds; -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

Feedback Integrators

NASA Astrophysics Data System (ADS)

Chang, Dong Eui; Jiménez, Fernando; Perlmutter, Matthew

2016-12-01

A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves the first integrals of the system. The idea is that given an initial point in the manifold we extend the dynamics from the manifold to its ambient Euclidean space and then modify the dynamics outside the intersection of the manifold and the level sets of the first integrals containing the initial point such that the intersection becomes a unique local attractor of the resultant dynamics. While the modified dynamics theoretically produces the same trajectory as the original dynamics, it yields a numerical trajectory that stably remains on the manifold and preserves the first integrals. The big merit of our method is that the modified dynamics can be integrated with any ordinary numerical integrator such as Euler or Runge-Kutta. We illustrate this method by applying it to three famous problems: the free rigid body, the Kepler problem and a perturbed Kepler problem with rotational symmetry. We also carry out simulation studies to demonstrate the excellence of our method and make comparisons with the standard projection method, a splitting method and Störmer-Verlet schemes.

Methods for disassembling, replacing and assembling parts of a steam cooling system for a gas turbine

DOEpatents

Wilson, Ian D.; Wesorick, Ronald R.

2002-01-01

The steam cooling circuit for a gas turbine includes a bore tube assembly supplying steam to circumferentially spaced radial tubes coupled to supply elbows for transitioning the radial steam flow in an axial direction along steam supply tubes adjacent the rim of the rotor. The supply tubes supply steam to circumferentially spaced manifold segments located on the aft side of the 1-2 spacer for supplying steam to the buckets of the first and second stages. Spent return steam from these buckets flows to a plurality of circumferentially spaced return manifold segments disposed on the forward face of the 1-2 spacer. Crossover tubes couple the steam supply from the steam supply manifold segments through the 1-2 spacer to the buckets of the first stage. Crossover tubes through the 1-2 spacer also return steam from the buckets of the second stage to the return manifold segments. Axially extending return tubes convey spent cooling steam from the return manifold segments to radial tubes via return elbows. The bore tube assembly, radial tubes, elbows, manifold segments and crossover tubes are removable from the turbine rotor and replaceable.

Principal Curves on Riemannian Manifolds.

PubMed

Hauberg, Soren

2016-09-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

3D spine reconstruction of postoperative patients from multi-level manifold ensembles.

PubMed

Kadoury, Samuel; Labelle, Hubert; Parent, Stefan

2014-01-01

The quantitative assessment of surgical outcomes using personalized anatomical models is an essential task for the treatment of spinal deformities such as adolescent idiopathic scoliosis. However an accurate 3D reconstruction of the spine from postoperative X-ray images remains challenging due to presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. In this paper, we formulate the reconstruction problem as an optimization over a manifold of articulated spine shapes learned from pathological training data. The manifold itself is represented using a novel data structure, a multi-level manifold ensemble, which contains links between nodes in a single hierarchical structure, as well as links between different hierarchies, representing overlapping partitions. We show that this data structure allows both efficient localization and navigation on the manifold, for on-the-fly building of local nonlinear models (manifold charting). Our reconstruction framework was tested on pre- and postoperative X-ray datasets from patients who underwent spinal surgery. Compared to manual ground-truth, our method achieves a 3D reconstruction accuracy of 2.37 +/- 0.85 mm for postoperative spine models and can deal with severe cases of scoliosis.

Fabrication of Compositionally and Topographically Complex Robust Tissue Forms by 3D-Electrochemical Compaction of Collagen

PubMed Central

Younesi, Mousa; Islam, Anowarul; Kishore, Vipuil; Panit, Stefi; Akkus, Ozan

2015-01-01

Collagen solutions are phase-transformed to mechanically robust shell structures with curviplanar topographies using electrochemically induced pH gradients. The process enables rapid layer-by-layer deposition of collagen-rich mixtures over the entire field simultaneously to obtain compositionally diverse multilayered structures. In-plane tensile strength and modulus of the electrocompacted collagen sheet samples were 5200 -fold and 2300 -fold greater than that of uncompacted collagen samples. Out of plane compression tests showed 27 -fold and fold increase in compressive stress and 46 -fold increase in compressive modulus compared to uncompacted collagen sheets. Cells proliferated 4.9 times faster, and cellular area spread was 2.7 times greater on compacted collagen sheets. Electrocompaction also resulted in 2.9 times greater focal adhesion area than on regular collagen hydrogel. The reported improvements in the cell-matrix interactions with electrocompaction would serve to expedite the population of electrocompacted collagen scaffolds by cells. The capacity of the method to fabricate nonlinear curved topographies with compositional heterogeneous layers is demonstrated by sequential deposition of collagenhydroxyapatite layer over a collagen layer. The complex curved topography of the nasal structure is replicated by the electrochemical compaction method. The presented electrochemical compaction process is an enabling modality which holds significant promise for reconstruction of a wide spectrum of topographically complex systems such as joint surfaces, craniofacial defects, ears, nose or urogenital forms. PMID:26069162

Computer calculation of Witten's 3-manifold invariant

NASA Astrophysics Data System (ADS)

Freed, Daniel S.; Gompf, Robert E.

1991-10-01

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.

Manifold Learning for 3D Shape Description and Classification

DTIC Science & Technology

2014-06-09

sportswear, personal protection clothing and equipment, office and health care device, etc. Therefore it is desirable to develop an effective shape...Modeling Figure 2: Toy example for submanifold decomposition. (a) The original data on the top are fused by two uncorrelated manifolds, blue and red... developed which is effective to extract two linear submanifolds. We demonstrated that comparing with existing manifold learning methods that only

Singularities and non-hyperbolic manifolds do not coincide

NASA Astrophysics Data System (ADS)

Simányi, Nándor

2013-06-01

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai ergodic hypothesis.

The relative isoperimetric inequality on a conformally parabolic manifold with boundary

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

Kesel'man, Vladimir M

2011-07-31

For an arbitrary noncompact n-dimensional Riemannian manifold with a boundary of conformally parabolic type it is proved that there exists a conformal change of metric such that a relative isoperimetric inequality of the same form as in the closed n-dimensional Euclidean half-space holds on the manifold with the new metric. This isoperimetric inequality is asymptotically sharp. Bibliography: 6 titles.

Equations of state for neutron stars and core-collapse supernovae

NASA Astrophysics Data System (ADS)

Oertel, Micaela; Providência, Constança

2018-04-01

Modelling compact stars is a complex task which depends on many ingredients, among others the properties of dense matter. In this contribution models for the equation of state (EoS) of dense matter will be discussed, relevant for the description of core-collapse supernovae, compact stars and compact star mergers. Such EoS models have to cover large ranges in baryon number density, temperature and isospin asymmetry. The characteristics of matter change dramatically within these ranges, from a mixture of nucleons, nuclei, and electrons to uniform, strongly interacting matter containing nucleons, and possibly other particles such as hyperons or quarks. Some implications for compact star astrophysics will be highlighted, too.

Scientific data interpolation with low dimensional manifold model

DOE PAGES

Zhu, Wei; Wang, Bao; Barnard, Richard C.; ...

2017-09-28

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on datamore » compression and interpolation from both regular and irregular samplings.« less

Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

NASA Astrophysics Data System (ADS)

Pogan, Alin; Zumbrun, Kevin

2018-06-01

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

5D Super Yang-Mills on Y p, q Sasaki-Einstein Manifolds

NASA Astrophysics Data System (ADS)

Qiu, Jian; Zabzine, Maxim

2015-01-01

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as Y p, q manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of a certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large N behaviour for the case of single hypermultiplet in adjoint representation and we derive the N 3-behaviour in this case.

Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

PubMed Central

Jun, Ding; Song, Chen; Wei-Bin, Wen; Shao-Ming, Luo; Xia, Huang

2014-01-01

A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method. PMID:24883403

Slow Invariant Manifolds in Chemically Reactive Systems

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Powers, Joseph M.

2006-11-01

The scientific design of practical gas phase combustion devices has come to rely on the use of mathematical models which include detailed chemical kinetics. Such models intrinsically admit a wide range of scales which renders their accurate numerical approximation difficult. Over the past decade, rational strategies, such as Intrinsic Low Dimensional Manifolds (ILDM) or Computational Singular Perturbations (CSP), for equilibrating fast time scale events have been successfully developed, though their computation can be challenging and their accuracy in most cases uncertain. Both are approximations to the preferable slow invariant manifold which best describes how the system evolves in the long time limit. Strategies for computing the slow invariant manifold are examined, and results are presented for practical combustion systems.

Scientific data interpolation with low dimensional manifold model

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

Zhu, Wei; Wang, Bao; Barnard, Richard C.

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on datamore » compression and interpolation from both regular and irregular samplings.« less

Unimodularity criteria for Poisson structures on foliated manifolds

NASA Astrophysics Data System (ADS)

Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

2018-03-01

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

Homoclinic Bifurcation in an SIQR Model for Childhood Diseases

NASA Astrophysics Data System (ADS)

Wu, Lih-Ing; Feng, Zhilan

2000-11-01

We consider a system of ODEs which describes the transmission dynamics of childhood diseases. A center manifold reduction at a bifurcation point has the normal form x‧=y, y‧=axy+bx2y+O(4), indicating a bifurcation of codimension greater than two. A three-parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations. It is shown that the perturbed system produces homoclinic bifurcation.

Star Products with Separation of Variables Admitting a Smooth Extension

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2012-08-01

Given a complex manifold M with an open dense subset Ω endowed with a pseudo-Kähler form ω which cannot be smoothly extended to a larger open subset, we consider various examples where the corresponding Kähler-Poisson structure and a star product with separation of variables on (Ω, ω) admit smooth extensions to M. We give a simple criterion of the existence of a smooth extension of a star product and apply it to these examples.

Teleman localization of Hochschild homology in a singular setting

NASA Astrophysics Data System (ADS)

Brasselet, J.-P.; Legrand, A.

2009-09-01

The aim of this paper is to generalize the Hochschild-Kostant-Rosenberg theorem to the case of singular varieties, more precisely, to manifolds with boundary and to varieties with isolated singularities. In these situations, we define suitable algebras of functions and study the localization of the corresponding Hochschild homology. The tool we use is the Teleman localization process. In the case of isolated singularities, the closed Hochschild homology corresponds to the intersection complex which relates the objects defined here to intersection homology.

Towards representation of a perceptual color manifold using associative memory for color constancy.

PubMed

Seow, Ming-Jung; Asari, Vijayan K

2009-01-01

In this paper, we propose the concept of a manifold of color perception through empirical observation that the center-surround properties of images in a perceptually similar environment define a manifold in the high dimensional space. Such a manifold representation can be learned using a novel recurrent neural network based learning algorithm. Unlike the conventional recurrent neural network model in which the memory is stored in an attractive fixed point at discrete locations in the state space, the dynamics of the proposed learning algorithm represent memory as a nonlinear line of attraction. The region of convergence around the nonlinear line is defined by the statistical characteristics of the training data. This learned manifold can then be used as a basis for color correction of the images having different color perception to the learned color perception. Experimental results show that the proposed recurrent neural network learning algorithm is capable of color balance the lighting variations in images captured in different environments successfully.

Reconstructing 3D Face Model with Associated Expression Deformation from a Single Face Image via Constructing a Low-Dimensional Expression Deformation Manifold.

PubMed

Wang, Shu-Fan; Lai, Shang-Hong

2011-10-01

Facial expression modeling is central to facial expression recognition and expression synthesis for facial animation. In this work, we propose a manifold-based 3D face reconstruction approach to estimating the 3D face model and the associated expression deformation from a single face image. With the proposed robust weighted feature map (RWF), we can obtain the dense correspondences between 3D face models and build a nonlinear 3D expression manifold from a large set of 3D facial expression models. Then a Gaussian mixture model in this manifold is learned to represent the distribution of expression deformation. By combining the merits of morphable neutral face model and the low-dimensional expression manifold, a novel algorithm is developed to reconstruct the 3D face geometry as well as the facial deformation from a single face image in an energy minimization framework. Experimental results on simulated and real images are shown to validate the effectiveness and accuracy of the proposed algorithm.

Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds

NASA Astrophysics Data System (ADS)

Gray, James; Haupt, Alexander S.; Lukas, Andre

2014-09-01

We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in ref. [1]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded from http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html.

Narrow groove welding gas diffuser assembly and welding torch

DOEpatents

Rooney, Stephen J.

2001-01-01

A diffuser assembly is provided for narrow groove welding using an automatic gas tungsten arc welding torch. The diffuser assembly includes a manifold adapted for adjustable mounting on the welding torch which is received in a central opening in the manifold. Laterally extending manifold sections communicate with a shield gas inlet such that shield gas supplied to the inlet passes to gas passages of the manifold sections. First and second tapered diffusers are respectively connected to the manifold sections in fluid communication with the gas passages thereof. The diffusers extend downwardly along the torch electrode on opposite sides thereof so as to release shield gas along the length of the electrode and at the distal tip of the electrode. The diffusers are of a transverse width which is on the order of the thickness of the electrode so that the diffusers can, in use, be inserted into a narrow welding groove before and after the electrode in the direction of the weld operation.

Steam cooling system for a gas turbine

DOEpatents

Wilson, Ian David; Barb, Kevin Joseph; Li, Ming Cheng; Hyde, Susan Marie; Mashey, Thomas Charles; Wesorick, Ronald Richard; Glynn, Christopher Charles; Hemsworth, Martin C.

2002-01-01

The steam cooling circuit for a gas turbine includes a bore tube assembly supplying steam to circumferentially spaced radial tubes coupled to supply elbows for transitioning the radial steam flow in an axial direction along steam supply tubes adjacent the rim of the rotor. The supply tubes supply steam to circumferentially spaced manifold segments located on the aft side of the 1-2 spacer for supplying steam to the buckets of the first and second stages. Spent return steam from these buckets flows to a plurality of circumferentially spaced return manifold segments disposed on the forward face of the 1-2 spacer. Crossover tubes couple the steam supply from the steam supply manifold segments through the 1-2 spacer to the buckets of the first stage. Crossover tubes through the 1-2 spacer also return steam from the buckets of the second stage to the return manifold segments. Axially extending return tubes convey spent cooling steam from the return manifold segments to radial tubes via return elbows.

Corners in M-theory

NASA Astrophysics Data System (ADS)

Sati, Hisham

2011-06-01

M-theory can be defined on closed manifolds as well as on manifolds with boundary. As an extension, we show that manifolds with corners appear naturally in M-theory. We illustrate this with four situations: the lift to bounding 12 dimensions of M-theory on anti-de Sitter spaces, ten-dimensional heterotic string theory in relation to 12 dimensions, and the two M-branes within M-theory in the presence of a boundary. The M2-brane is taken with (or as) a boundary and the worldvolume of the M5-brane is viewed as a tubular neighborhood. We then concentrate on the (variant) of the heterotic theory as a corner and explore analytical and geometric consequences. In particular, we formulate and study the phase of the partition function in this setting and identify the corrections due to the corner(s). The analysis involves considering M-theory on disconnected manifolds and makes use of the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners and the b-calculus of Melrose.

Integral manifolding structure for fuel cell core having parallel gas flow

DOEpatents

Herceg, Joseph E.

1984-01-01

Disclosed herein are manifolding means for directing the fuel and oxidant gases to parallel flow passageways in a fuel cell core. Each core passageway is defined by electrolyte and interconnect walls. Each electrolyte and interconnect wall consists respectively of anode and cathode materials layered on the opposite sides of electrolyte material, or on the opposite sides of interconnect material. A core wall projects beyond the open ends of the defined core passageways and is disposed approximately midway between and parallel to the adjacent overlaying and underlying interconnect walls to define manifold chambers therebetween on opposite sides of the wall. Each electrolyte wall defining the flow passageways is shaped to blend into and be connected to this wall in order to redirect the corresponding fuel and oxidant passageways to the respective manifold chambers either above or below this intermediate wall. Inlet and outlet connections are made to these separate manifold chambers respectively, for carrying the fuel and oxidant gases to the core, and for carrying their reaction products away from the core.

Integral manifolding structure for fuel cell core having parallel gas flow

DOEpatents

Herceg, J.E.

1983-10-12

Disclosed herein are manifolding means for directing the fuel and oxidant gases to parallel flow passageways in a fuel cell core. Each core passageway is defined by electrolyte and interconnect walls. Each electrolyte and interconnect wall consists respectively of anode and cathode materials layered on the opposite sides of electrolyte material, or on the opposite sides of interconnect material. A core wall projects beyond the open ends of the defined core passageways and is disposed approximately midway between and parallel to the adjacent overlaying and underlying interconnect walls to define manifold chambers therebetween on opposite sides of the wall. Each electrolyte wall defining the flow passageways is shaped to blend into and be connected to this wall in order to redirect the corresponding fuel and oxidant passageways to the respective manifold chambers either above or below this intermediate wall. Inlet and outlet connections are made to these separate manifold chambers respectively, for carrying the fuel and oxidant gases to the core, and for carrying their reaction products away from the core.

Perspective: Sloppiness and emergent theories in physics, biology, and beyond.

PubMed

Transtrum, Mark K; Machta, Benjamin B; Brown, Kevin S; Daniels, Bryan C; Myers, Christopher R; Sethna, James P

2015-07-07

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are "sloppy," i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher information matrix, which is interpreted as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. The manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

Gauged supergravities from M-theory reductions

NASA Astrophysics Data System (ADS)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

Real-time probabilistic covariance tracking with efficient model update.

PubMed

Wu, Yi; Cheng, Jian; Wang, Jinqiao; Lu, Hanqing; Wang, Jun; Ling, Haibin; Blasch, Erik; Bai, Li

2012-05-01

The recently proposed covariance region descriptor has been proven robust and versatile for a modest computational cost. The covariance matrix enables efficient fusion of different types of features, where the spatial and statistical properties, as well as their correlation, are characterized. The similarity between two covariance descriptors is measured on Riemannian manifolds. Based on the same metric but with a probabilistic framework, we propose a novel tracking approach on Riemannian manifolds with a novel incremental covariance tensor learning (ICTL). To address the appearance variations, ICTL incrementally learns a low-dimensional covariance tensor representation and efficiently adapts online to appearance changes of the target with only O(1) computational complexity, resulting in a real-time performance. The covariance-based representation and the ICTL are then combined with the particle filter framework to allow better handling of background clutter, as well as the temporary occlusions. We test the proposed probabilistic ICTL tracker on numerous benchmark sequences involving different types of challenges including occlusions and variations in illumination, scale, and pose. The proposed approach demonstrates excellent real-time performance, both qualitatively and quantitatively, in comparison with several previously proposed trackers.

Inferring imagined speech using EEG signals: a new approach using Riemannian manifold features

NASA Astrophysics Data System (ADS)

Nguyen, Chuong H.; Karavas, George K.; Artemiadis, Panagiotis

2018-02-01

Objective. In this paper, we investigate the suitability of imagined speech for brain-computer interface (BCI) applications. Approach. A novel method based on covariance matrix descriptors, which lie in Riemannian manifold, and the relevance vector machines classifier is proposed. The method is applied on electroencephalographic (EEG) signals and tested in multiple subjects. Main results. The method is shown to outperform other approaches in the field with respect to accuracy and robustness. The algorithm is validated on various categories of speech, such as imagined pronunciation of vowels, short words and long words. The classification accuracy of our methodology is in all cases significantly above chance level, reaching a maximum of 70% for cases where we classify three words and 95% for cases of two words. Significance. The results reveal certain aspects that may affect the success of speech imagery classification from EEG signals, such as sound, meaning and word complexity. This can potentially extend the capability of utilizing speech imagery in future BCI applications. The dataset of speech imagery collected from total 15 subjects is also published.

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.

Shelterin Protects Chromosome Ends by Compacting Telomeric Chromatin

PubMed Central

Bandaria, Jigar N.; Qin, Peiwu; Berk, Veysel; Chu, Steven; Yildiz, Ahmet

2016-01-01

SUMMARY Telomeres, repetitive DNA sequences at chromosome ends, are shielded against the DNA damage response (DDR) by the shelterin complex. To understand how shelterin protects telomere ends, we investigated the structural organization of telomeric chromatin in human cells using super-resolution microscopy. We found that telomeres form compact globular structures through a complex network of interactions between shelterin subunits and telomeric DNA, and not by DNA methylation, histone deacetylation or histone trimethylation at telomeres and subtelomeric regions. Mutations that abrogate shelterin assembly or removal of individual subunits from telomeres cause up to a 10-fold increase in telomere volume. Decompacted telomeres become more accessible to telomere-associated proteins and accumulate DDR signals. Recompaction of telomeric chromatin using an orthogonal method displaces DDR signals from telomeres. These results reveal the chromatin remodeling activity of shelterin and demonstrate that shelterin-mediated compaction of telomeric chromatin provides robust protection of chromosome ends against the DDR machinery. PMID:26871633

Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds

NASA Astrophysics Data System (ADS)

Chikin, V. M.

2017-07-01

In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular n-gons with n≥ 7 their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles.

Solid state optical refrigeration using stark manifold resonances in crystals

DOEpatents

Seletskiy, Denis V.; Epstein, Richard; Hehlen, Markus P.; Sheik-Bahae, Mansoor

2017-02-21

A method and device for cooling electronics is disclosed. The device includes a doped crystal configured to resonate at a Stark manifold resonance capable of cooling the crystal to a temperature of from about 110K to about 170K. The crystal host resonates in response to input from an excitation laser tuned to exploit the Stark manifold resonance corresponding to the cooling of the crystal.

Environmental continuous air monitor inlet with combined preseparator and virtual impactor

DOEpatents

Rodgers, John C [Santa Fe, NM

2007-06-19

An inlet for an environmental air monitor is described wherein a pre-separator interfaces with ambient environment air and removes debris and insects commonly associated with high wind outdoors and a deflector plate in communication with incoming air from the pre-separator stage, that directs the air radially and downward uniformly into a plurality of accelerator jets located in a manifold of a virtual impactor, the manifold being cylindrical and having a top, a base, and a wall, with the plurality of accelerator jets being located in the top of the manifold and receiving the directed air and accelerating directed air, thereby creating jets of air penetrating into the manifold, where a major flow is deflected to the walls of the manifold and extracted through ports in the walls. A plurality of receiver nozzles are located in the base of the manifold coaxial with the accelerator jets, and a plurality of matching flow restrictor elements are located in the plurality of receiver nozzles for balancing and equalizing the total minor flow among all the plurality of receiver nozzles, through which a lower, fractional flow extracts large particle constituents of the air for collection on a sample filter after passing through the plurality of receiver nozzles and the plurality of matching flow restrictor elements.

Fedosov Deformation Quantization as a BRST Theory

NASA Astrophysics Data System (ADS)

Grigoriev, M. A.; Lyakhovich, S. L.

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle ?*ρM which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?*ρM and the tangent bundle TM. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables.

Nonlinear dynamic model for visual object tracking on Grassmann manifolds with partial occlusion handling.

PubMed

Khan, Zulfiqar Hasan; Gu, Irene Yu-Hua

2013-12-01

This paper proposes a novel Bayesian online learning and tracking scheme for video objects on Grassmann manifolds. Although manifold visual object tracking is promising, large and fast nonplanar (or out-of-plane) pose changes and long-term partial occlusions of deformable objects in video remain a challenge that limits the tracking performance. The proposed method tackles these problems with the main novelties on: 1) online estimation of object appearances on Grassmann manifolds; 2) optimal criterion-based occlusion handling for online updating of object appearances; 3) a nonlinear dynamic model for both the appearance basis matrix and its velocity; and 4) Bayesian formulations, separately for the tracking process and the online learning process, that are realized by employing two particle filters: one is on the manifold for generating appearance particles and another on the linear space for generating affine box particles. Tracking and online updating are performed in an alternating fashion to mitigate the tracking drift. Experiments using the proposed tracker on videos captured by a single dynamic/static camera have shown robust tracking performance, particularly for scenarios when target objects contain significant nonplanar pose changes and long-term partial occlusions. Comparisons with eight existing state-of-the-art/most relevant manifold/nonmanifold trackers with evaluations have provided further support to the proposed scheme.

Investigation of the Behavior of Fuel in the Intake Manifold and its Relation to S. I. Engines, 1980-1983

NASA Astrophysics Data System (ADS)

Servati, Hamid Beyragh

A liquid fuel film formation on the walls of an intake manifold adversely affects the engine performance and alters the overall air/fuel ratio from that scheduled by a fuel injector or carburetor and leads to adverse effects in vehicle driveability, exhaust emissions, and fuel economy. In this dissertation, the intake manifold is simulated by a horizontal circular duct. A model is provided to predict the rate of deposition and evaporation of the droplets in the intake manifold. The liquid fuel flow rate into the cylinders, mean film velocity and film thickness are determined as functions of engine parameters for both steady and transient operating conditions of the engine. A mathematical engine model is presented to simulate the dynamic interactions of the various engine components such as the air/fuel inlet element, intake manifold, combustion, dynamics and exhaust emissions. Inputs of the engine model are the intake manifold pressure and temperature, throttle angle, and air/fuel ratio. The observed parameters are the histories of fuel film thickness and velocity, fuel consumption, engine speed, engine speed hesitation time, and histories of CO, CO(,2), NO(,x), CH(,n), and O(,2). The effects of different air/fuel ratio control strategies on engine performance and observed parameters are also shown.

Liver DCE-MRI Registration in Manifold Space Based on Robust Principal Component Analysis.

PubMed

Feng, Qianjin; Zhou, Yujia; Li, Xueli; Mei, Yingjie; Lu, Zhentai; Zhang, Yu; Feng, Yanqiu; Liu, Yaqin; Yang, Wei; Chen, Wufan

2016-09-29

A technical challenge in the registration of dynamic contrast-enhanced magnetic resonance (DCE-MR) imaging in the liver is intensity variations caused by contrast agents. Such variations lead to the failure of the traditional intensity-based registration method. To address this problem, a manifold-based registration framework for liver DCE-MR time series is proposed. We assume that liver DCE-MR time series are located on a low-dimensional manifold and determine intrinsic similarities between frames. Based on the obtained manifold, the large deformation of two dissimilar images can be decomposed into a series of small deformations between adjacent images on the manifold through gradual deformation of each frame to the template image along the geodesic path. Furthermore, manifold construction is important in automating the selection of the template image, which is an approximation of the geodesic mean. Robust principal component analysis is performed to separate motion components from intensity changes induced by contrast agents; the components caused by motion are used to guide registration in eliminating the effect of contrast enhancement. Visual inspection and quantitative assessment are further performed on clinical dataset registration. Experiments show that the proposed method effectively reduces movements while preserving the topology of contrast-enhancing structures and provides improved registration performance.

Parts-based stereoscopic image assessment by learning binocular manifold color visual properties

NASA Astrophysics Data System (ADS)

Xu, Haiyong; Yu, Mei; Luo, Ting; Zhang, Yun; Jiang, Gangyi

2016-11-01

Existing stereoscopic image quality assessment (SIQA) methods are mostly based on the luminance information, in which color information is not sufficiently considered. Actually, color is part of the important factors that affect human visual perception, and nonnegative matrix factorization (NMF) and manifold learning are in line with human visual perception. We propose an SIQA method based on learning binocular manifold color visual properties. To be more specific, in the training phase, a feature detector is created based on NMF with manifold regularization by considering color information, which not only allows parts-based manifold representation of an image, but also manifests localized color visual properties. In the quality estimation phase, visually important regions are selected by considering different human visual attention, and feature vectors are extracted by using the feature detector. Then the feature similarity index is calculated and the parts-based manifold color feature energy (PMCFE) for each view is defined based on the color feature vectors. The final quality score is obtained by considering a binocular combination based on PMCFE. The experimental results on LIVE I and LIVE Π 3-D IQA databases demonstrate that the proposed method can achieve much higher consistency with subjective evaluations than the state-of-the-art SIQA methods.

Thermooptic two-mode interference device for reconfigurable quantum optic circuits

NASA Astrophysics Data System (ADS)

Sahu, Partha Pratim

2018-06-01

Reconfigurable large-scale integrated quantum optic circuits require compact component having capability of accurate manipulation of quantum entanglement for quantum communication and information processing applications. Here, a thermooptic two-mode interference coupler has been introduced as a compact component for generation of reconfigurable complex multi-photons quantum interference. Both theoretical and experimental approaches are used for the demonstration of two-photon and four-photon quantum entanglement manipulated with thermooptic phase change in TMI region. Our results demonstrate complex multi-photon quantum interference with high fabrication tolerance and quantum fidelity in smaller dimension than previous thermooptic Mach-Zehnder implementations.

Independent-Cluster Parametrizations of Wave Functions in Model Field Theories III. The Coupled-Cluster Phase Spaces and Their Geometrical Structure

NASA Astrophysics Data System (ADS)

Arponen, J. S.; Bishop, R. F.

1993-11-01

In this third paper of a series we study the structure of the phase spaces of the independent-cluster methods. These phase spaces are classical symplectic manifolds which provide faithful descriptions of the quantum mechanical pure states of an arbitrary system. They are "superspaces" in the sense that the full physical many-body or field-theoretic system is described by a point of the space, in contrast to "ordinary" spaces for which the state of the physical system is described rather by the whole space itself. We focus attention on the normal and extended coupled-cluster methods (NCCM and ECCM). Both methods provide parametrizations of the Hilbert space which take into account in increasing degrees of completeness the connectivity properties of the associated perturbative diagram structure. This corresponds to an increasing incorporation of locality into the description of the quantum system. As a result the degree of nonlinearity increases in the dynamical equations that govern the temporal evolution and determine the equilibrium state. Because of the nonlinearity, the structure of the manifold becomes geometrically complicated. We analyse the neighbourhood of the ground state of the one-mode anharmonic bosonic field theory and derive the nonlinear expansion beyond the linear response regime. The expansion is given in terms of normal-mode amplitudes, which provide the best local coordinate system close to the ground state. We generalize the treatment to other nonequilibrium states by considering the similarly defined normal coordinates around the corresponding phase space point. It is pointed out that the coupled-cluster method (CCM) maps display such features as (an)holonomy, or geometric phase. For example, a physical state may be represented by a number of different points on the CCM manifold. For this reason the whole phase spaces in the NCCM or ECCM cannot be covered by a single chart. To account for this non-Euclidean nature we introduce a suitable pseudo-Riemannian metric structure which is compatible with an important subset of all canonical transformations. It is then shown that the phase space of the configuration-interaction method is flat, namely the complex Euclidean space; that the NCCM manifold has zero curvature even though its Reimann tensor does not vanish; and that the ECCM manifold is intrinsically curved. It is pointed out that with the present metrization many of the dimensions of the ECCM phase space are effectively compactified and that the overall topological structure of the space is related to the distribution of the zeros of the Bargmann wave function.

Parametrization of local CR automorphisms by finite jets and applications

NASA Astrophysics Data System (ADS)

Lamel, Bernhard; Mir, Nordine

2007-04-01

For any real-analytic hypersurface Msubset {C}^N , which does not contain any complex-analytic subvariety of positive dimension, we show that for every point pin M the local real-analytic CR automorphisms of M fixing p can be parametrized real-analytically by their ell_p jets at p . As a direct application, we derive a Lie group structure for the topological group operatorname{Aut}(M,p) . Furthermore, we also show that the order ell_p of the jet space in which the group operatorname{Aut}(M,p) embeds can be chosen to depend upper-semicontinuously on p . As a first consequence, it follows that given any compact real-analytic hypersurface M in {C}^N , there exists an integer k depending only on M such that for every point pin M germs at p of CR diffeomorphisms mapping M into another real-analytic hypersurface in {C}^N are uniquely determined by their k -jet at that point. Another consequence is the following boundary version of H. Cartan's uniqueness theorem: given any bounded domain Ω with smooth real-analytic boundary, there exists an integer k depending only on partial Ω such that if H\\colon Ωto Ω is a proper holomorphic mapping extending smoothly up to partial Ω near some point pin partial Ω with the same k -jet at p with that of the identity mapping, then necessarily H=Id . Our parametrization theorem also holds for the stability group of any essentially finite minimal real-analytic CR manifold of arbitrary codimension. One of the new main tools developed in the paper, which may be of independent interest, is a parametrization theorem for invertible solutions of a certain kind of singular analytic equations, which roughly speaking consists of inverting certain families of parametrized maps with singularities.

Local, smooth, and consistent Jacobi set simplification

DOE PAGES

Bhatia, Harsh; Wang, Bei; Norgard, Gregory; ...

2014-10-31

The relation between two Morse functions defined on a smooth, compact, and orientable 2-manifold can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the two functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces, have shown to be useful in various applications. In practice, unfortunately, functions often contain noise and discretization artifacts, causing their Jacobi set to become unmanageably large and complex. Although there exist techniques to simplify Jacobi sets, they are unsuitable for most applications as they lackmore » fine-grained control over the process, and heavily restrict the type of simplifications possible. In this paper, we introduce a new framework that generalizes critical point cancellations in scalar functions to Jacobi set in two dimensions. We present a new interpretation of Jacobi set simplification based on the perspective of domain segmentation. Generalizing the cancellation of critical points from scalar functions to Jacobi sets, we focus on simplifications that can be realized by smooth approximations of the corresponding functions, and show how these cancellations imply simultaneous simplification of contiguous subsets of the Jacobi set. Using these extended cancellations as atomic operations, we introduce an algorithm to successively cancel subsets of the Jacobi set with minimal modifications to some user-defined metric. We show that for simply connected domains, our algorithm reduces a given Jacobi set to its minimal configuration, that is, one with no birth–death points (a birth–death point is a specific type of singularity within the Jacobi set where the level sets of the two functions and the Jacobi set have a common normal direction).« less

Postoperative 3D spine reconstruction by navigating partitioning manifolds

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

Kadoury, Samuel, E-mail: samuel.kadoury@polymtl.ca; Labelle, Hubert, E-mail: hubert.labelle@recherche-ste-justine.qc.ca; Parent, Stefan, E-mail: stefan.parent@umontreal.ca

Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological casesmore » who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.« less

On spectral synthesis on element-wise compact Abelian groups

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2015-08-01

Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.