Sample records for infinite dimensional groups

  1. Geometry of quantum dynamics in infinite-dimensional Hilbert space

    NASA Astrophysics Data System (ADS)

    Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

    2018-04-01

    We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

  2. On infinite-dimensional state spaces

    NASA Astrophysics Data System (ADS)

    Fritz, Tobias

    2013-05-01

    It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.

  3. Variational optimization algorithms for uniform matrix product states

    NASA Astrophysics Data System (ADS)

    Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

    2018-01-01

    We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

  4. On infinite-dimensional state spaces

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

    Fritz, Tobias

    It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context frommore » which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V{sup -1}U{sup 2}V=U{sup 3}, then finite-dimensionality entails the relation UV{sup -1}UV=V{sup -1}UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V{sup -1}U{sup 2}V=U{sup 3} holds only up to {epsilon} and then yields a lower bound on the dimension.« less

  5. The quantum-field renormalization group in the problem of a growing phase boundary

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

    Antonov, N.V.; Vasil`ev, A.N.

    1995-09-01

    Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik`s assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants ({open_quotes}charge{close_quotes}). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundarymore » and time, {delta}{sub h} and {delta}{sub t}, which satisfy the exact relationship 2 {delta}{sub h}= {delta}{sub t} + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab.« less

  6. Functors of White Noise Associated to Characters of the Infinite Symmetric Group

    NASA Astrophysics Data System (ADS)

    Bożejko, Marek; Guţă, Mădălin

    The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state: The algebras are type factors. Functors of white noise are constructed and proved to be non-equivalent for different values of N.

  7. Spinors in Hilbert Space

    NASA Astrophysics Data System (ADS)

    Plymen, Roger; Robinson, Paul

    1995-01-01

    Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

  8. On the symmetries of integrability

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

    Bellon, M.; Maillard, J.M.; Viallet, C.

    1992-06-01

    In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiatemore » the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.« less

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

    Koenig, Robert; Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125; Mitchison, Graeme

    In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choicemore » of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.« less

  10. Eisenstein series for infinite-dimensional U-duality groups

    NASA Astrophysics Data System (ADS)

    Fleig, Philipp; Kleinschmidt, Axel

    2012-06-01

    We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.

  11. Orthogonality preserving infinite dimensional quadratic stochastic operators

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

    Akın, Hasan; Mukhamedov, Farrukh

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  12. Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations

    NASA Astrophysics Data System (ADS)

    Morozov, Oleg I.

    2018-06-01

    The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.

  13. Entanglement entropy at infinite-randomness fixed points in higher dimensions.

    PubMed

    Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko

    2007-10-05

    The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.

  14. Lyapunov exponents for infinite dimensional dynamical systems

    NASA Technical Reports Server (NTRS)

    Mhuiris, Nessan Mac Giolla

    1987-01-01

    Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

  15. Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

    2017-12-01

    Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

  16. Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

    NASA Astrophysics Data System (ADS)

    Platonov, S. S.

    2018-02-01

    We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.

  17. Boundary Conditions for Infinite Conservation Laws

    NASA Astrophysics Data System (ADS)

    Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

    2016-12-01

    Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

  18. Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

    NASA Astrophysics Data System (ADS)

    Hermann, Robert

    1982-07-01

    Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

  19. On physical property tensors invariant under line groups.

    PubMed

    Litvin, Daniel B

    2014-03-01

    The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of an infinite number of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an index n and a physical property tensor of rank m, the form of the tensor for all line group types indexed with n > m is the same, leaving only a finite number of tensor forms to be determined.

  20. Vertex Operators, Grassmannians, and Hilbert Schemes

    NASA Astrophysics Data System (ADS)

    Carlsson, Erik

    2010-12-01

    We approximate the infinite Grassmannian by finite-dimensional cutoffs, and define a family of fermionic vertex operators as the limit of geometric correspondences on the equivariant cohomology groups, with respect to a one-dimensional torus action. We prove that in the localization basis, these are the well-known fermionic vertex operators on the infinite wedge representation. Furthermore, the boson-fermion correspondence, locality, and intertwining properties with the Virasoro algebra are the limits of relations on the finite-dimensional cutoff spaces, which are true for geometric reasons. We then show that these operators are also, almost by definition, the vertex operators defined by Okounkov and the author in Carlsson and Okounkov ( http://arXiv.org/abs/0801.2565v2 [math.AG], 2009), on the equivariant cohomology groups of the Hilbert scheme of points on {mathbb C^2} , with respect to a special torus action.

  1. Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Wang, C.

    1989-01-01

    A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

  2. Mathematical Techniques for Nonlinear System Theory.

    DTIC Science & Technology

    1981-09-01

    This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

  3. Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

    NASA Technical Reports Server (NTRS)

    Balas, M. J.; Kaufman, H.; Wen, J.

    1985-01-01

    A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

  4. On six-dimensional pseudo-Riemannian almost g.o. spaces

    NASA Astrophysics Data System (ADS)

    Dušek, Zdeněk; Kowalski, Oldřich

    2007-09-01

    We modify the "Kaplan example" (a six-dimensional nilpotent Lie group which is a Riemannian g.o. space) and we obtain two pseudo-Riemannian homogeneous spaces with noncompact isotropy group. These examples have the property that all geodesics are homogeneous up to a set of measure zero. We also show that the (incomplete) geodesic graphs are strongly discontinuous at the boundary, i.e., the limits along certain curves are always infinite.

  5. Boundary control for a flexible manipulator based on infinite dimensional disturbance observer

    NASA Astrophysics Data System (ADS)

    Jiang, Tingting; Liu, Jinkun; He, Wei

    2015-07-01

    This paper focuses on disturbance observer and boundary control design for the flexible manipulator in presence of both boundary disturbance and spatially distributed disturbance. Taking the infinite-dimensionality of the flexural dynamics into account, this study proposes a partial differential equation (PDE) model. Since the spatially distributed disturbance is infinite dimensional, it cannot be compensated by the typical disturbance observer, which is designed by finite dimensional approach. To estimate the spatially distributed disturbance, we propose a novel infinite dimensional disturbance observer (IDDO). Applying the IDDO as a feedforward compensator, a boundary control scheme is designed to regulate the joint position and eliminate the elastic vibration simultaneously. Theoretical analysis validates the stability of both the proposed disturbance observer and the boundary controller. The performance of the closed-loop system is demonstrated by numerical simulations.

  6. On l(1): Optimal decentralized performance

    NASA Technical Reports Server (NTRS)

    Sourlas, Dennis; Manousiouthakis, Vasilios

    1993-01-01

    In this paper, the Manousiouthakis parametrization of all decentralized stabilizing controllers is employed in mathematically formulating the l(sup 1) optimal decentralized controller synthesis problem. The resulting optimization problem is infinite dimensional and therefore not directly amenable to computations. It is shown that finite dimensional optimization problems that have value arbitrarily close to the infinite dimensional one can be constructed. Based on this result, an algorithm that solves the l(sup 1) decentralized performance problems is presented. A global optimization approach to the solution of the infinite dimensional approximating problems is also discussed.

  7. OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

    PubMed Central

    OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

    2016-01-01

    Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

  8. OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

    PubMed

    Ott, William; Rivas, Mauricio A; West, James

    2015-12-01

    Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

  9. Axial point groups: rank 1, 2, 3 and 4 property tensor tables.

    PubMed

    Litvin, Daniel B

    2015-05-01

    The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.

  10. Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

  11. Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

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

    Thapliyal, Kishore, E-mail: tkishore36@yahoo.com; Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in; Pathak, Anirban, E-mail: anirban.pathak@gmail.com

    Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained frommore » experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.« less

  12. Arrowheaded enhanced multivariance products representation for matrices (AEMPRM): Specifically focusing on infinite matrices and converting arrowheadedness to tridiagonality

    NASA Astrophysics Data System (ADS)

    Özdemir, Gizem; Demiralp, Metin

    2015-12-01

    In this work, Enhanced Multivariance Products Representation (EMPR) approach which is a Demiralp-and-his- group extension to the Sobol's High Dimensional Model Representation (HDMR) has been used as the basic tool. Their discrete form have also been developed and used in practice by Demiralp and his group in addition to some other authors for the decomposition of the arrays like vectors, matrices, or multiway arrays. This work specifically focuses on the decomposition of infinite matrices involving denumerable infinitely many rows and columns. To this end the target matrix is first decomposed to the sum of certain outer products and then each outer product is treated by Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) which has been developed by Demiralp and his group. The result is a three-matrix- factor-product whose kernel (the middle factor) is an arrowheaded matrix while the pre and post factors are invertable matrices decomposed of the support vectors of TMEMPR. This new method is called as Arrowheaded Enhanced Multivariance Products Representation for Matrices. The general purpose is approximation of denumerably infinite matrices with the new method.

  13. Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

    1985-01-01

    The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

  14. Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

    PubMed

    Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

    2008-12-19

    We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

  15. Nonlinear Control Systems

    DTIC Science & Technology

    2007-03-01

    Finite -dimensional regulators for a class of infinite dimensional systems ,” Systems and Control Letters, 3 (1983), 7-12. [11] B...semiglobal stabilizability by encoded state feedback,” to appear in Systems and Control Letters. 22 29. C. De Persis, A. Isidori, “Global stabilization of...nonequilibrium setting, for both finite and infinite dimensional control systems . Our objectives for distributed parameter systems included

  16. Synthesis, crystal structure and optical properties of a novel sodium lead pentaborate, NaPbB{sub 5}O{sub 9}

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

    Zhang, Min; Graduate University of Chinese Academy of Sciences, Beijing 100049; Pan, Shilie, E-mail: slpan@ms.xjb.ac.c

    A novel sodium lead pentaborate, NaPbB{sub 5}O{sub 9}, has been successfully synthesized by standard solid-state reaction. The single-crystal X-ray structural analysis showed that NaPbB{sub 5}O{sub 9} crystallizes in the monoclinic space group P2{sub 1}/c with a=6.5324(10) A, b=13.0234(2) A, c=8.5838(10) A, {beta}=104.971(10){sup o}, and Z=4. The crystal structure is composed of double ring [B{sub 5}O{sub 9}]{sup 3-} units, [PbO{sub 7}] and [NaO{sub 7}] polyhedra. [B{sub 5}O{sub 9}]{sup 3-} groups connect with each other forming two-dimensional infinite {sub {infinity}}[B{sub 5}O{sub 9}]{sup 3-} layers, while [PbO{sub 7}] and [NaO{sub 7}] polyhedra are located between the layers. [PbO{sub 7}] polyhedra linked together viamore » corner-sharing O atom forming novel infinite {sub {infinity}}[PbO{sub 6}] chains along the c axis. The thermal behavior, IR spectrum and the optical diffuse reflectance spectrum of NaPbB{sub 5}O{sub 9} were reported. -- Graphical abstract: A new phase, NaPbB{sub 5}O{sub 9}, has been discovered in the ternary M{sub 2}O-PbO-B{sub 2}O{sub 3} (M=alkali-metal) system. The crystal structure consists of a novel infinite {sub {infinity}}[PbO{sub 6}] chains. Display Omitted Research highlights: NaPbB{sub 5}O{sub 9} is the first borate discovered in the ternary M{sub 2}O-PbO-B{sub 2}O{sub 3} (M=alkali-metal) system. NaPbB{sub 5}O{sub 9} crystal structure includes a two-dimensional infinite {sub {infinity}}[B{sub 5}O{sub 9}]{sup 3-} layers and a novel one-dimensional infinite {sub {infinity}}[PbO{sub 6}] chains. [PbO{sub 7}] polyhedron has a highly asymmetric bonding configuration.« less

  17. Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

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

    Benatti, Fabio, E-mail: benatti@ts.infn.it; Oskouei, Samad Khabbazi, E-mail: kh.oskuei@ut.ac.ir; Deh Abad, Ahmad Shafiei, E-mail: shafiei@khayam.ut.ac.ir

    We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

  18. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  19. Fractional Quantum Hall Effect in Infinite-Layer Systems

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

    Naud, J. D.; Pryadko, Leonid P.; Sondhi, S. L.

    2000-12-18

    Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases host ''one and a half'' dimensional surface phases in which motion in one direction is chiral. We offer a general analysis of conduction in the latter by combining sum rule and renormalization group arguments, and find that when interlayer tunneling is marginal or irrelevant they are chiral semimetals that conduct only at T>0 or with disorder.

  20. Classification of Kantowski-Sachs metric via conformal Ricci collineations

    NASA Astrophysics Data System (ADS)

    Hussain, Tahir; Khan, Fawad; Bokhari, Ashfaque H.; Akhtar, Sumaira Saleem

    In this paper, we present a classification of the Kantowski-Sachs spacetime metric according to its conformal Ricci collineations (CRCs). Solving the CRC equations, it is shown that the Kantowski-Sachs metric admits 15-dimensional Lie algebra of CRCs when its Ricci tensor is non-degenerate and an infinite dimensional group of CRCs when the Ricci tensor is degenerate. Some examples of Kantowski-Sachs metric admitting nontrivial CRCs are presented and their physical interpretation is provided.

  1. Computational Methods for Control and Estimation of Distributed System

    DTIC Science & Technology

    1988-08-01

    prey example. [1987, August] Estimation of Nonlinearities in Parabolic Models for Growth, Predation and Dispersal of Populations. S a ON A VARIATIONAL ...NOTATION 17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROUP 19. ABSTRACT (Continue...techniques for infinite dimensional systems. (v) Control and stabilization of visco-elastic structures. (vi) Approximation in delay and Volterra type

  2. De Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography.

    PubMed

    Renner, R; Cirac, J I

    2009-03-20

    We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.

  3. Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

    NASA Astrophysics Data System (ADS)

    Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

    2018-03-01

    The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

  4. Relative Yetter-Drinfeld modules and comodules over braided groups

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

    Zhu, Haixing, E-mail: zhuhaixing@163.com, E-mail: haxing.zhu@njfu.edu.cn

    Let H{sub 1} be a quantum group and f : H{sub 1}⟶H{sub 2} a Hopf algebra homomorphism. Assume that B is some braided group obtained by Majid’s transmutation process. We first show that there is a tensor equivalence between the category of comodules over the braided group B and that of relative Yetter-Drinfeld modules. Next, we prove that the Drinfeld centers of the two categories mentioned above are equivalent to the category of modules over some quantum double, namely, the category of ordinary Yetter-Drinfeld modules over some Radford’s biproduct Hopf algebra. Importantly, the above results not only hold for amore » finite dimensional quantum group but also for an infinite dimensional one.« less

  5. Temperature field determination in slabs, circular plates and spheres with saw tooth heat generating sources

    NASA Astrophysics Data System (ADS)

    Diestra Cruz, Heberth Alexander

    The Green's functions integral technique is used to determine the conduction heat transfer temperature field in flat plates, circular plates, and solid spheres with saw tooth heat generating sources. In all cases the boundary temperature is specified (Dirichlet's condition) and the thermal conductivity is constant. The method of images is used to find the Green's function in infinite solids, semi-infinite solids, infinite quadrants, circular plates, and solid spheres. The saw tooth heat generation source has been modeled using Dirac delta function and Heaviside step function. The use of Green's functions allows obtain the temperature distribution in the form of an integral that avoids the convergence problems of infinite series. For the infinite solid and the sphere, the temperature distribution is three-dimensional and in the cases of semi-infinite solid, infinite quadrant and circular plate the distribution is two-dimensional. The method used in this work is superior to other methods because it obtains elegant analytical or quasi-analytical solutions to complex heat conduction problems with less computational effort and more accuracy than the use of fully numerical methods.

  6. Irreducible representations of finitely generated nilpotent groups

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

    Beloshapka, I V; Gorchinskiy, S O

    2016-01-31

    We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field. Bibliography: 21 titles.

  7. Synthesis, structure characterization and optical properties of a new tripotassium cadmium pentaborate, K{sub 3}CdB{sub 5}O{sub 10}

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

    Yu Hongwei; Graduate school of Chinese Academy of Sciences, Beijing 100049; Pan Shilie, E-mail: slpan@ms.xjb.ac.cn

    A new ternary borate oxide, K{sub 3}CdB{sub 5}O{sub 10}, has been synthesized by solid-state reaction at 580 deg. C. The compound crystallizes in the monoclinic space group P2{sub 1}/n with a=7.6707 (7) A, b=19.1765 (17) A, c=7.8784 (6) A, {beta}=115.6083 (49){sup o}, and Z=4. The crystal structure consists of a two-dimensional infinite [CdB{sub 5}O{sub 10}] layer, which forms by connecting isolated double ring [B{sub 5}O{sub 10}] groups and CdO{sub 4} tetrahedra. K atoms filling in the interlayer and intralayer link the layers together and balance charge. The IR spectrum has been studied and confirmed the presence of both BO{sub 3}more » and BO{sub 4} groups, and the UV-vis-IR diffuse reflectance spectrum exhibits a band gap of about 3.4 eV. The DSC analysis proves that K{sub 3}CdB{sub 5}O{sub 10} is a congruent melting compound. - Graphical abstract: A new phase, K{sub 3}CdB{sub 5}O{sub 10}, has been discovered in the ternary K{sub 2}O-CdO-B{sub 2}O{sub 3} system. The crystal structure consists of a two-dimensional infinite [CdB{sub 5}O{sub 10}] layer. Highlights: > The compound, K{sub 3}CdB{sub 5}O{sub 10}, was synthesized and characterized for the first time. {yields}K{sub 3}CdB{sub 5}O{sub 10} is a congruent melting compound, which means the large single crystals could be grown from the melt using the Czochralski pulling method. {yields}The crystal structure consists of a two-dimensional infinite [CdB{sub 5}O{sub 10}].« less

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

    Giorda, Paolo; Zanardi, Paolo; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

    We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi and S. Lloyd, e-print quant-ph/0305013. The quantum state space H encoding information decomposes into irreducible sectors and subsystems associated with the group of available evolutions. If this group coincides with the unitary part of the group algebra CK of some group K then universal control is achievable over the K-irreducible components of H. This general strategy is applied to different kinds of bosonic systems. We first consider massive bosons in a double well and show how to achieve universal control over all finite-dimensional Fock sectors. We thenmore » discuss a multimode massless case giving the conditions for generating the whole infinite-dimensional multimode Heisenberg-Weyl enveloping algebra. Finally we show how to use an auxiliary bosonic mode coupled to finite-dimensional systems to generate high-order nonlinearities needed for universal control.« less

  9. A Reduced Basis Method with Exact-Solution Certificates for Symmetric Coercive Equations

    DTIC Science & Technology

    2013-11-06

    the energy associated with the infinite - dimensional weak solution of parametrized symmetric coercive partial differential equations with piecewise...builds bounds with respect to the infinite - dimensional weak solution, aims to entirely remove the issue of the “truth” within the certified reduced basis...framework. We in particular introduce a reduced basis method that provides rigorous upper and lower bounds

  10. Robustness of controllers designed using Galerkin type approximations

    NASA Technical Reports Server (NTRS)

    Morris, K. A.

    1990-01-01

    One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.

  11. KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Chierchia, Luigi; You, Jiangong

    In this paper, one-dimensional (1D) nonlinear wave equations with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.

  12. Viscous/potential flow about multi-element two-dimensional and infinite-span swept wings: Theory and experiment

    NASA Technical Reports Server (NTRS)

    Olson, L. E.; Dvorak, F. A.

    1975-01-01

    The viscous subsonic flow past two-dimensional and infinite-span swept multi-component airfoils is studied theoretically and experimentally. The computerized analysis is based on iteratively coupled boundary layer and potential flow analysis. The method, which is restricted to flows with only slight separation, gives surface pressure distribution, chordwise and spanwise boundary layer characteristics, lift, drag, and pitching moment for airfoil configurations with up to four elements. Merging confluent boundary layers are treated. Theoretical predictions are compared with an exact theoretical potential flow solution and with experimental measures made in the Ames 40- by 80-Foot Wind Tunnel for both two-dimensional and infinite-span swept wing configurations. Section lift characteristics are accurately predicted for zero and moderate sweep angles where flow separation effects are negligible.

  13. On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

    NASA Astrophysics Data System (ADS)

    Hu, Zixi; Yao, Zhewei; Li, Jinglai

    2017-03-01

    Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

  14. Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

    NASA Astrophysics Data System (ADS)

    Bischoff, Jan-Moritz; Jeckelmann, Eric

    2017-11-01

    We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

  15. Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane

    DTIC Science & Technology

    2014-07-01

    Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane Peijun Li 1 and Aihua W. Wood 2 1 Department of...of the electromagnetic wave scattering by multiple open cavities, which are embedded in an infinite two-dimensional ground plane . By introducing a...equation, variational formulation. I. INTRODUCTION A cavity is referred to as a local perturbation of the infinite ground plane . Given the cavity

  16. G-Strands on symmetric spaces

    PubMed Central

    2017-01-01

    We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa–Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions. PMID:28413343

  17. Spillover, nonlinearity, and flexible structures

    NASA Technical Reports Server (NTRS)

    Bass, Robert W.; Zes, Dean

    1991-01-01

    Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

  18. Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

    NASA Astrophysics Data System (ADS)

    Sakuraba, Takao

    The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A rigorous construction of measures quasi-invariant under the group of diffeomorphisms of d-dimensional space stabilizing a point is given.

  19. Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential

    NASA Astrophysics Data System (ADS)

    Hussin, Véronique; Marquette, Ian

    2011-03-01

    We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry.

  20. Analysis of transitional separation bubbles on infinite swept wings

    NASA Technical Reports Server (NTRS)

    Davis, R. L.; Carter, J. E.

    1986-01-01

    A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

  1. Continuous spin representations from group contraction

    NASA Astrophysics Data System (ADS)

    Khan, Abu M.; Ramond, Pierre

    2005-05-01

    We consider how the continuous spin representation (CSR) of the Poincaré group in four dimensions can be generated by dimensional reduction. The analysis uses the front-form little group in five dimensions, which must yield the Euclidean group E(2), the little group of the CSR. We consider two cases, one is the single spin massless representation of the Poincaré group in five dimensions, the other is the infinite component Majorana equation, which describes an infinite tower of massive states in five dimensions. In the first case, the double singular limit j, R →∞, with j /R fixed, where R is the Kaluza-Klein radius of the fifth dimension, and j is the spin of the particle in five dimensions, yields the CSR in four dimensions. It amounts to the Inönü-Wigner contraction, with the inverse Kaluza-Klein radius as contraction parameter. In the second case, the CSR appears only by taking a triple singular limit, where an internal coordinate of the Majorana theory goes to infinity, while leaving its ratio to the Kaluza-Klein radius fixed.

  2. Geometric MCMC for infinite-dimensional inverse problems

    NASA Astrophysics Data System (ADS)

    Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

    2017-04-01

    Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

  3. On some structure-turbulence interaction problems

    NASA Technical Reports Server (NTRS)

    Maekawa, S.; Lin, Y. K.

    1976-01-01

    The interactions between a turbulent flow structure; responding to its excitation were studied. The turbulence was typical of those associated with a boundary layer, having a cross-spectral density indicative of convection and statistical decay. A number of structural models were considered. Among the one-dimensional models were an unsupported infinite beam and a periodically supported infinite beam. The fuselage construction of an aircraft was then considered. For the two-dimensional case a simple membrane was used to illustrate the type of formulation applicable to most two-dimensional structures. Both the one-dimensional and two-dimensional structures studied were backed by a cavity filled with an initially quiescent fluid to simulate the acoustic environment when the structure forms one side of a cabin of a sea vessel or aircraft.

  4. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

    An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

  5. Hypercyclic subspaces for Frechet space operators

    NASA Astrophysics Data System (ADS)

    Petersson, Henrik

    2006-07-01

    A continuous linear operator is hypercyclic if there is an such that the orbit {Tnx} is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that it is possible to characterize Banach space operators that have a hypercyclic subspace, i.e., an infinite dimensional closed subspace of, except for zero, hypercyclic vectors. The following is known to hold: A Banach space operator T has a hypercyclic subspace if there is a sequence (ni) and an infinite dimensional closed subspace such that T is hereditarily hypercyclic for (ni) and Tni->0 pointwise on E. In this note we extend this result to the setting of Frechet spaces that admit a continuous norm, and study some applications for important function spaces. As an application we also prove that any infinite dimensional separable Frechet space with a continuous norm admits an operator with a hypercyclic subspace.

  6. A Heisenberg Algebra Bundle of a Vector Field in Three-Space and its Weyl Quantization

    NASA Astrophysics Data System (ADS)

    Binz, Ernst; Pods, Sonja

    2006-01-01

    In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group HX∞. A representation of the C*-group algebra of HX∞ is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.

  7. Geometric structures of super-(Diff(S/sup 1/)/S/sup 1/)*

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

    Schmidke, W.B.; Vokos, S.P.

    Superconformal invariance is of central importance to a perturbative and non-perturbative formulation of stringy theory. The group that describes the invariances of the superstring is the super-Virasoro group, Super-Diff(S/sup 1/). The super-reparameterizations of the circle that leave a point fixed compose the quotient space Super-(Diff(S/sup 1/)/S/sup 1/). We investigate the holomorphic geometry of this infinite-dimensional Kaehler supermanifold and calculate its curvature. copyright 1989 Academic Press, Inc.

  8. Casimir interaction of rodlike particles in a two-dimensional critical system.

    PubMed

    Eisenriegler, E; Burkhardt, T W

    2016-09-01

    We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.

  9. Private algebras in quantum information and infinite-dimensional complementarity

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

    Crann, Jason, E-mail: jason-crann@carleton.ca; Laboratoire de Mathématiques Paul Painlevé–UMR CNRS 8524, UFR de Mathématiques, Université Lille 1–Sciences et Technologies, 59655 Villeneuve d’Ascq Cédex; Kribs, David W., E-mail: dkribs@uoguelph.ca

    We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.

  10. Generalized continued fractions and ergodic theory

    NASA Astrophysics Data System (ADS)

    Pustyl'nikov, L. D.

    2003-02-01

    In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

  11. The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C)

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Rezende, Alex C.; Oliveira, Regilene D. S.

    Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure /line{QsnSN(C)} within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of /line{QsnSN(C)} is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the presence of a double limit cycle.

  12. Identities of Finitely Generated Algebras Over AN Infinite Field

    NASA Astrophysics Data System (ADS)

    Kemer, A. R.

    1991-02-01

    It is proved that for each finitely generated associative PI-algebra U over an infinite field F, there is a finite-dimensional F-algebra C such that the ideals of identities of the algebras U and C coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for T-ideals.

  13. Chain of point-like potentials in Script R3 and infiniteness of the number of bound states

    NASA Astrophysics Data System (ADS)

    Boitsev, A. A.; Popov, I. Yu; Sokolov, O. V.

    2014-10-01

    Infinite chain of point-like potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The background of the model is the theory of self-adjoint extensions of symmetric operators in the Hilbert space. The analogous example of the Hamiltonian is obtained for the system of three-dimensional waveguides coupled through point-like windows.

  14. Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

    NASA Astrophysics Data System (ADS)

    Chruściel, Piotr T.; Delay, Erwann; Klinger, Paul

    2018-02-01

    We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein–Maxwell-dilaton-scalar fields-Yang–Mills–Higgs–Chern–Simons-f(R) equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

  15. A supersonic three-dimensional code for flow over blunt bodies: Program documentation and test cases

    NASA Technical Reports Server (NTRS)

    Chaussee, D. S.; Mcmillan, O. J.

    1980-01-01

    The use of a computer code for the calculation of steady, supersonic, three dimensional, inviscid flow over blunt bodies is illustrated. Input and output are given and explained for two cases: a pointed code of 20 deg half angle at 15 deg angle of attack in a free stream with M sub infinite = 7, and a cone-ogive-cylinder at 10 deg angle of attack with M sub infinite = 2.86. A source listing of the computer code is provided.

  16. Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

    NASA Astrophysics Data System (ADS)

    Kogelbauer, Florian; Haller, George

    2018-06-01

    We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

  17. COBE satellite measurement, hyperspheres, superstrings and the dimension of spacetime.

    NASA Astrophysics Data System (ADS)

    El Naschie, M. S.

    1998-08-01

    The first part of the paper attempts to establish connections between hypersphere backing in infinite dimensions, the expectation value of dimE(∞) spacetime and the COBE measurement of the microwave background radiation. One of the main results reported here is that the mean sphere in S(∞) spans a four dimensional manifold and is thus equal to the expectation value of the topological dimension of E(∞). In the second part the author introduces within a general theory, a probabilistic justification for a compactification which reduces an infinite dimensional spacetime E(∞) (n = ∞) to a four dimensional one (DT = n = 4).

  18. Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

    NASA Astrophysics Data System (ADS)

    Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

    2018-03-01

    By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

  19. A Lie based 4-dimensional higher Chern-Simons theory

    NASA Astrophysics Data System (ADS)

    Zucchini, Roberto

    2016-05-01

    We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.

  20. 2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

    NASA Astrophysics Data System (ADS)

    Yang, Y. B.; Hung, H. H.; Kao, J. C.

    2010-05-01

    The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

  1. Statistical symmetries of the Lundgren-Monin-Novikov hierarchy.

    PubMed

    Wacławczyk, Marta; Staffolani, Nicola; Oberlack, Martin; Rosteck, Andreas; Wilczek, Michael; Friedrich, Rudolf

    2014-07-01

    It was shown by Oberlack and Rosteck [Discr. Cont. Dyn. Sys. S, 3, 451 2010] that the infinite set of multipoint correlation (MPC) equations of turbulence admits a considerable extended set of Lie point symmetries compared to the Galilean group, which is implied by the original set of equations of fluid mechanics. Specifically, a new scaling group and an infinite set of translational groups of all multipoint correlation tensors have been discovered. These new statistical groups have important consequences for our understanding of turbulent scaling laws as they are essential ingredients of, e.g., the logarithmic law of the wall and other scaling laws, which in turn are exact solutions of the MPC equations. In this paper we first show that the infinite set of translational groups of all multipoint correlation tensors corresponds to an infinite dimensional set of translations under which the Lundgren-Monin-Novikov (LMN) hierarchy of equations for the probability density functions (PDF) are left invariant. Second, we derive a symmetry for the LMN hierarchy which is analogous to the scaling group of the MPC equations. Most importantly, we show that this symmetry is a measure of the intermittency of the velocity signal and the transformed functions represent PDFs of an intermittent (i.e., turbulent or nonturbulent) flow. Interesting enough, the positivity of the PDF puts a constraint on the group parameters of both shape and intermittency symmetry, leading to two conclusions. First, the latter symmetries may no longer be Lie group as under certain conditions group properties are violated, but still they are symmetries of the LMN equations. Second, as the latter two symmetries in its MPC versions are ingredients of many scaling laws such as the log law, the above constraints implicitly put weak conditions on the scaling parameter such as von Karman constant κ as they are functions of the group parameters. Finally, let us note that these kind of statistical symmetries are of much more general type, i.e., not limited to MPC or PDF equations emerging from Navier-Stokes, but instead they are admitted by other nonlinear partial differential equations like, for example, the Burgers equation when in conservative form and if the nonlinearity is quadratic.

  2. Thermodynamics of a periodically driven qubit

    NASA Astrophysics Data System (ADS)

    Donvil, Brecht

    2018-04-01

    We present a new approach to the open system dynamics of a periodically driven qubit in contact with a temperature bath. We are specifically interested in the thermodynamics of the qubit. It is well known that by combining the Markovian approximation with Floquet theory it is possible to derive a stochastic Schrödinger equation in for the state of the qubit. We follow here a different approach. We use Floquet theory to embed the time-non autonomous qubit dynamics into time-autonomous yet infinite dimensional dynamics. We refer to the resulting infinite dimensional system as the dressed-qubit. Using the Markovian approximation we derive the stochastic Schrödinger equation for the dressed-qubit. The advantage of our approach is that the jump operators are ladder operators of the Hamiltonian. This simplifies the formulation of the thermodynamics. We use the thermodynamics of the infinite dimensional system to recover the thermodynamical description for the driven qubit. We compare our results with the existing literature and recover the known results.

  3. Fragmentary and incidental behaviour of columns, slabs and crystals

    PubMed Central

    Whiteley, Walter

    2014-01-01

    Between the study of small finite frameworks and infinite incidentally periodic frameworks, we find the real materials which are large, but finite, fragments that fit into the infinite periodic frameworks. To understand these materials, we seek insights from both (i) their analysis as large frameworks with associated geometric and combinatorial properties (including the geometric repetitions) and (ii) embedding them into appropriate infinite periodic structures with motions that may break the periodic structure. A review of real materials identifies a number of examples with a local appearance of ‘unit cells’ which repeat under isometries but perhaps in unusual forms. These examples also refocus attention on several new classes of infinite ‘periodic’ frameworks: (i) columns—three-dimensional structures generated with one repeating isometry and (ii) slabs—three-dimensional structures with two independent repeating translations. With this larger vision of structures to be studied, we find some patterns and partial results that suggest new conjectures as well as many additional open questions. These invite a search for new examples and additional theorems. PMID:24379423

  4. High-pressure synthesis and characterization of the first cerium fluoride borate CeB{sub 2}O{sub 4}F

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

    Hinteregger, Ernst; Wurst, Klaus; Tribus, Martina

    2013-08-15

    CeB{sub 2}O{sub 4}F is the first cerium fluoride borate, which is exclusively built up of one-dimensional, infinite chains of condensed trigonal-planar [BO{sub 3}]{sup 3−} groups. This new cerium fluoride borate was synthesized under high-pressure/high-temperature conditions of 0.9 GPa and 1450 °C in a Walker-type multianvil apparatus. The compound crystallizes in the orthorhombic space group Pbca (No. 61) with eight formula units and the lattice parameters a=821.63(5), b=1257.50(9), c=726.71(6) pm, V=750.84(9) Å{sup 3}, R{sub 1}=0.0698, and wR{sub 2}=0.0682 (all data). The structure exhibits a 9+1 coordinated cerium ion, one three-fold coordinated fluoride ion and a one-dimensional chain of [BO{sub 3}]{sup 3−}more » groups. Furthermore, IR spectroscopy, Electron Micro Probe Analysis and temperature-dependent X-ray powder diffraction measurements were performed. - Graphical abstract: A new rare-earth fluoride borate CeB{sub 2}O{sub 4}F could be synthesized under high-pressure/high-temperature conditions of 0.9 °GPa and 1450 °Cin a Walker-type multianvil apparatus. The crystal structure represents a new structure type in the class of rare-earth fluoride borates. The structure exhibits a 9+1 coordinated cerium ion, one three-fold coordinated fluoride ion and a one-dimensional chain of [BO{sub 3}]{sup 3−} groups. A closer view on the ac-plane shows an interesting wave-like modulation of the borate chains. Highlights: • CeB{sub 2}O{sub 4}F is the first fluoride borate exclusively built up of one-dimensional, infinite chains of condensed trigonal-planar [BO{sub 3}]{sup 3−} groups. • CeB{sub 2}O{sub 4}F is the first cerium fluoride borate. • High-pressure conditions were necessary to synthesize CeB{sub 2}O{sub 4}F.« less

  5. Predictive Rate-Distortion for Infinite-Order Markov Processes

    NASA Astrophysics Data System (ADS)

    Marzen, Sarah E.; Crutchfield, James P.

    2016-06-01

    Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.

  6. Lie group classification of first-order delay ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

    2018-05-01

    A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

  7. Three-dimensional dualities with bosons and fermions

    NASA Astrophysics Data System (ADS)

    Benini, Francesco

    2018-02-01

    We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and fermions in the fundamental representation. In all cases we study the phase diagram as we vary two relevant couplings, finding interesting lines of phase transitions. In various cases the dualities lead to predictions about multi-critical fixed points and the emergence of IR quantum symmetries. For unitary groups we also discuss the coupling to background gauge fields and the map of simple monopole operators.

  8. Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

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

    Bagarello, F., E-mail: fabio.bagarello@unipa.it

    In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

  9. Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

    NASA Astrophysics Data System (ADS)

    Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

    2018-05-01

    A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

  10. Studying critical string emerging from non-Abelian vortex in four dimensions

    DOE PAGES

    Koroteev, P.; Shifman, M.; Yung, A.

    2016-05-26

    Recently a special vortex string was found in a class of soliton vortices supported in four-dimensional Yang–Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang–Mills theory has the U(2) gauge group and the Fayet–Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. Here, the full target space ismore » $$\\mathbb R$$ 4 x Y 6 where is a non-compact Calabi–Yau space.« less

  11. New infinite-dimensional hidden symmetries for heterotic string theory

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

    Gao Yajun

    The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected.

  12. Necessary optimality conditions for infinite dimensional state constrained control problems

    NASA Astrophysics Data System (ADS)

    Frankowska, H.; Marchini, E. M.; Mazzola, M.

    2018-06-01

    This paper is concerned with first order necessary optimality conditions for state constrained control problems in separable Banach spaces. Assuming inward pointing conditions on the constraint, we give a simple proof of Pontryagin maximum principle, relying on infinite dimensional neighboring feasible trajectories theorems proved in [20]. Further, we provide sufficient conditions guaranteeing normality of the maximum principle. We work in the abstract semigroup setting, but nevertheless we apply our results to several concrete models involving controlled PDEs. Pointwise state constraints (as positivity of the solutions) are allowed.

  13. Self-dual Skyrmions on the spheres S2 N +1

    NASA Astrophysics Data System (ADS)

    Amari, Y.; Ferreira, L. A.

    2018-04-01

    We construct self-dual sectors for scalar field theories on a (2 N +2 )-dimensional Minkowski space-time with the target space being the 2 N +1 -dimensional sphere S2 N +1. The construction of such self-dual sectors is made possible by the introduction of an extra functional in the action that renders the static energy and the self-duality equations conformally invariant on the (2 N +1 )-dimensional spatial submanifold. The conformal and target-space symmetries are used to build an ansatz that leads to an infinite number of exact self-dual solutions with arbitrary values of the topological charge. The five-dimensional case is discussed in detail, where it is shown that two types of theories admit self-dual sectors. Our work generalizes the known results in the three-dimensional case that lead to an infinite set of self-dual Skyrmion solutions.

  14. Infinite family of three-dimensional Floquet topological paramagnets

    NASA Astrophysics Data System (ADS)

    Potter, Andrew C.; Vishwanath, Ashvin; Fidkowski, Lukasz

    2018-06-01

    We uncover an infinite family of time-reversal symmetric 3 d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium and are governed by an infinite set of Z2-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3 d FTPMs are not captured by group cohomology methods and cannot be obtained from equilibrium classifications simply by treating the discrete time translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous Z2 (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2 d system without breaking time reversal symmetry.

  15. Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems

    NASA Astrophysics Data System (ADS)

    Skardal, Per Sebastian; Restrepo, Juan G.; Ott, Edward

    2017-08-01

    In the last decade, it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper, we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description, we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.

  16. HUFF, a One-Dimensional Hydrodynamics Code for Strong Shocks

    DTIC Science & Technology

    1978-12-01

    results for two sample problems. The first problem discussed is a one-kiloton nuclear burst in infinite sea level air. The second problem is the one...of HUFF as an effective first order hydro- dynamic computer code. 1 KT Explosion The one-kiloton nuclear explosion in infinite sea level air was

  17. Backscatter RCS for TE and TM excitations of dielectric-filled cavity-backed apertures in two-dimensional bodies

    NASA Technical Reports Server (NTRS)

    Goggans, Paul M.; Shumpert, Thomas H.

    1991-01-01

    Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section.

  18. Travelling Fronts and Entire Solutionsof the Fisher-KPP Equation in N

    NASA Astrophysics Data System (ADS)

    Hamel, François; Nadirashvili, Nikolaï

    This paper is devoted to time-global solutions of the Fisher-KPP equation in N: where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.

  19. Solutions of evolution equations associated to infinite-dimensional Laplacian

    NASA Astrophysics Data System (ADS)

    Ouerdiane, Habib

    2016-05-01

    We study an evolution equation associated with the integer power of the Gross Laplacian ΔGp and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiane for the case p=1 (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).

  20. Revised Geometric Measure of Entanglement in Infinite Dimensional Multipartite Quantum Systems

    NASA Astrophysics Data System (ADS)

    Wang, Yinzhu; Wang, Danxia; Huang, Li

    2018-05-01

    In Cao and Wang (J. Phys.: Math. Theor. 40, 3507-3542, 2007), the revised geometric measure of entanglement (RGME) for states in finite dimensional bipartite quantum systems was proposed. Furthermore, in Cao and Wang (Commun. Theor. Phys. 51(4), 613-620, 2009), the authors obtained the revised geometry measure of entanglement for multipartite states including three-qubit GHZ state, W state, and the generalized Smolin state in the presence of noise and the two-mode squeezed thermal state, and defined the Gaussian geometric entanglement measure. In this paper, we generalize the RGME to infinite dimensional multipartite quantum systems, and prove that this measure satisfies some necessary properties as a well-defined entanglement measure, including monotonicity under local operations and classical communications.

  1. Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group

    NASA Astrophysics Data System (ADS)

    Ardentov, Andrei A.; Sachkov, Yuri L.

    2017-12-01

    We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kinematic models of a car with a trailer). On the other hand, this is the simplest sub-Riemannian structure of step three. We describe the global structure of the cut locus (the set of points where geodesics lose their global optimality), the Maxwell set (the set of points that admit more than one minimizer), and the intersection of the cut locus with the caustic (the set of conjugate points along all geodesics). The group of symmetries of the cut locus is described: it is generated by a one-parameter group of dilations R+ and a discrete group of reflections Z2 × Z2 × Z2. The cut locus admits a stratification with 6 three-dimensional strata, 12 two-dimensional strata, and 2 one-dimensional strata. Three-dimensional strata of the cut locus are Maxwell strata of multiplicity 2 (for each point there are 2 minimizers). Two-dimensional strata of the cut locus consist of conjugate points. Finally, one-dimensional strata are Maxwell strata of infinite multiplicity, they consist of conjugate points as well. Projections of sub-Riemannian geodesics to the 2-dimensional plane of the distribution are Euler elasticae. For each point of the cut locus, we describe the Euler elasticae corresponding to minimizers coming to this point. Finally, we describe the structure of the optimal synthesis, i. e., the set of minimizers for each terminal point in the Engel group.

  2. Gauging hidden symmetries in two dimensions

    NASA Astrophysics Data System (ADS)

    Samtleben, Henning; Weidner, Martin

    2007-08-01

    We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine fraktur e9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of fraktur e9. This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of fraktur e9.

  3. The Geometric Nature of the Flaschka Transformation

    NASA Astrophysics Data System (ADS)

    Bloch, Anthony M.; Gay-Balmaz, François; Ratiu, Tudor S.

    2017-06-01

    We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semisimple Lie algebras, the rigid body system on Toda orbits, and to coadjoint orbits of semidirect products groups. In addition, we develop an infinite-dimensional generalization for the group of area preserving diffeomorphisms of the annulus and apply it to the analysis of the dispersionless Toda lattice PDE and the solvable rigid body PDE.

  4. 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.

  5. Perfect commuting-operator strategies for linear system games

    NASA Astrophysics Data System (ADS)

    Cleve, Richard; Liu, Li; Slofstra, William

    2017-01-01

    Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

  6. Wave packet dynamics for a system with position and time-dependent effective mass in an infinite square well

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

    Vubangsi, M.; Tchoffo, M.; Fai, L. C.

    The problem of a particle with position and time-dependent effective mass in a one-dimensional infinite square well is treated by means of a quantum canonical formalism. The dynamics of a launched wave packet of the system reveals a peculiar revival pattern that is discussed. .

  7. Inflation in Flatland

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

    Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin, E-mail: kurt.hinterbichler@case.edu, E-mail: austin.joyce@columbia.edu, E-mail: jkhoury@sas.upenn.edu

    We investigate the symmetry structure of inflation in 2+1 dimensions. In particular, we show that the asymptotic symmetries of three-dimensional de Sitter space are in one-to-one correspondence with cosmological adiabatic modes for the curvature perturbation. In 2+1 dimensions, the asymptotic symmetry algebra is infinite-dimensional, given by two copies of the Virasoro algebra, and can be traced to the conformal symmetries of the two-dimensional spatial slices of de Sitter. We study the consequences of this infinite-dimensional symmetry for inflationary correlation functions, finding new soft theorems that hold only in 2+1 dimensions. Expanding the correlation functions as a power series in themore » soft momentum q , these relations constrain the traceless part of the tensorial coefficient at each order in q in terms of a lower-point function. As a check, we verify that the O( q {sup 2}) identity is satisfied by inflationary correlation functions in the limit of small sound speed.« less

  8. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

    Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

    We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

  9. Quantum solution for the one-dimensional Coulomb problem

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

    Nunez-Yepez, H. N.; Salas-Brito, A. L.; Solis, Didier A.

    2011-06-15

    The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is notmore » its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.« less

  10. Modeling and control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Mingori, D. L.

    1988-01-01

    This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

  11. Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

    NASA Astrophysics Data System (ADS)

    Baek, Seung Ki; Um, Jaegon; Yi, Su Do; Kim, Beom Jun

    2011-11-01

    In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and on the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both of the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

  12. Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

    NASA Astrophysics Data System (ADS)

    Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

    2017-04-01

    We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

  13. Nonlinear damping model for flexible structures. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Zang, Weijian

    1990-01-01

    The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

  14. Aeroacoustic theory for noncompact wing-gust interaction

    NASA Technical Reports Server (NTRS)

    Martinez, R.; Widnall, S. E.

    1981-01-01

    Three aeroacoustic models for noncompact wing-gust interaction were developed for subsonic flow. The first is that for a two dimensional (infinite span) wing passing through an oblique gust. The unsteady pressure field was obtained by the Wiener-Hopf technique; the airfoil loading and the associated acoustic field were calculated, respectively, by allowing the field point down on the airfoil surface, or by letting it go to infinity. The second model is a simple spanwise superposition of two dimensional solutions to account for three dimensional acoustic effects of wing rotation (for a helicopter blade, or some other rotating planform) and of finiteness of wing span. A three dimensional theory for a single gust was applied to calculate the acoustic signature in closed form due to blade vortex interaction in helicopters. The third model is that of a quarter infinite plate with side edge through a gust at high subsonic speed. An approximate solution for the three dimensional loading and the associated three dimensional acoustic field in closed form was obtained. The results reflected the acoustic effect of satisfying the correct loading condition at the side edge.

  15. Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

    NASA Astrophysics Data System (ADS)

    Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

    2017-03-01

    We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

  16. Momentum Probabilities for a Single Quantum Particle in Three-Dimensional Regular "Infinite" Wells: One Way of Promoting Understanding of Probability Densities

    ERIC Educational Resources Information Center

    Riggs, Peter J.

    2013-01-01

    Students often wrestle unsuccessfully with the task of correctly calculating momentum probability densities and have difficulty in understanding their interpretation. In the case of a particle in an "infinite" potential well, its momentum can take values that are not just those corresponding to the particle's quantised energies but…

  17. A note on the regularity of solutions of infinite dimensional Riccati equations

    NASA Technical Reports Server (NTRS)

    Burns, John A.; King, Belinda B.

    1994-01-01

    This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement.

  18. Numerical procedure to determine geometric view factors for surfaces occluded by cylinders

    NASA Technical Reports Server (NTRS)

    Sawyer, P. L.

    1978-01-01

    A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.

  19. Quantum networks in divergence-free circuit QED

    NASA Astrophysics Data System (ADS)

    Parra-Rodriguez, A.; Rico, E.; Solano, E.; Egusquiza, I. L.

    2018-04-01

    Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analogue quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.

  20. Generalized analytic solutions and response characteristics of magnetotelluric fields on anisotropic infinite faults

    NASA Astrophysics Data System (ADS)

    Bing, Xue; Yicai, Ji

    2018-06-01

    In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.

  1. Higgs mechanism for gravity. II. Higher spin connections

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

    Boulanger, Nicolas; Kirsch, Ingo; Jefferson Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

    We continue the work of [Phys. Rev. D 72, 024001 (2005)] in which gravity is considered as the Goldstone realization of a spontaneously broken diffeomorphism group. We complete the discussion of the coset space Diff (d,R)/SO(1,d-1) formed by the d-dimensional group of analytic diffeomorphisms and the Lorentz group. We find that this coset space is parametrized by coordinates, a metric, and an infinite tower of higher-spin or generalized connections. We then study effective actions for the corresponding symmetry breaking which gives mass to the higher spin connections. Our model predicts that gravity is modified at high energies by the exchangemore » of massive higher spin particles.« less

  2. Double line groups: structure, irreducible representations and spin splitting of the bands

    NASA Astrophysics Data System (ADS)

    Lazić, N.; Milivojević, M.; Vuković, T.; Damnjanović, M.

    2018-06-01

    Double line groups are derived, structurally examined and classified within 13 infinite families. Their irreducible representations, found and tabulated, single out the complete set of conserved quantum numbers in fermionic quasi-one-dimensional systems possessing either translational periodicity or incommensurate helical symmetry. Spin–orbit interaction is analyzed: the induced orbital band splitting and the consequent removal of the spin degeneracy are completely explained. Being incompatible with vertical mirror symmetry, as well as with simultaneous invariance under time-reversal and horizontal (roto)reflections, spin splitting and spin polarized currents may occur only in the systems with the first and the fifth family double line group symmetry. The effects are illustrated on carbon nanotubes.

  3. 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.

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

    Kawaguchi, Io; Yoshida, Kentaroh

    We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices.more » The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.« less

  5. From sine-Gordon to vacuumless systems in flat and curved spacetimes

    NASA Astrophysics Data System (ADS)

    Bazeia, D.; Moreira, D. C.

    2017-12-01

    In this work we start from the Higgs prototype model to introduce a new model, which makes a smooth transition between systems with well-located minima and systems that support no minima at all. We implement this possibility using the deformation procedure, which allows the obtaining a sine-Gordon-like model, controlled by a real parameter that gives rise to a family of models, reproducing the sine-Gordon and the so-called vacuumless models. We also study the thick brane scenarios associated with these models and investigate their stability and renormalization group flow. In particular, it is shown how gravity can change from the 5-dimensional warped geometry with a single extra dimension of infinite extent to the conventional 5-dimensional Minkowski geometry.

  6. A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls

    NASA Technical Reports Server (NTRS)

    Noh, H. M.; Pathak, P. H.

    1986-01-01

    An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.

  7. One-dimensional gravity in infinite point distributions.

    PubMed

    Gabrielli, A; Joyce, M; Sicard, F

    2009-10-01

    The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties of the evolution (notably its "self-similarity") like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.

  8. Synthesis, crystal structure and characterization of chiral, three-dimensional anhydrous potassium tris(oxalato)ferrate(III)

    NASA Astrophysics Data System (ADS)

    Saritha, A.; Raju, B.; Ramachary, M.; Raghavaiah, P.; Hussain, K. A.

    2012-11-01

    The synthesis, crystal structure and physical properties of chiral, three-dimensional anhydrous potassium tris(oxalato)ferrate(III) [K3Fe(C2O4)3] are described. X-ray analysis reveals that the compound crystallized in the chiral space group P4132 of cubic system with a=b=c=13.5970(2), Z=4. The structure of the complex consists of infinite anionic [Fe(C2O4)3]3- units with distorted octahedral environment of iron surrounded by six oxygen atoms of three oxalato groups. The anionic units are interlinked through K+ ions of three different coordination environments of distorted octahedral, bicapped trigonal prismatic and trigonal prismatic yielding a three-dimensional motif. The two broad absorption bands at 644 and 924 nm from UV-vis-NIR transmittance spectra were ascribed to a ligand-to-metal charge transfer. The room temperature crystalline EPR spectra indicate the high-spin (S=5/2) of Fe(III) ion. The vibrating sample magnetometer measurement shows the paramagnetic nature at room temperature. Thermal studies of the compound confirm the absence of water molecule.

  9. Estimates of Lagrangian particle transport by wave groups: forward transport by Stokes drift and backward transport by the return flow

    NASA Astrophysics Data System (ADS)

    van den Bremer, Ton S.; Taylor, Paul H.

    2014-11-01

    Although the literature has examined Stokes drift, the net Lagrangian transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the Eulerian return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the Lagrangian transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and finite depth. We then provide dimensional estimates of the net horizontal Lagrangian transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which Lagrangian particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.

  10. Yangians, S-matrices and AdS/CFT

    NASA Astrophysics Data System (ADS)

    Torrielli, Alessandro

    2011-07-01

    This review is meant to be an account of the properties of the infinite-dimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected in a 5 year span of research on the subject. We hope this exercise will be useful for future attempts to study Yangians in field and string theories, with or without supersymmetry.

  11. Infinite time interval backward stochastic differential equations with continuous coefficients.

    PubMed

    Zong, Zhaojun; Hu, Feng

    2016-01-01

    In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).

  12. Infinite Dimensional Dynamical Systems and their Finite Dimensional Analogues.

    DTIC Science & Technology

    1987-01-01

    Rolla ____t___e ___o, __.Paul Steen Cornell Univ.Andrew Szeri Cornell Univ. ByEdriss Titi Univ. of Chicago _Distributi-on/ -S. Tsaltas Unvcrsity of...Cornell University Ithaca, NY 14853 Edriss Titi University of Chicago Dept. of Mathematics 5734 S. University Ave.Chicago, IL 60637 Spiros Tsaltas Dept

  13. Two-Dimensional Diffusion Theory Analysis of Reactivity Effects of a Fuel-Plate-Removal Experiment

    NASA Technical Reports Server (NTRS)

    Gotsky, Edward R.; Cusick, James P.; Bogart, Donald

    1959-01-01

    Two-dimensional two-group diffusion calculations were performed on the NASA reactor simulator in order to evaluate the reactivity effects of fuel plates removed successively from the center experimental fuel element of a seven- by three-element core loading at the Oak Ridge Bulk Shielding Facility. The reactivity calculations were performed by two methods: In the first, the slowing-down properties of the experimental fuel element were represented by its infinite media parameters; and, in the second, the finite size of the experimental fuel element was recognized, and the slowing-down properties of the surrounding core were attributed to this small region. The latter calculation method agreed very well with the experimented reactivity effects; the former method underestimated the experimental reactivity effects.

  14. The half-filled Landau level: The case for Dirac composite fermions

    NASA Astrophysics Data System (ADS)

    Geraedts, Scott D.; Zaletel, Michael P.; Mong, Roger S. K.; Metlitski, Max A.; Vishwanath, Ashvin; Motrunich, Olexei I.

    2016-04-01

    In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that “composite fermions”—bound states of an electron with two magnetic flux quanta—can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2kF backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

  15. Propagation of acoustic waves in a stratified atmosphere, 1

    NASA Technical Reports Server (NTRS)

    Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.

    1994-01-01

    This work is motivated by the chromospheric 3 minute oscillations observed in the K(sub 2v) bright points. We study acoustic gravity waves in a one-dimensional, gravitationally stratified, isothermal atmosphere. The oscillations are excited either by a velocity pulse imparted to a layer in an atmosphere of infinite vertical extent, or by a piston forming the lower boundary of a semi-infinite medium. We consider both linear and non-linear waves.

  16. Spectral feature design in high dimensional multispectral data

    NASA Technical Reports Server (NTRS)

    Chen, Chih-Chien Thomas; Landgrebe, David A.

    1988-01-01

    The High resolution Imaging Spectrometer (HIRIS) is designed to acquire images simultaneously in 192 spectral bands in the 0.4 to 2.5 micrometers wavelength region. It will make possible the collection of essentially continuous reflectance spectra at a spectral resolution sufficient to extract significantly enhanced amounts of information from return signals as compared to existing systems. The advantages of such high dimensional data come at a cost of increased system and data complexity. For example, since the finer the spectral resolution, the higher the data rate, it becomes impractical to design the sensor to be operated continuously. It is essential to find new ways to preprocess the data which reduce the data rate while at the same time maintaining the information content of the high dimensional signal produced. Four spectral feature design techniques are developed from the Weighted Karhunen-Loeve Transforms: (1) non-overlapping band feature selection algorithm; (2) overlapping band feature selection algorithm; (3) Walsh function approach; and (4) infinite clipped optimal function approach. The infinite clipped optimal function approach is chosen since the features are easiest to find and their classification performance is the best. After the preprocessed data has been received at the ground station, canonical analysis is further used to find the best set of features under the criterion that maximal class separability is achieved. Both 100 dimensional vegetation data and 200 dimensional soil data were used to test the spectral feature design system. It was shown that the infinite clipped versions of the first 16 optimal features had excellent classification performance. The overall probability of correct classification is over 90 percent while providing for a reduced downlink data rate by a factor of 10.

  17. Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

    NASA Technical Reports Server (NTRS)

    Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

    1991-01-01

    The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

  18. Computer simulation of plasma and N-body problems

    NASA Technical Reports Server (NTRS)

    Harries, W. L.; Miller, J. B.

    1975-01-01

    The following FORTRAN language computer codes are presented: (1) efficient two- and three-dimensional central force potential solvers; (2) a three-dimensional simulator of an isolated galaxy which incorporates the potential solver; (3) a two-dimensional particle-in-cell simulator of the Jeans instability in an infinite self-gravitating compressible gas; and (4) a two-dimensional particle-in-cell simulator of a rotating self-gravitating compressible gaseous system of which rectangular coordinate and superior polar coordinate versions were written.

  19. Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

    PubMed

    Ran, Shi-Ju

    2016-05-01

    In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

  20. Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices

    NASA Astrophysics Data System (ADS)

    Kong, Yong

    2007-05-01

    By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. AJCBTA70097-316510.1006/jcta.2001.3201 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite ∞×n lattices in terms of dimer density are obtained for small values of n , at both high- and low-dimer-density limits. In the high-dimer-density limit, the theoretical results confirm the dependence of the free energy on the parity of n , a result obtained previously by computational methods by Y. Kong [Y. Kong, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.061102 74, 061102 (2006); Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.73.016106 73, 016106 (2006);Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.011102 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder ∞×n lattice strip has exactly the same first n terms in the series expansion as that of an infinite ∞×∞ lattice.

  1. Edge waves and resonances in two-dimensional phononic crystal plates

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

    Hsu, Jin-Chen, E-mail: hsujc@yuntech.edu.tw; Hsu, Chih-Hsun

    2015-05-07

    We present a numerical study on phononic band gaps and resonances occurring at the edge of a semi-infinite two-dimensional (2D) phononic crystal plate. The edge supports localized edge waves coupling to evanescent phononic plate modes that decay exponentially into the semi-infinite phononic crystal plate. The band-gap range and the number of edge-wave eigenmodes can be tailored by tuning the distance between the edge and the semi-infinite 2D phononic lattice. As a result, a phononic band gap for simultaneous edge waves and plate waves is created, and phononic cavities beside the edge can be built to support high-frequency edge resonances. Wemore » design an L3 edge cavity and analyze its resonance characteristics. Based on the band gap, high quality factor and strong confinement of resonant edge modes are achieved. The results enable enhanced control over acoustic energy flow in phononic crystal plates, which can be used in designing micro and nanoscale resonant devices and coupling of edge resonances to other types of phononic or photonic crystal cavities.« less

  2. Trading spaces: building three-dimensional nets from two-dimensional tilings

    PubMed Central

    Castle, Toen; Evans, Myfanwy E.; Hyde, Stephen T.; Ramsden, Stuart; Robins, Vanessa

    2012-01-01

    We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. PMID:24098839

  3. Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

    USGS Publications Warehouse

    Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

    2004-01-01

    This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

  4. Toward a proof of Montonen-Olive duality via multiple M2-branes

    NASA Astrophysics Data System (ADS)

    Hashimoto, Koji; Tai, Ta-Sheng; Terashima, Seiji

    2009-04-01

    We derive 4-dimensional Script N = 4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group (U(N))2n. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2,Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2,Z) redefinition of the gauge coupling τ = θ/2π + 4πi/g2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2,Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.

  5. Limitations of discrete-time quantum walk on a one-dimensional infinite chain

    NASA Astrophysics Data System (ADS)

    Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun

    2018-04-01

    How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form eiξ A ⊗1p, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form eiξ A ⊗1p. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σx.

  6. Two types of modes in finite size one-dimensional coaxial photonic crystals: General rules and experimental evidence

    NASA Astrophysics Data System (ADS)

    El Boudouti, E. H.; El Hassouani, Y.; Djafari-Rouhani, B.; Aynaou, H.

    2007-08-01

    We demonstrate analytically and experimentally the existence and behavior of two types of modes in finite size one-dimensional coaxial photonic crystals made of N cells with vanishing magnetic field on both sides. We highlight the existence of N-1 confined modes in each band and one mode by gap associated to either one or the other of the two surfaces surrounding the structure. The latter modes are independent of N . These results generalize our previous findings on the existence of surface modes in two semi-infinite superlattices obtained from the cleavage of an infinite superlattice between two cells. The analytical results are obtained by means of the Green’s function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime.

  7. On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity

    NASA Astrophysics Data System (ADS)

    Shi, Yanling; Xu, Junxiang; Xu, Xindong

    2015-02-01

    In this paper, one-dimensional generalized Boussinesq equation: utt - uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.

  8. Computation of canonical correlation and best predictable aspect of future for time series

    NASA Technical Reports Server (NTRS)

    Pourahmadi, Mohsen; Miamee, A. G.

    1989-01-01

    The canonical correlation between the (infinite) past and future of a stationary time series is shown to be the limit of the canonical correlation between the (infinite) past and (finite) future, and computation of the latter is reduced to a (generalized) eigenvalue problem involving (finite) matrices. This provides a convenient and essentially, finite-dimensional algorithm for computing canonical correlations and components of a time series. An upper bound is conjectured for the largest canonical correlation.

  9. On the stability of an infinite swept attachment line boundary layer

    NASA Technical Reports Server (NTRS)

    Hall, P.; Mallik, M. R.; Poll, D. I. A.

    1984-01-01

    The instability of an infinite swept attachment line boundary layer is considered in the linear regime. The basic three dimensional flow is shown to be susceptible to travelling wave disturbances which propagate along the attachment line. The effect of suction on the instability is discussed and the results suggest that the attachment line boundary layer on a swept wing can be significantly stabilized by extremely small amounts of suction. The results obtained are in excellent agreement with the available experimental observations.

  10. A note on blowup of smooth solutions for relativistic Euler equations with infinite initial energy

    NASA Astrophysics Data System (ADS)

    Dong, Jianwei; Zhu, Junhui

    2018-04-01

    We study the singularity formation of smooth solutions of the relativistic Euler equations in (3+1)-dimensional spacetime for infinite initial energy. We prove that the smooth solution blows up in finite time provided that the radial component of the initial generalized momentum is sufficiently large without the conditions M(0)>0 and s2<1/3c2 , which were two key constraints stated in Pan and Smoller (Commun Math Phys 262:729-755, 2006).

  11. Infinite Multiplets

    DOE R&D Accomplishments Database

    Nambu, Y.

    1967-01-01

    The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.

  12. Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

    PubMed Central

    Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

    2014-01-01

    Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

  13. Non-pairwise additivity of the leading-order dispersion energy

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

    Hollett, Joshua W., E-mail: j.hollett@uwinnipeg.ca

    2015-02-28

    The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained inmore » terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is −0.11 kJ mol{sup −1} well{sup −1}, which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.« less

  14. Unlabored system motion by specially conditioned electromagnetic fields in higher dimensional realms

    NASA Astrophysics Data System (ADS)

    David Froning, H.; Meholic, Gregory V.

    2010-01-01

    This third of three papers explores the possibility of swift, stress-less system transitions between slower-than-light and faster-than-light speeds with negligible net expenditure of system energetics. The previous papers derived a realm of higher dimensionality than 4-D spacetime that enabled such unlabored motion; and showed that fields that could propel and guide systems on unlabored paths in the higher dimensional realm must be fields that have been conditioned to SU(2) (or higher) Lie group symmetry. This paper shows that the system's surrounding vacuum dielectric ɛμ, within the higher dimensional realm's is a vector (not scalar) quantity with fixed magnitude ɛ0μ0 and changing direction within the realm with changing system speed. Thus, ɛμ generated by the system's EM field must remain tuned to vacuum ɛ0μ0 in both magnitude and direction during swift, unlabored system transitions between slower and faster than light speeds. As a result, the system's changing path and speed is such that the magnitude of the higher dimensional realm's ɛ0μ0 is not disturbed. And it is shown that a system's flight trajectories associated with its swift, unlabored transitions between zero and infinite speed can be represented by curved paths traced-out within the higher dimensional realm.

  15. Higher-order nonclassicalities of finite dimensional coherent states: A comparative study

    NASA Astrophysics Data System (ADS)

    Alam, Nasir; Verma, Amit; Pathak, Anirban

    2018-07-01

    Conventional coherent states (CSs) are defined in various ways. For example, CS is defined as an infinite Poissonian expansion in Fock states, as displaced vacuum state, or as an eigenket of annihilation operator. In the infinite dimensional Hilbert space, these definitions are equivalent. However, these definitions are not equivalent for the finite dimensional systems. In this work, we present a comparative description of the lower- and higher-order nonclassical properties of the finite dimensional CSs which are also referred to as qudit CSs (QCSs). For the comparison, nonclassical properties of two types of QCSs are used: (i) nonlinear QCS produced by applying a truncated displacement operator on the vacuum and (ii) linear QCS produced by the Poissonian expansion in Fock states of the CS truncated at (d - 1)-photon Fock state. The comparison is performed using a set of nonclassicality witnesses (e.g., higher order antibunching, higher order sub-Poissonian statistics, higher order squeezing, Agarwal-Tara parameter, Klyshko's criterion) and a set of quantitative measures of nonclassicality (e.g., negativity potential, concurrence potential and anticlassicality). The higher order nonclassicality witnesses have found to reveal the existence of higher order nonclassical properties of QCS for the first time.

  16. The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

    PubMed

    Langley, Robin S; Cotoni, Vincent

    2010-04-01

    Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.

  17. Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

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

    Pal, Karoly F.; Vertesi, Tamas

    2010-08-15

    The I{sub 3322} inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I{sub 3322} inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enoughmore » to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I{sub 3322} inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.« less

  18. A Functional Central Limit Theorem for the Becker-Döring Model

    NASA Astrophysics Data System (ADS)

    Sun, Wen

    2018-04-01

    We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

  19. Resonant scattering from a two-dimensional honeycomb PT dipole structure

    NASA Astrophysics Data System (ADS)

    Markoš, P.; Kuzmiak, V.

    2018-05-01

    We studied numerically the electromagnetic response of the finite periodic structure consisting of the PT dipoles represented by two infinitely long, parallel cylinders with the opposite sign of the imaginary part of a refractive index, which are centered at the positions of a two-dimensional honeycomb lattice. We observed that the total scattered energy reveals a series of sharp resonances at which the energy increases by two orders of magnitude and an incident wave is scattered only in a few directions given by spatial symmetry of the periodic structure. We explain this behavior by analysis of the complex frequency spectra associated with an infinite honeycomb array of the PT dipoles and identify the lowest resonance with the broken PT -symmetry mode formed by a doubly degenerate pair with complex conjugate eigenfrequencies corresponding to the K point of the reciprocal lattice.

  20. An analytical and experimental study of the behavior of semi-infinite metal targets under hypervelocity impact

    NASA Technical Reports Server (NTRS)

    Chakrapani, B.; Rand, J. L.

    1971-01-01

    The material strength and strain rate effects associated with the hypervelocity impact problem were considered. A yield criterion involving the second and third invariants of the stress deviator and a strain rate sensitive constitutive equation were developed. The part of total deformation which represents change in shape is attributable to the stress deviator. Constitutive equation is a means for analytically describing the mechanical response of a continuum under study. The accuracy of the yield criterion was verified utilizing the published two and three dimensional experimental data. The constants associated with the constitutive equation were determined from one dimensional quasistatic and dynamic experiments. Hypervelocity impact experiments were conducted on semi-infinite targets of 1100 aluminum, 6061 aluminum alloy, mild steel, and commercially pure lead using spherically shaped and normally incident pyrex projectiles.

  1. A selection principle for Benard-type convection

    NASA Technical Reports Server (NTRS)

    Knightly, G. H.; Sather, D.

    1985-01-01

    In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions are often cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.

  2. Bath-induced correlations in an infinite-dimensional Hilbert space

    NASA Astrophysics Data System (ADS)

    Nizama, Marco; Cáceres, Manuel O.

    2017-09-01

    Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

  3. A characterization of positive linear maps and criteria of entanglement for quantum states

    NASA Astrophysics Data System (ADS)

    Hou, Jinchuan

    2010-09-01

    Let H and K be (finite- or infinite-dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from {\\mathcal B}(H) into {\\mathcal B}(K) is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied to give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is given which shows that a state ρ on HotimesK is separable if and only if (ΦotimesI)ρ >= 0 for all positive finite-rank elementary operators Φ. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.

  4. A selection principle in Benard-type convection

    NASA Technical Reports Server (NTRS)

    Knightly, G. H.; Sather, D.

    1983-01-01

    In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions areoften cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.

  5. Synthesis, crystal structure, and electrical and magnetic properties of BaMo{sub 6}Te{sub 6}: A novel reduced molybdenum telluride containing infinite chains of trans-face shared Mo{sub 6} octahedra

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

    Gall, Philippe; Guizouarn, Thierry; Potel, Michel

    Powder samples and single crystals of the new ternary compound BaMo{sub 6}Te{sub 6} were obtained by solid state reaction. The structure was determined by single-crystal X-ray diffraction. BaMo{sub 6}Te{sub 6} crystallizes in the hexagonal space group P6{sub 3}/m (No. 176) with unit-cell parameters a=9.3941(2) Å, c=4.5848(1) Å and Z=1. Full-matrix least-squares refinement on F{sup 2} using 452 independent reflections for 17 refinable parameters resulted in R1=0.0208 and wR2=0.0539. The structure consists of one-dimensional infinite chains of trans-face shared Mo{sub 6} octahedra capped by Se atoms. These chains that are running along the c axis are separated from each other bymore » nine-coordinate Ba atoms. Resistivity measurements on a single crystal indicated that the BaMo{sub 6}Te{sub 6} compound is metallic down to 160 K and semiconductor below. Magnetic susceptibility measurements showed that BaMo{sub 6}Te{sub 6} is weakly diamagnetic with no anomaly at the metal–semiconductor transition. - Graphical abstract: We present here the synthesis, the crystal structure, and the electrical and magnetic properties of the new compound BaMo{sub 6}Te{sub 6} containing infinite chains of trans-face shared Mo{sub 6} octahedra. - Highlights: • BaMo{sub 6}Te{sub 6} contains infinite chains of trans-face-sharing Mo{sub 6} octahedra |Mo{sub 6/2}|{sub ∞}{sup 1}. • Synthesis by solid state reaction. • Single-crystal X-ray study. • Continuous metal–nonmetal transition. • Anderson localization.« less

  6. Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss

    NASA Astrophysics Data System (ADS)

    Kiefer-Emmanouilidis, M.; Sirker, J.

    2017-12-01

    We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization-group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent—in a loose sense—of Hawking radiation.

  7. Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

    NASA Astrophysics Data System (ADS)

    Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

    2018-04-01

    Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

  8. Infinitely divisible cascades to model the statistics of natural images.

    PubMed

    Chainais, Pierre

    2007-12-01

    We propose to model the statistics of natural images thanks to the large class of stochastic processes called Infinitely Divisible Cascades (IDC). IDC were first introduced in one dimension to provide multifractal time series to model the so-called intermittency phenomenon in hydrodynamical turbulence. We have extended the definition of scalar infinitely divisible cascades from 1 to N dimensions and commented on the relevance of such a model in fully developed turbulence in [1]. In this article, we focus on the particular 2 dimensional case. IDC appear as good candidates to model the statistics of natural images. They share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature. We point out the interest of IDC for applications to procedural texture synthesis.

  9. Classical and quantum production of cornucopions at energies below 1018 GeV

    NASA Astrophysics Data System (ADS)

    Banks, T.; O'loughlin, M.

    1993-01-01

    We argue that the paradoxes associated with infinitely degenerate states, which plague relic particle scenarios for the end point of black hole evaporation, may be absent when the relics are horned particles. Most of our arguments are based on simple observations about the classical geometry of extremal dilaton black holes, but at a crucial point we are forced to speculate about classical solutions to string theory in which the infinite coupling singularity of the extremal dilaton solution is shielded by a condensate of massless modes propagating in its infinite horn. We use the nonsingular c=1 solution of (1+1)-dimensional string theory as a crude model for the properties of the condensate. We also present a brief discussion of more general relic scenarios based on large relics of low mass.

  10. Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery

    NASA Astrophysics Data System (ADS)

    Mansfield, Paul

    1994-04-01

    We solve Schrödinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero.

  11. Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

    NASA Astrophysics Data System (ADS)

    Chang, Jing; Gao, Yixian; Li, Yong

    2015-05-01

    Consider the one dimensional nonlinear beam equation utt + uxxxx + mu + u3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.

  12. Direct Numerical Simulation of a Temporally Evolving Incompressible Plane Wake: Effect of Initial Conditions on Evolution and Topology

    NASA Technical Reports Server (NTRS)

    Sondergaard, R.; Cantwell, B.; Mansour, N.

    1997-01-01

    Direct numerical simulations have been used to examine the effect of the initial disturbance field on the development of three-dimensionality and the transition to turbulence in the incompressible plane wake. The simulations were performed using a new numerical method for solving the time-dependent, three-dimensional, incompressible Navier-Stokes equations in flows with one infinite and two periodic directions. The method uses standard Fast Fourier Transforms and is applicable to cases where the vorticity field is compact in the infinite direction. Initial disturbances fields examined were combinations of two-dimensional waves and symmetric pairs of 60 deg oblique waves at the fundamental, subharmonic, and sub-subharmonic wavelengths. The results of these simulations indicate that the presence of 60 deg disturbances at the subharmonic streamwise wavelength results in the development of strong coherent three-dimensional structures. The resulting strong three-dimensional rate-of-strain triggers the growth of intense fine scale motions. Wakes initiated with 60 deg disturbances at the fundamental streamwise wavelength develop weak coherent streamwise structures, and do not develop significant fine scale motions, even at high Reynolds numbers. The wakes which develop strong three-dimensional structures exhibit growth rates on par with experimentally observed turbulent plane wakes. Wakes which develop only weak three-dimensional structures exhibit significantly lower late time growth rates. Preliminary studies of wakes initiated with an oblique fundamental and a two-dimensional subharmonic, which develop asymmetric coherent oblique structures at the subharmonic wavelength, indicate that significant fine scale motions only develop if the resulting oblique structures are above an angle of approximately 45 deg.

  13. The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

  14. Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models II: The Role of Quantum Affine Symmetry

    NASA Astrophysics Data System (ADS)

    Jimbo, Michio

    2013-03-01

    Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.

  15. Affine Kac-Moody symmetric spaces related with A1^{(1)}, A2^{(1)},} A2^{(2)}

    NASA Astrophysics Data System (ADS)

    Nayak, Saudamini; Pati, K. C.

    2014-08-01

    Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A1^{(1)}, A2^{(1)}, A2^{(2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.

  16. Interband excitations in the 1D limit of two-band fractional Chern insulators

    NASA Astrophysics Data System (ADS)

    Jaworowski, Błażej; Kaczmarkiewicz, Piotr; Potasz, Paweł; Wójs, Arkadiusz

    2018-05-01

    We investigate the stability of the one-dimensional limit of ν = 1 / 3 Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system - the checkerboard lattice.

  17. Curvature of Super Diff(S/sup 1/)/S/sup 1/

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

    Oh, P.; Ramond, P.

    Motivated by the work of Bowick and Rajeev, we calculate the curvature of the infinite-dimensional flag manifolds DiffS/sup 1//S/sup 1/ and Super DiffS/sup 1//S/sup 1/ using standard finite-dimensional coset space techniques. We regularize the infinity by zeta-function regularization and recover the conformal and superconformal anomalies respectively for a specific choice of the torsion.

  18. Analytical three-dimensional neutron transport benchmarks for verification of nuclear engineering codes. Final report

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

    Ganapol, B.D.; Kornreich, D.E.

    Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) pointmore » source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green`s function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade.« less

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

    Shirokov, M. E.

    We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information ismore » proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.« less

  20. Monte-Carlo simulations of the clean and disordered contact process in three space dimensions

    NASA Astrophysics Data System (ADS)

    Vojta, Thomas

    2013-03-01

    The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte-Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality. This work has been supported in part by the NSF under grants no. DMR-0906566 and DMR-1205803.

  1. Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol Concentration from Transdermal Biosensor Data.

    PubMed

    Rosen, I G; Luczak, Susan E; Weiss, Jordan

    2014-03-15

    We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

  2. Fast generation of three-dimensional computational boundary-conforming periodic grids of C-type. [for turbine blades and propellers

    NASA Technical Reports Server (NTRS)

    Dulikravich, D. S.

    1982-01-01

    A fast computer program, GRID3C, was developed to generate multilevel three dimensional, C type, periodic, boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields. The technique is based on two analytic functions that conformally map a cascade of semi-infinite slits to a cascade of doubly infinite strips on different Riemann sheets. Up to four consecutively refined three dimensional grids are automatically generated and permanently stored on four different computer tapes. Grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions. The grids are easily clustered closer to the blade surface, the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters. Hub and duct (or outer free boundary) have different axisymmetric shapes. A vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by GRID3C. Blade cross sectional shape, chord length, twist angle, sweep angle, and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction.

  3. Asymptotic symmetries of Rindler space at the horizon and null infinity

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

    Chung, Hyeyoun

    2010-08-15

    We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler spacemore » at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.« less

  4. Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl (M | N)

    NASA Astrophysics Data System (ADS)

    Tsuboi, Zengo

    2013-05-01

    In [1] (Z. Tsuboi, Nucl. Phys. B 826 (2010) 399, arxiv:arXiv:0906.2039), we proposed Wronskian-like solutions of the T-system for [ M , N ]-hook of the general linear superalgebra gl (M | N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1 ,N1 ]-hook and [M2 ,N2 ]-hook (M =M1 +M2, N =N1 +N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl (M | N). Our solutions also include a Wronskian-like solution discussed in [2] (N. Gromov, V. Kazakov, S. Leurent, Z. Tsuboi, JHEP 1101 (2011) 155, arxiv:arXiv:1010.2720) in relation to the AdS5 /CFT4 spectral problem.

  5. Universal moduli spaces of Riemann surfaces

    NASA Astrophysics Data System (ADS)

    Ji, Lizhen; Jost, Jürgen

    2017-04-01

    We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is a connected complex subspace of an infinite dimensional complex space, and is stratified according to genus such that each stratum has a compact closure, and it carries a metric and a measure that induce a Riemannian metric and a finite volume measure on each stratum. Applications to the Plateau-Douglas problem for minimal surfaces of varying genus and to the partition function of Bosonic string theory are outlined. The construction starts with a universal moduli space of Abelian varieties. This space carries a structure of an infinite dimensional locally symmetric space which is of interest in its own right. The key to our construction of the universal moduli space then is the Torelli map that assigns to every Riemann surface its Jacobian and its extension to the Satake-Baily-Borel compactifications.

  6. Stability diagram for the forced Kuramoto model.

    PubMed

    Childs, Lauren M; Strogatz, Steven H

    2008-12-01

    We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

  7. Back-propagation learning of infinite-dimensional dynamical systems.

    PubMed

    Tokuda, Isao; Tokunaga, Ryuji; Aihara, Kazuyuki

    2003-10-01

    This paper presents numerical studies of applying back-propagation learning to a delayed recurrent neural network (DRNN). The DRNN is a continuous-time recurrent neural network having time delayed feedbacks and the back-propagation learning is to teach spatio-temporal dynamics to the DRNN. Since the time-delays make the dynamics of the DRNN infinite-dimensional, the learning algorithm and the learning capability of the DRNN are different from those of the ordinary recurrent neural network (ORNN) having no time-delays. First, two types of learning algorithms are developed for a class of DRNNs. Then, using chaotic signals generated from the Mackey-Glass equation and the Rössler equations, learning capability of the DRNN is examined. Comparing the learning algorithms, learning capability, and robustness against noise of the DRNN with those of the ORNN and time delay neural network, advantages as well as disadvantages of the DRNN are investigated.

  8. Two novel copper(II) complexes constructed from dicarboxylate ligands with different spacer lengths and 2-phenylimidazo[4,5- f]1,10-phenanthroline (PIP): Synthesis, structures and properties

    NASA Astrophysics Data System (ADS)

    Wang, X.-L.; Chen, Yongqiang; Liu, Guocheng; Lin, Hongyan; Zhang, Jinxia

    2009-09-01

    Two novel metal-organic coordination polymers [Cu(PIP)(bpea)(H 2O)]·H 2O ( 1) and [Cu(PIP)(1,4-bdc)] ( 2) have been obtained from hydrothermal reaction of copper(II) with the mixed ligands [biphenylethene-4,4'-dicarboxylic acid (bpea) for 1, benzene-1,4-dicarboxylic acid (1,4-H 2bdc) for 2, and 2-phenylimidazo[4,5- f]1,10-phenanthroline (PIP)]. Both complexes have been structurally characterized by elemental analyses, IR and single-crystal X-ray diffraction analyses. Structural analyses reveal that complex 1 possesses infinite one-dimensional zigzag chain, 2 exhibits a two-dimensional (4,4) network, both of which are extended into three-dimensional supramolecular network by weak interactions. The different structures of the title complexes illustrate the influence of the flexibility (the spacer length of carboxyl groups and the structural rigidity of the spacer) of organic dicarboxylate ligands on the formation of such coordination architectures. Moreover, the thermal properties and the voltammetric behavior of complexes 1 and 2 have been reported.

  9. Critical behavior of two-dimensional vesicles in the deflated regime

    NASA Technical Reports Server (NTRS)

    Banavar, Jayanth R.; Maritan, Amos; Stella, Attilio

    1991-01-01

    The critical behavior of two-dimensional vesicles in the deflated regime is studied analytically using a mapping onto a gauge model, scaling arguments, and exact inequalities. In agreement with the results of earlier studies the critical behavior is governed by a branched-polymer fixed point. The shape of the critical line in the gauge model is deduced in the weak and in the infinitely deflated regime.

  10. Nonlinear Control Systems

    DTIC Science & Technology

    2009-11-18

    J.M. Schumacher, Finite -dimensional regulators for a class of infinite dimensional systems . Systems and Control Letters, 3 (1983), 7-12. [39J J.M...for the control of certain examples or system classes us- ing particular feedback design methods ([20, 21, 16, 17, 19, 18]). Still, the control of...long time existence and asymptotic behavior for certain examples or system classes using particular feedback design methods (see, e.g., [20, 21, 16, 17

  11. Data-Adaptive Bias-Reduced Doubly Robust Estimation.

    PubMed

    Vermeulen, Karel; Vansteelandt, Stijn

    2016-05-01

    Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

  12. Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

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

    Burdik, C., E-mail: burdik@kmlinux.fjfi.cvut.cz; Navratil, O.

    2011-06-15

    We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

  13. Geometry, topology, and response in condensed matter systems

    NASA Astrophysics Data System (ADS)

    Varjas, Daniel

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

  14. The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

    NASA Astrophysics Data System (ADS)

    Merdan, Ziya; Karakuş, Özlem

    2016-11-01

    The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

  15. Iterative adaption of the bidimensional wall of the French T2 wind tunnel around a C5 axisymmetrical model: Infinite variation of the Mach number at zero incidence and a test at increased incidence

    NASA Technical Reports Server (NTRS)

    Archambaud, J. P.; Dor, J. B.; Payry, M. J.; Lamarche, L.

    1986-01-01

    The top and bottom two-dimensional walls of the T2 wind tunnel are adapted through an iterative process. The adaptation calculation takes into account the flow three-dimensionally. This method makes it possible to start with any shape of walls. The tests were performed with a C5 axisymmetric model at ambient temperature. Comparisons are made with the results of a true three-dimensional adaptation.

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

    Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au; Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au

    The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem ofmore » optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.« less

  17. A motif for infinite metal atom wires.

    PubMed

    Yin, Xi; Warren, Steven A; Pan, Yung-Tin; Tsao, Kai-Chieh; Gray, Danielle L; Bertke, Jeffery; Yang, Hong

    2014-12-15

    A new motif for infinite metal atom wires with tunable compositions and properties is developed based on the connection between metal paddlewheel and square planar complex moieties. Two infinite Pd chain compounds, [Pd4(CO)4(OAc)4Pd(acac)2] 1 and [Pd4(CO)4(TFA)4Pd(acac)2] 2, and an infinite Pd-Pt heterometallic chain compound, [Pd4(CO)4(OAc)4Pt(acac)2] 3, are identified by single-crystal X-ray diffraction analysis. In these new structures, the paddlewheel moiety is a Pd four-membered ring coordinated by bridging carboxylic ligands and μ2 carbonyl ligands. The planar moiety is either Pd(acac)2 or Pt(acac)2 (acac = acetylacetonate). These moieties are connected by metallophilic interactions. The results showed that these one-dimensional metal wire compounds have photoluminescent properties that are tunable by changing ligands and metal ions. 3 can also serve as a single source precursor for making Pd4Pt bimetallic nanostructures with precise control of metal composition. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  18. Fermionic entanglement that survives a black hole

    NASA Astrophysics Data System (ADS)

    Martín-Martínez, Eduardo; León, Juan

    2009-10-01

    We introduce an arbitrary number of accessible modes when analyzing bipartite entanglement degradation due to Unruh effect between two partners Alice and Rob. Under the single mode approximation (SMA) a fermion field only had a few accessible levels due to Pauli exclusion principle conversely to bosonic fields which had an infinite number of excitable levels. This was argued to justify entanglement survival in the fermionic case in the SMA infinite acceleration limit. Here we relax SMA. Hence, an infinite number of modes are excited as the observer Rob accelerates, even for a fermion field. We will prove that, despite this analogy with the bosonic case, entanglement loss is limited. We will show that this comes from fermionic statistics through the characteristic structure it imposes on the infinite dimensional density matrix for Rob. Surprisingly, the surviving entanglement is independent of the specific maximally entangled state chosen, the kind of fermionic field analyzed, and the number of accessible modes considered. We shall discuss whether this surviving entanglement goes beyond the purely statistical correlations, giving insight concerning the black hole information paradox.

  19. Investigation of the High, Finite n Ballooning Mode Limit for Compact Quasi-Axially Symmetric Stellarators

    NASA Astrophysics Data System (ADS)

    Redi, Martha; Canik, John; Fredrickson, E.; Fu, G.; Nuehrenberg, C.; Boozer, A. H.

    2000-10-01

    The standard ballooning-mode beta limit comes from an infinite-n, radially local, ideal magnetohydrodynamic (MHD) calculation. Finite-n ballooning modes have been observed in tokamak plasmas [1]. Investigations of optimized quasiaxially symmetric stellarators with three dimensional, global, ideal MHD codes have recently shown good stability for the external kink, ``vertical" and infinite-n ballooning modes [2,3]. However, infinite-n ballooning stability may be too restrictive, due to its sensitivity to features in the local shear and curvature. The CAS3D [4] code is being used to compare the stability of the high-n ballooning modes to the infinite-n calculations from TERPSICHORE [5]. [1] E. Fredrickson, et al. Phys. Plas. 3 (1996) 2620. [2] G. Fu, Phys. Plas. 7 (2000)1079; Phys. Plas. 7 (2000) 1809. M. Redi, et al. Phys. Plas 7 (2000)1911. [3] A. Reiman, et al., Plas. Phys. Cont. Fus. 41 (1999) B273. [4] C. Nuehrenberg, Phys. Plas. 6 (1999) 275. C. Nuehrenberg, Phys. Plas. 3 (1996) 2401. C. Schwab, Phys. Fluids B5 (1993) 3195. [5] W. A. Cooper, Phys. Plas. 3 (1996) 275.

  20. Generalized -deformed correlation functions as spectral functions of hyperbolic geometry

    NASA Astrophysics Data System (ADS)

    Bonora, L.; Bytsenko, A. A.; Guimarães, M. E. X.

    2014-08-01

    We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with , is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to . With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry.

  1. Weyl calculus in QED I. The unitary group

    NASA Astrophysics Data System (ADS)

    Amour, L.; Lascar, R.; Nourrigat, J.

    2017-01-01

    In this work, we consider fixed 1/2 spin particles interacting with the quantized radiation field in the context of quantum electrodynamics. We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in Amour et al. [J. Funct. Anal. 269(9), 2747-2812 (2015)] on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states.

  2. Piston flow in a two-dimensional channel

    NASA Astrophysics Data System (ADS)

    Katopodes, Fotini V.; Davis, A. M. J.; Stone, H. A.

    2000-05-01

    A solution using biorthogonal eigenfunctions is presented for viscous flow caused by a piston in a two-dimensional channel. The resulting infinite set of linear equations is solved using Spence's optimal weighting function method [IMA J. Appl. Math. 30, 107 (1983)]. The solution is compared to that with a shear-free piston surface; in the latter configuration the fluid more rapidly approaches the Poiseuille flow profile established away from the face of the piston.

  3. Electronic excitations in finite and infinite polyenes

    NASA Astrophysics Data System (ADS)

    Tavan, Paul; Schulten, Klaus

    1987-09-01

    We study electronic excitations in long polyenes, i.e., in one-dimensional strongly correlated electron systems which are neither infinite nor small. The excitations are described within Hubbard and Pariser-Parr-Pople (PPP) models by means of a multiple-reference double-excitation expansion [P. Tavan and K. Schulten, J. Chem. Phys. 85, 6602 (1986)]. We find that quantized ``transition'' momenta can be assigned to electronic excitations in finite chains. These momenta link excitation energies of finite chains to dispersion relations of infinite chains, i.e., they bridge the gap between finite and infinite systems. A key result is the following: Excitation energies E in polyenes with N carbon atoms are described very accurately by the formula Eβ=ΔEβ0+αβk(N)q, q=1,2,..., where β denotes the excitation class, ΔEβ0 the energy gap in the infinite system [αβk(N)>0], and k(N) the elementary transition momentum. The parameters ΔEβ0 and αβ are determined for covalent and ionic excitations in alternating and nonalternating polyenes. The covalent excitations are combinations of triplet excitations T, i.e., T, TT, TTT, . . . . The lowest singlet excitations in the infinite polyene, e.g., in polyacetylene or polydiacetylene, are TT states. Available evidence proves that these states can dissociate into separate triplets. The bond structure of TT states is that of a neutral soliton-antisoliton pair. The level density of TT states in long polyenes is high enough to allow dissociation into separate solitons.

  4. Successful refolding and NMR structure of rMagi3: A disulfide-rich insecticidal spider toxin.

    PubMed

    Titaux-Delgado, Gustavo; Carrillo, Elisa; Mendoza, Angeles; Mayorga-Flores, Marlen; Escobedo-González, Fátima C; Cano-Sánchez, Patricia; López-Vera, Estuardo; Corzo, Gerardo; Del Rio-Portilla, Federico

    2018-03-01

    The need for molecules with high specificity against noxious insects leads the search towards spider venoms that have evolved highly selective toxins for insect preys. In this respect, spiders as a highly diversified group of almost exclusive insect predators appear to possess infinite potential for the discovery of novel insect-selective toxins. In 2003, a group of toxins was isolated from the spider Macrothele gigas and the amino acid sequence was reported. We obtained, by molecular biology techniques in a heterologous system, one of these toxins. Purification process was optimized by chromatographic methods to determine the three-dimensional structure by nuclear magnetic resonance in solution, and, finally, their biological activity was tested. rMagi3 resulted to be a specific insect toxin with no effect on mice. © 2017 The Protein Society.

  5. Riemann-Hilbert technique scattering analysis of metamaterial-based asymmetric 2D open resonators

    NASA Astrophysics Data System (ADS)

    Kamiński, Piotr M.; Ziolkowski, Richard W.; Arslanagić, Samel

    2017-12-01

    The scattering properties of metamaterial-based asymmetric two-dimensional open resonators excited by an electric line source are investigated analytically. The resonators are, in general, composed of two infinite and concentric cylindrical layers covered with an infinitely thin, perfect conducting shell that has an infinite axial aperture. The line source is oriented parallel to the cylinder axis. An exact analytical solution of this problem is derived. It is based on the dual-series approach and its transformation to the equivalent Riemann-Hilbert problem. Asymmetric metamaterial-based configurations are found to lead simultaneously to large enhancements of the radiated power and to highly steerable Huygens-like directivity patterns; properties not attainable with the corresponding structurally symmetric resonators. The presented open resonator designs are thus interesting candidates for many scientific and engineering applications where enhanced directional near- and far-field responses, tailored with beam shaping and steering capabilities, are highly desired.

  6. Infinite lattices of vortex molecules in Rabi-coupled condensates

    NASA Astrophysics Data System (ADS)

    Mencia Uranga, B.; Lamacraft, Austen

    2018-04-01

    Vortex molecules can form in a two-component superfluid when a Rabi field drives transitions between the two components. We study the ground state of an infinite system of vortex molecules in two dimensions, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of intercomponent interactions and strength of the Rabi field. In the limit of large field when molecules are tightly bound, we develop a complementary analytical description. The energy governing the alignment of molecules on a triangular lattice is found to correspond to that of an infinite system of two-dimensional quadrupoles, which may be written in terms of an elliptic function Q (zi j;ω1,ω2) . This allows for a numerical evaluation of the energy which enables us to find the ground state configuration of the molecules.

  7. The converse approach to NMR chemical shifts from first-principles: application to finite and infinite aromatic compounds

    NASA Astrophysics Data System (ADS)

    Thonhauser, T.; Ceresoli, D.; Marzari, N.

    2009-03-01

    We present first-principles, density-functional theory calculations of the NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene and increasing sizes up to the one- and two-dimensional infinite limits of graphene ribbons and sheets. Our calculations are performed using a combination of the recently developed theory of orbital magnetization in solids, and a novel approach to NMR calculations where chemical shifts are obtained from the derivative of the orbital magnetization with respect to a microscopic, localized magnetic dipole. Using these methods we study on equal footing the ^1H and ^13C shifts in benzene, pyrene, coronene, in naphthalene, anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and an infinite graphene ribbon. Our results show very good agreement with experiments and allow us to characterize the trends for the chemical shifts as a function of system size.

  8. Fast computation of the electrolyte-concentration transfer function of a lithium-ion cell model

    NASA Astrophysics Data System (ADS)

    Rodríguez, Albert; Plett, Gregory L.; Trimboli, M. Scott

    2017-08-01

    One approach to creating physics-based reduced-order models (ROMs) of battery-cell dynamics requires first generating linearized Laplace-domain transfer functions of all cell internal electrochemical variables of interest. Then, the resulting infinite-dimensional transfer functions can be reduced by various means in order to find an approximate low-dimensional model. These methods include Padé approximation or the Discrete-Time Realization algorithm. In a previous article, Lee and colleagues developed a transfer function of the electrolyte concentration for a porous-electrode pseudo-two-dimensional lithium-ion cell model. Their approach used separation of variables and Sturm-Liouville theory to compute an infinite-series solution to the transfer function, which they then truncated to a finite number of terms for reasons of practicality. Here, we instead use a variation-of-parameters approach to arrive at a different representation of the identical solution that does not require a series expansion. The primary benefits of the new approach are speed of computation of the transfer function and the removal of the requirement to approximate the transfer function by truncating the number of terms evaluated. Results show that the speedup of the new method can be more than 3800.

  9. Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components

    NASA Astrophysics Data System (ADS)

    Kuzmiak, Vladimir; Maradudin, Alexei A.

    1998-09-01

    We study the distribution of the electromagnetic field of the eigenmodes and corresponding group velocities associated with the photonic band structures of two-dimensional periodic systems consisting of an array of infinitely long parallel metallic rods whose intersections with a perpendicular plane form a simple square lattice. We consider both nondissipative and lossy metallic components characterized by a complex frequency-dependent dielectric function. Our analysis is based on the calculation of the complex photonic band structure obtained by using a modified plane-wave method that transforms the problem of solving Maxwell's equations into the problem of diagonalizing an equivalent non-Hermitian matrix. In order to investigate the nature and the symmetry properties of the eigenvectors, which significantly affect the optical properties of the photonic lattices, we evaluate the associated field distribution at the high symmetry points and along high symmetry directions in the two-dimensional first Brillouin zone of the periodic system. By considering both lossless and lossy metallic rods we study the effect of damping on the spatial distribution of the eigenvectors. Then we use the Hellmann-Feynman theorem and the eigenvectors and eigenfrequencies obtained from a photonic band-structure calculation based on a standard plane-wave approach applied to the nondissipative system to calculate the components of the group velocities associated with individual bands as functions of the wave vector in the first Brillouin zone. From the group velocity of each eigenmode the flow of energy is examined. The results obtained indicate a strong directional dependence of the group velocity, and confirm the experimental observation that a photonic crystal is a potentially efficient tool in controlling photon propagation.

  10. Coherent and radiative couplings through two-dimensional structured environments

    NASA Astrophysics Data System (ADS)

    Galve, F.; Zambrini, R.

    2018-03-01

    We study coherent and radiative interactions induced among two or more quantum units by coupling them to two-dimensional (2D) lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals, or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g., related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details such as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Furthermore, we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally, we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.

  11. On the tensionless limit of gauged WZW models

    NASA Astrophysics Data System (ADS)

    Bakas, I.; Sourdis, C.

    2004-06-01

    The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional black-hole coset SL(2,Bbb R)k/U(1) as illustrative example, we find for k = 2 that the world-sheet symmetry is described by a truncated version of Winfty generated by chiral fields with integer spin s geq 3, whereas the Virasoro algebra becomes abelian and it can be consistently factored out. The geometry of target space looks like an infinitely curved hyperboloid, which invalidates the effective field theory description and conformal invariance can no longer be used to yield reliable space-time interpretation. We also compare our results with the null gauging of WZW models, which correspond to infinite boost in target space and they describe the Liouville mode that decouples in the tensionless limit. A formal BRST analysis of the world-sheet symmetry suggests that the central charge of all higher spin generators should be fixed to a critical value, which is not seen by the contracted Virasoro symmetry. Generalizations to higher dimensional coset models are also briefly discussed in the tensionless limit, where similar observations are made.

  12. Separation behavior of boundary layers on three-dimensional wings

    NASA Technical Reports Server (NTRS)

    Stock, H. W.

    1981-01-01

    An inverse boundary layer procedure for calculating separated, turbulent boundary layers at infinitely long, crabbing wing was developed. The procedure was developed for calculating three dimensional, incompressible turbulent boundary layers was expanded to adiabatic, compressible flows. Example calculations with transsonic wings were made including viscose effects. In this case an approximated calculation method described for areas of separated, turbulent boundary layers, permitting calculation of this displacement thickness. The laminar boundary layer development was calculated with inclined ellipsoids.

  13. A Novel 2-D Programmable Photonic Time Delay Device for MM-Wave Signal Processing Applications

    NASA Technical Reports Server (NTRS)

    Yao, X.; Maleki, L.

    1994-01-01

    We describe a novel programmable photonic true time delay device that has the properties of low loss, inherent two dimensionality with a packing density exceeding 25 lines/cm super 2, virtually infinite bandwidth, and is easy to manufacture.

  14. Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo-Miwa equation with time-dependent coefficients

    NASA Astrophysics Data System (ADS)

    Deng, Gao-Fu; Gao, Yi-Tian; Gao, Xin-Yi

    2018-07-01

    In this paper, an extended (3+1)-dimensional Jimbo-Miwa equation with time-dependent coefficients is investigated, which comes from the second member of the Kadomtsev-Petviashvili hierarchy and is shown to be conditionally integrable. Bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are derived via the binary Bell polynomials and symbolic computation. With the help of the bilinear form, one-, two- and three-soliton solutions are obtained via the Hirota method, one-periodic wave solutions are constructed via the Riemann theta function. Additionally, propagation and interaction of the solitons are investigated analytically and graphically, from which we find that the interaction between the solitons is elastic and the time-dependent coefficients can affect the soliton velocities, but the soliton amplitudes remain unchanged. One-periodic waves approach the one-solitary waves with the amplitudes vanishing and can be viewed as a superposition of the overlapping solitary waves, placed one period apart.

  15. Multigrid one shot methods for optimal control problems: Infinite dimensional control

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Taasan, Shlomo

    1994-01-01

    The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

  16. Optimal Control for Stochastic Delay Evolution Equations

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

    Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

    2016-08-15

    In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

  17. Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons

    NASA Astrophysics Data System (ADS)

    Veretenov, N. A.; Fedorov, S. V.; Rosanov, N. N.

    2017-12-01

    We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., Nc knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M0 (Nc , M , and M0 are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines Nc=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M =1 , 2, and 3.

  18. The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

    NASA Technical Reports Server (NTRS)

    Adamczyk, J. L.

    1974-01-01

    An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

  19. Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons.

    PubMed

    Veretenov, N A; Fedorov, S V; Rosanov, N N

    2017-12-29

    We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.

  20. A non-local computational boundary condition for duct acoustics

    NASA Technical Reports Server (NTRS)

    Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.

    1994-01-01

    A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.

  1. Unified control/structure design and modeling research

    NASA Technical Reports Server (NTRS)

    Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

    1986-01-01

    To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

  2. Electromagnetic scattering analysis of a three-dimensional-cavity-backed aperture in an infinite ground plane using a combined finite element method/method of moments approach

    NASA Technical Reports Server (NTRS)

    Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, F. B.

    1995-01-01

    A combined finite element method/method of moments (FEM/MoM) approach is used to analyze the electromagnetic scattering properties of a three-dimensional-cavity-backed aperture in an infinite ground plane. The FEM is used to formulate the fields inside the cavity, and the MoM (with subdomain bases) in both spectral and spatial domains is used to formulate the fields above the ground plane. Fields in the aperture and the cavity are solved using a system of equations resulting from the combination of the FEM and the MoM. By virtue of the FEM, this combined approach is applicable to all arbitrarily shaped cavities with inhomogeneous material fillings, and because of the subdomain bases used in the MoM, the apertures can be of any arbitrary shape. This approach leads to a partly sparse and partly full symmetric matrix, which is efficiently solved using a biconjugate gradient algorithm. Numerical results are presented to validate the analysis.

  3. Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

    NASA Astrophysics Data System (ADS)

    Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

    2018-04-01

    This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

  4. The conformal characters

    NASA Astrophysics Data System (ADS)

    Bourget, Antoine; Troost, Jan

    2018-04-01

    We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules. The Kazhdan-Lusztig polynomials code the relation between the Verma modules and the irreducible modules in the category and are the key to the characters of the conformal multiplets (whether finite dimensional, infinite dimensional, unitary or non-unitary). We discuss the representation theory and review in full generality which representations are unitarizable. The mathematical theory that allows for both the general treatment of characters and the full analysis of unitarity is made accessible. A good understanding of the mathematics of conformal multiplets renders the treatment of all highest weight representations in any dimension uniform, and provides an overarching comprehension of case-by-case results. Unitary highest weight representations and their characters are classified and computed in terms of data associated to cosets of the Weyl group of the conformal algebra. An executive summary is provided, as well as look-up tables up to and including rank four.

  5. Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

    NASA Astrophysics Data System (ADS)

    Pillay, Jason C.; McCulloch, Ian P.

    2018-05-01

    The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

  6. Numerical experiments with flows of elongated granules

    NASA Technical Reports Server (NTRS)

    Elrod, Harold G.; Brewe, David E.

    1992-01-01

    Theory and numerical results are given for a program simulating two dimensional granular flow (1) between two infinite, counter-moving, parallel, roughened walls, and (2) for an infinitely wide slider. Each granule is simulated by a central repulsive force field ratcheted with force restitution factor to introduce dissipation. Transmission of angular momentum between particles occurs via Coulomb friction. The effect of granular hardness is explored. Gaps from 7 to 28 particle diameters are investigated, with solid fractions ranging from 0.2 to 0.9. Among features observed are: slip flow at boundaries, coagulation at high densities, and gross fluctuation in surface stress. A videotape has been prepared to demonstrate the foregoing effects.

  7. Low Temperature Analysis of Correlation Functions of the Blume-Emery-Griffiths Model at the Antiquadrupolar-Disordered Interface

    NASA Astrophysics Data System (ADS)

    Lima, Paulo C.

    2016-11-01

    We show that at low temperatures the d dimensional Blume-Emery-Griffiths model in the antiquadrupolar-disordered interface has all its infinite volume correlation functions < prod _{iin A}σ _i^{n_i}rangle _{τ }, where Asubset Z^d is finite and sum _{iin A}n_i is odd, equal zero, regardless of the boundary condition τ . In particular, the magnetization < σ _irangle _{τ } is zero, for all τ . We also show that the infinite volume mean magnetization lim _{Λ → ∞}Big < 1/|Λ |sum _{iin Λ }σ _iBig rangle _{Λ ,τ } is zero, for all τ.

  8. Unidirectional invisibility and non-reciprocal transmission in two and three dimensions.

    PubMed

    Loran, Farhang; Mostafazadeh, Ali

    2016-07-01

    We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations and discuss its three-dimensional generalization. In particular, we construct an infinite class of unidirectionally invisible optical potentials that describe the scattering of normally incident transverse electric waves by an infinite planar slab with refractive-index modulations along both the normal directions to the electric field. A by-product of this investigation is a demonstration of non-reciprocal transmission in two dimensions. To elucidate this phenomenon, we state and prove a general reciprocity theorem that applies to quantum scattering theory of real and complex potentials in two and three dimensions.

  9. Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

    DOE PAGES

    Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

    2015-01-01

    We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

  10. The smooth entropy formalism for von Neumann algebras

    NASA Astrophysics Data System (ADS)

    Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

    2016-01-01

    We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

  11. Viscous Dissipation in One-Dimensional Quantum Liquids

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

    Matveev, K. A.; Pustilnik, M.

    We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zerotemperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. In conclusion, our consideration is applicable to all single-component Galilean- invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.

  12. Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

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

    Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

    We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

  13. The smooth entropy formalism for von Neumann algebras

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

    Berta, Mario, E-mail: berta@caltech.edu; Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp; Scholz, Volkher B., E-mail: scholz@phys.ethz.ch

    2016-01-15

    We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

  14. Viscous Dissipation in One-Dimensional Quantum Liquids

    DOE PAGES

    Matveev, K. A.; Pustilnik, M.

    2017-07-20

    We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zerotemperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. In conclusion, our consideration is applicable to all single-component Galilean- invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.

  15. Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws

    NASA Astrophysics Data System (ADS)

    Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen

    2017-01-01

    With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

  16. A remark on the phase transitions of modified action spin and gauge models

    NASA Astrophysics Data System (ADS)

    Seiberg, Nathan; Solomon, Sorin

    1983-06-01

    We consider the phase diagrams of modified action gauge and spin models and concentrate on their periphery - infinitely far from their origins (zero temperature - β-1 = 0). In this limit the exact positions of the phase transitions are found by looking for the global minimum of the single plaquette action (for a spin system - the single link energy). As the parameters of the model are varied, the position of such a global minimum is in general changed. When this changed is non-analytic, a phase transition takes place. The phase structure for finite β is clearly similar, but not identical to the infinite β one. We discuss several finite β corrections that should be applied to the exactly known infinite β picture. We confront our analysis for infinite β2 = ∑ iβ2i with the Monte Carlo simulations for two four-dimensional gauge systems: an SU(3) gauge model with action S=-Re∑ p( β1tr Up+ β2(tr Up) 2) and an SU(2) model with S=- Re Σ p[β 1{1}/{2}trU p+β 2( {1}/{2}trU p) 2+β 3( {1}/{2}trU p) 3] .

  17. Near-Wall Measurements of a Three-Dimensional Turbulent Boundary Layer.

    DTIC Science & Technology

    1995-08-01

    Baskaran, Pontikis , and Bradshaw (1989) extended the infinite swept wing study of Bradshaw and Pontikos, by adding surface curvature, both concave...on a concave surface," Thermosciences Div., Stanford University, Stanford, CA, Report MD-47. Baskaran, V., Pontikis , Y.G., k Bradshaw, P. (1989

  18. Electrically Tunable Optical Delay Lines

    DTIC Science & Technology

    2003-04-01

    layers [24]. References [1] Bendickson, J. M., J. P. Dowling, and M. Scalora , “Analytic expressions for the electromagnetic mode density in...finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107 (1996). [2] Scalora , M., R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J

  19. A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

    EPA Science Inventory

    Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

  20. Human pose tracking from monocular video by traversing an image motion mapped body pose manifold

    NASA Astrophysics Data System (ADS)

    Basu, Saurav; Poulin, Joshua; Acton, Scott T.

    2010-01-01

    Tracking human pose from monocular video sequences is a challenging problem due to the large number of independent parameters affecting image appearance and nonlinear relationships between generating parameters and the resultant images. Unlike the current practice of fitting interpolation functions to point correspondences between underlying pose parameters and image appearance, we exploit the relationship between pose parameters and image motion flow vectors in a physically meaningful way. Change in image appearance due to pose change is realized as navigating a low dimensional submanifold of the infinite dimensional Lie group of diffeomorphisms of the two dimensional sphere S2. For small changes in pose, image motion flow vectors lie on the tangent space of the submanifold. Any observed image motion flow vector field is decomposed into the basis motion vector flow fields on the tangent space and combination weights are used to update corresponding pose changes in the different dimensions of the pose parameter space. Image motion flow vectors are largely invariant to style changes in experiments with synthetic and real data where the subjects exhibit variation in appearance and clothing. The experiments demonstrate the robustness of our method (within +/-4° of ground truth) to style variance.

  1. Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

    PubMed

    Buican, Matthew; Laczko, Zoltan

    2018-02-23

    In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

  2. Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

    NASA Astrophysics Data System (ADS)

    Buican, Matthew; Laczko, Zoltan

    2018-02-01

    In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

  3. An Extended Optional Infinitive Stage in German-Speaking Children with Specific Language Impairment.

    ERIC Educational Resources Information Center

    Rice, Mabel L.; Noll, Karen Ruff; Grimm, Hannelore

    1997-01-01

    Predictions were formulated for extended Optional Infinitives (OIs) stage in German-speaking children with specific language impairment and evaluated in clinical sample of 8 SLI German-speaking children, ages 4; 0 to 4; 8; and control group of 8 younger utterance-equivalent children, ages 2; 1 to 2; 7. Samples reveal that affected group more…

  4. Alternative dimensional reduction via the density matrix

    NASA Astrophysics Data System (ADS)

    de Carvalho, C. A.; Cornwall, J. M.; da Silva, A. J.

    2001-07-01

    We give graphical rules, based on earlier work for the functional Schrödinger equation, for constructing the density matrix for scalar and gauge fields in equilibrium at finite temperature T. More useful is a dimensionally reduced effective action (DREA) constructed from the density matrix by further functional integration over the arguments of the density matrix coupled to a source. The DREA is an effective action in one less dimension which may be computed order by order in perturbation theory or by dressed-loop expansions; it encodes all thermal matrix elements. We term the DREA procedure alternative dimensional reduction, to distinguish it from the conventional dimensionally reduced field theory (DRFT) which applies at infinite T. The DREA is useful because it gives a dimensionally reduced theory usable at any T including infinity, where it yields the DRFT, and because it does not and cannot have certain spurious infinities which sometimes occur in the density matrix itself or the conventional DRFT; these come from ln T factors at infinite temperature. The DREA can be constructed to all orders (in principle) and the only regularizations needed are those which control the ultraviolet behavior of the zero-T theory. An example of spurious divergences in the DRFT occurs in d=2+1φ4 theory dimensionally reduced to d=2. We study this theory and show that the rules for the DREA replace these ``wrong'' divergences in physical parameters by calculable powers of ln T; we also compute the phase transition temperature of this φ4 theory in one-loop order. Our density-matrix construction is equivalent to a construction of the Landau-Ginzburg ``coarse-grained free energy'' from a microscopic Hamiltonian.

  5. Experimental Investigation of Shock-Shock Interactions Over a 2-D Wedge at M=6

    NASA Technical Reports Server (NTRS)

    Jones, Michelle L.

    2013-01-01

    The effects of fin-leading-edge radius and sweep angle on peak heating rates due to shock-shock interactions were investigated in the NASA Langley Research Center 20-inch Mach 6 Air Tunnel. The fin model leading edges, which represent cylindrical leading edges or struts on hypersonic vehicles, were varied from 0.25 inches to 0.75 inches in radius. A 9deg wedge generated a planar oblique shock at 16.7deg to the flow that intersected the fin bow shock, producing a shock-shock interaction that impinged on the fin leading edge. The fin angle of attack was varied from 0deg (normal to the free-stream) to 15deg and 25deg swept forward. Global temperature data was obtained from the surface of the fused silica fins through phosphor thermography. Metal oil flow models with the same geometries as the fused silica models were used to visualize the streamline patterns for each angle of attack. High-speed zoom-schlieren videos were recorded to show the features and temporal unsteadiness of the shock-shock interactions. The temperature data were analyzed using one-dimensional semi-infinite as well as one- and two-dimensional finite-volume methods to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock interactions. The general trends in the leading-edge heat transfer behavior were similar for the three shock-shock interactions, respectively, between the test articles with varying leading-edge radius. The dimensional peak heat transfer coefficient augmentation increased with decreasing leading-edge radius. The dimensional peak heat transfer output from the two-dimensional code was about 20% higher than the value from a standard, semi-infinite one-dimensional method.

  6. 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).

  7. Hydrogen-bonded structures from adamantane-based catechols

    NASA Astrophysics Data System (ADS)

    Kawahata, Masatoshi; Matsuura, Miku; Tominaga, Masahide; Katagiri, Kosuke; Yamaguchi, Kentaro

    2018-07-01

    Adamantane-based bis- and tris-catechols were synthesized to examine the effect of hydrogen bonds on the arrangement and packing of the components in the crystalline state. Single-crystal X-ray crystallographic analysis revealed that hydrogen bonds formed by the hydroxyl groups of catechol groups play essential roles in the production of various types of unique structures. 1,3-Bis(3,4-dihydroxyphenyl)adamantane (1) provided hydrogen-bonded network structures composed of helical chains in crystal from chloroform/methanol, and layer structures in crystal from ethyl acetate/hexane. The complexation of 1 with 1,3,5-trinitrobenzene or 1,2,4,5-tetracyanobenzene resulted in the formation of co-crystals, respectively. One-dimensional hydrogen-bonded structures were constructed from the adamantane-based molecules, which participated in charge-transfer interactions with guests. 1,3,5-Tris(3,4-dihydroxyphenyl)adamantane also afforded crystal, and the components were assembled into infinite polymers.

  8. Effect of Surface Waviness on Transition in Three-Dimensional Boundary-Layer Flow

    NASA Technical Reports Server (NTRS)

    Masad, Jamal A.

    1996-01-01

    The effect of a surface wave on transition in three-dimensional boundary-layer flow over an infinite swept wing was studied. The mean flow computed using interacting boundary-layer theory, and transition was predicted using linear stability theory coupled with the empirical eN method. It was found that decreasing the wave height, sweep angle, or freestream unit Reynolds number, and increasing the freestream Mach number or suction level all stabilized the flow and moved transition onset to downstream locations.

  9. Estimation on nonlinear damping in second order distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1989-01-01

    An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

  10. Feasibility of High Energy Lasers for Interdiction Activities

    DTIC Science & Technology

    2017-12-01

    2.3.2 Power in the Bucket Another parameter we will use in this study is the power-in-the-bucket. The “bucket” is defined as the area on the target we...the heat diffusion equation for a one -dimensional case (where the x-direction is into the target) and assuming a semi-infinite slab of material. The... studied and modeled. One of the approaches to describe these interactions is by making a one -dimensional mathematical model assuming [8]: 1. A semi

  11. Naked singularities in higher dimensional Vaidya space-times

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

    Ghosh, S. G.; Dadhich, Naresh

    We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension.

  12. Transverse spin correlations of the random transverse-field Ising model

    NASA Astrophysics Data System (ADS)

    Iglói, Ferenc; Kovács, István A.

    2018-03-01

    The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in d =1 ,2 , and 3 dimensions. At the critical point an algebraic decay of the form ˜r-ηt is found, with a decay exponent being approximately ηt≈2 +2 d . In d =1 the results are related to dimer-dimer correlations in the random antiferromagnetic X X chain and have been tested by numerical calculations using free-fermionic techniques.

  13. Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}

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

    Nayak, Saudamini, E-mail: anumama.nayak07@gmail.com; Pati, K. C., E-mail: kcpati@nitrkl.ac.in

    Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A{sub 1}{sup (1)},A{sub 2}{sup (1)},A{sub 2}{sup (2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.

  14. Coupling coefficients for tensor product representations of quantum SU(2)

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

    Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

    2014-10-15

    We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

  15. Modularity of logarithmic parafermion vertex algebras

    NASA Astrophysics Data System (ADS)

    Auger, Jean; Creutzig, Thomas; Ridout, David

    2018-05-01

    The parafermionic cosets Ck = {Com} ( H , Lk(sl2) ) are studied for negative admissible levels k, as are certain infinite-order simple current extensions Bk of Ck . Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to Ck , irreducible Ck - and Bk -modules are obtained from those of Lk(sl2) . Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible Bk -modules. The irreducible Ck - and Bk -characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the Bk are C_2 -cofinite vertex operator algebras.

  16. The Crystalline Dynamics of Spiral-Shaped Curves

    NASA Astrophysics Data System (ADS)

    Dudziński, Marcin; Górka, Przemysław

    2015-07-01

    We study the motion of spiral-shaped polygonal curves by crystalline curvature. We describe this dynamics by the corresponding infinitely dimensional system of ordinary differential equations and show that the considered model is uniquely solvable. Banach's Contraction Mapping Theorem and the Bellman-Gronwall inequality are the main tools applied in our proof.

  17. A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

    EPA Science Inventory

    Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

  18. Mathematical model of a smoldering log.

    Treesearch

    Fernando de Souza Costa; David Sandberg

    2004-01-01

    A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts...

  19. Affine q-deformed symmetry and the classical Yang-Baxter σ-model

    NASA Astrophysics Data System (ADS)

    Delduc, F.; Kameyama, T.; Magro, M.; Vicedo, B.

    2017-03-01

    The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank( G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank( G) local charges, form a Poisson algebra [InlineMediaObject not available: see fulltext.], which is the semiclassical limit of the quantum group {U}_q(g) , with g the Lie algebra of G. For a general Lie group G with rank( G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra [InlineMediaObject not available: see fulltext.], the classical analogue of the quantum loop algebra {U}_q(Lg) , where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.

  20. Interpenetrating and non-interpenetrating 3-dimensional coordination polymer frameworks from multiple building blocks

    NASA Astrophysics Data System (ADS)

    Bradshaw, Darren; Rosseinsky, Matthew J.

    2005-12-01

    Reaction of Co(NO3)2ṡ6H2O with the multidentate ligands benzene-1,3,5-tricarboxylate (btc) and the flexible bipyridyl ligand 1,2-bis(4-pyridyl)ethane (bpe) affords the 3-dimensional coordination polymers [Co3(btc)2(bpe)3(eg)2]ṡ(guests) 1, where eg = ethylene glycol, and [Co2(Hbtc)2(bpe)2]ṡ(bpe) 2. Both phases are comprised of infinite metal-carboxylate dimer chains, linked into 2-dimensional sheets by the bpe ligands. These sheets are further linked to adjacent sheets through covalent interactions, 1, or through hydrogen-bonding interactions, 2, to yield the 3-dimensional structures. Phase 1 exhibits solvent filled 1-dimensional pores, whereas 2 is triply-interpenetrated to form a dense solid array.

  1. The Role of Frequency on the Acquisition of L2 English Infinitive and Gerund Complements by L1 Thai Learners

    ERIC Educational Resources Information Center

    Keawchaum, Raksina; Pongpairoj, Nattama

    2017-01-01

    This study investigated how frequency influenced acquisition of L2 English infinitive and gerund complements among L1 Thai learners. Participants were separated into low and high proficiency groups based on their CU-TEP scores. Each group consisted of 30 participants. Data were collected using the Word Selection Task (WST) and the Grammaticality…

  2. Bifurcating fronts for the Taylor-Couette problem in infinite cylinders

    NASA Astrophysics Data System (ADS)

    Hărăguş-Courcelle, M.; Schneider, G.

    We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.

  3. On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.; Wang, C.

    1990-01-01

    The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

  4. Is the tautochrone curve unique?

    NASA Astrophysics Data System (ADS)

    Terra, Pedro; de Melo e Souza, Reinaldo; Farina, C.

    2016-12-01

    We show that there are an infinite number of tautochrone curves in addition to the cycloid solution first obtained by Christiaan Huygens in 1658. We begin by reviewing the inverse problem of finding the possible potential energy functions that lead to periodic motions of a particle whose period is a given function of its mechanical energy. There are infinitely many such solutions, called "sheared" potentials. As an interesting example, we show that a Pöschl-Teller potential and the one-dimensional Morse potentials are sheared relative to one another for negative energies, clarifying why they share the same oscillation periods for their bounded solutions. We then consider periodic motions of a particle sliding without friction over a track around its minimum under the influence of a constant gravitational field. After a brief historical survey of the tautochrone problem we show that, given the oscillation period, there is an infinity of tracks that lead to the same period. As a bonus, we show that there are infinitely many tautochrones.

  5. Galilean field theories and conformal structure

    NASA Astrophysics Data System (ADS)

    Bagchi, Arjun; Chakrabortty, Joydeep; Mehra, Aditya

    2018-04-01

    We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories. We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory. We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions). The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two. We then couple matter with Galilean gauge theories and show that there is a myriad of different sectors that arise in the non-relativistic limit from the parent relativistic theories. In every case, if the parent relativistic theory exhibited conformal invariance, we find an infinitely enhanced Galilean conformal invariance in the non-relativistic case. This leads us to suggest that infinite enhancement of symmetries in the non-relativistic limit is a generic feature of conformal field theories in any dimension.

  6. Localized transversal-rotational modes in linear chains of equal masses.

    PubMed

    Pichard, H; Duclos, A; Groby, J-P; Tournat, V; Gusev, V E

    2014-01-01

    The propagation and localization of transversal-rotational waves in a two-dimensional granular chain of equal masses are analyzed in this study. The masses are infinitely long cylinders possessing one translational and one rotational degree of freedom. Two dispersive propagating modes are predicted in this granular crystal. By considering the semi-infinite chain with a boundary condition applied at its beginning, the analytical study demonstrates the existence of localized modes, each mode composed of two evanescent modes. Their existence, position (either in the gap between the propagating modes or in the gap above the upper propagating mode), and structure of spatial localization are analyzed as a function of the relative strength of the shear and bending interparticle interactions and for different boundary conditions. This demonstrates the existence of a localized mode in a semi-infinite monatomic chain when transversal-rotational waves are considered, while it is well known that these types of modes do not exist when longitudinal waves are considered.

  7. On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.; Wang, C.

    1992-01-01

    The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

  8. Option pricing for stochastic volatility model with infinite activity Lévy jumps

    NASA Astrophysics Data System (ADS)

    Gong, Xiaoli; Zhuang, Xintian

    2016-08-01

    The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

  9. Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

    NASA Astrophysics Data System (ADS)

    Minami, Kazuhiko

    2017-12-01

    An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c = m / 2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

  10. The efficient simulation of separated three-dimensional viscous flows using the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Van Dalsem, W. R.; Steger, J. L.

    1985-01-01

    A simple and computationally efficient algorithm for solving the unsteady three-dimensional boundary-layer equations in the time-accurate or relaxation mode is presented. Results of the new algorithm are shown to be in quantitative agreement with detailed experimental data for flow over a swept infinite wing. The separated flow over a 6:1 ellipsoid at angle of attack, and the transonic flow over a finite-wing with shock-induced 'mushroom' separation are also computed and compared with available experimental data. It is concluded that complex, separated, three-dimensional viscous layers can be economically and routinely computed using a time-relaxation boundary-layer algorithm.

  11. Effect of Body Perturbations on Hypersonic Flow Over Slender Power Law Bodies

    NASA Technical Reports Server (NTRS)

    Mirels, Harold; Thornton, Philip R.

    1959-01-01

    Hypersonic-slender-body theory, in the limit as the free-stream Mach number becomes infinite, is used to find the effect of slightly perturbing the surface of slender two-dimensional and axisymmetric power law bodies, The body perturbations are assumed to have a power law variation (with streamwise distance downstream of the nose of the body). Numerical results are presented for (1) the effect of boundary-layer development on two dimensional and axisymmetric bodies, (2) the effect of very small angles of attack (on tow[dimensional bodies), and (3) the effect of blunting the nose of very slender wedges and cones.

  12. Linear stability of three-dimensional boundary layers - Effects of curvature and non-parallelism

    NASA Technical Reports Server (NTRS)

    Malik, M. R.; Balakumar, P.

    1993-01-01

    In this paper we study the effect of in-plane (wavefront) curvature on the stability of three-dimensional boundary layers. It is found that this effect is stabilizing or destabilizing depending upon the sign of the crossflow velocity profile. We also investigate the effects of surface curvature and nonparallelism on crossflow instability. Computations performed for an infinite-swept cylinder show that while convex curvature stabilizes the three-dimensional boundary layer, nonparallelism is, in general, destabilizing and the net effect of the two depends upon meanflow and disturbance parameters. It is also found that concave surface curvature further destabilizes the crossflow instability.

  13. Magnetohydrodynamic motion of a two-fluid plasma

    DOE PAGES

    Burby, Joshua W.

    2017-07-21

    Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

  14. Magnetohydrodynamic motion of a two-fluid plasma

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

    Burby, Joshua W.

    Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

  15. Three-dimensional supramolecular architecture in imidazolium hydrogen 2,3,5,6-tetrafluoroterephthalate.

    PubMed

    Yu, Li-Li; Cheng, Mei-Ling; Liu, Qi; Zhang, Zhi-Hui; Chen, Qun

    2010-04-01

    The asymmetric unit of the title salt formed between 2,3,5,6-tetrafluoroterephthalic acid (H(2)tfbdc) and imidazolium (ImH), C(3)H(5)N(2)(+).C(8)HF(4)O(4)(-), contains one Htfbdc(-) anion and one ImH(2)(+) cation, joined by a classical N-H...O hydrogen bond. The acid and base subunits are further linked by N-H...O and O-H...O hydrogen bonds into infinite two-dimensional layers with R(6)(5)(32) hydrogen-bond motifs. The resulting (4,4) network layers interpenetrate to produce an interlocked three-dimensional structure. The final three-dimensional supramolecular architecture is further stabilized by the linkages of two C-H...O interactions.

  16. Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

    NASA Astrophysics Data System (ADS)

    Park, Su-Chan

    2017-09-01

    The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006), 10.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

  17. A new antibacterial silver(I) complex incorporating 2,5-dimethylpyrazine and the anti-inflammatory diclofenac.

    PubMed

    Hamamci Alisir, Sevim; Dege, Necmi

    2016-12-01

    Ag I -containing coordination complexes have attracted attention because of their photoluminescence properties and antimicrobial activities and, in principle, these properties depend on the nature of the structural topologies. A novel two-dimensional silver(I) complex with the anti-inflammatory diclofenac molecule, namely bis{μ-2-[2-(2,6-dichloroanilino)phenyl]acetato-κ 3 O,O':O}bis(μ-2,5-dimethylpyrazine-κ 2 N:N')silver(I), [Ag 2 (C 14 H 10 Cl 2 NO 2 ) 2 (C 6 H 8 N 2 )] n , (I), has been synthesized and characterized by single-crystal X-ray diffraction, revealing that the Ag I ions are chelated by the carboxylate groups of the anionic 2-[2-(2,6-dichloroanilino)phenyl]acetate (dicl) ligand in a μ 3 -η 1 :η 2 coordination mode. Each dicl ligand links three Ag I atoms to generate a one-dimensional infinite chain. Adjacent chains are connected through 2,5-dimethylpyrazine (dmpyz) ligands to form a two-dimensional layer structure parallel to the crystallographic bc plane. The layers are further connected by C-H...π interactions to generate a three-dimensional supramolecular structure. Additionally, the most striking feature is that the structure contains an intramolecular C-H ...Ag anagostic interaction. Furthermore, the title complex has been tested for its in vitro antibacterial activity and is determined to be highly effective on the studied microorganisms.

  18. Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Bernstein, Dennis S.; Rosen, I. G.

    1988-01-01

    In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

  19. Dynamic Vision for Control

    DTIC Science & Technology

    2009-02-05

    the best of our knowledge, the first approach to design a proper filter (observer) in the infinite - dimensional space of shapes (closed Jordan...curves). This is based on endowing the space with a Riemaimian (Sobolev) metric , then shooting geodesies from the current best estimate of the state...handing nuisance transformations and endowing the models with a

  20. Buckling of beams supported by Pasternak foundation.

    NASA Technical Reports Server (NTRS)

    Murthy, G. K. N.

    1973-01-01

    The determination of buckling loads for infinitely long beams resting on a Pasternak (1954) foundation is considered. It is assumed that the onset of buckling takes place at neutral equilibrium. The effect of extending the foundation beyond the width of the beam is determined by comparing the results obtained for two- and three-dimensional foundations.

  1. Stresses and strains in thick perforated orthotropic plates

    Treesearch

    A. Alshaya; John Hunt; R. Rowlands

    2016-01-01

    Stress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka Spruce wood are emphasized, although some for carbon...

  2. Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

    PubMed

    Zhao, Ying; Shi, Luoyi

    2017-01-01

    This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.

  3. Electrical Resistance of the Low Dimensional Critical Branching Random Walk

    NASA Astrophysics Data System (ADS)

    Járai, Antal A.; Nachmias, Asaf

    2014-10-01

    We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d < 6 is O( n 1- α ) for some universal constant α > 0. This answers a question of Barlow et al. (Commun Math Phys 278:385-431, 2008).

  4. Marginally specified priors for non-parametric Bayesian estimation

    PubMed Central

    Kessler, David C.; Hoff, Peter D.; Dunson, David B.

    2014-01-01

    Summary Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables. PMID:25663813

  5. Averaging of random walks and shift-invariant measures on a Hilbert space

    NASA Astrophysics Data System (ADS)

    Sakbaev, V. Zh.

    2017-06-01

    We study random walks in a Hilbert space H and representations using them of solutions of the Cauchy problem for differential equations whose initial conditions are numerical functions on H. We construct a finitely additive analogue of the Lebesgue measure: a nonnegative finitely additive measure λ that is defined on a minimal subset ring of an infinite-dimensional Hilbert space H containing all infinite-dimensional rectangles with absolutely converging products of the side lengths and is invariant under shifts and rotations in H. We define the Hilbert space H of equivalence classes of complex-valued functions on H that are square integrable with respect to a shift-invariant measure λ. Using averaging of the shift operator in H over random vectors in H with a distribution given by a one-parameter semigroup (with respect to convolution) of Gaussian measures on H, we define a one-parameter semigroup of contracting self-adjoint transformations on H, whose generator is called the diffusion operator. We obtain a representation of solutions of the Cauchy problem for the Schrödinger equation whose Hamiltonian is the diffusion operator.

  6. Diffusiophoresis in one-dimensional solute gradients

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

    Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo

    Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics.more » The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.« less

  7. Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

    PubMed

    Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

    2018-04-01

    This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

  8. Smoothing of Transport Plans with Fixed Marginals and Rigorous Semiclassical Limit of the Hohenberg-Kohn Functional

    NASA Astrophysics Data System (ADS)

    Cotar, Codina; Friesecke, Gero; Klüppelberg, Claudia

    2018-06-01

    We prove rigorously that the exact N-electron Hohenberg-Kohn density functional converges in the strongly interacting limit to the strictly correlated electrons (SCE) functional, and that the absolute value squared of the associated constrained search wavefunction tends weakly in the sense of probability measures to a minimizer of the multi-marginal optimal transport problem with Coulomb cost associated to the SCE functional. This extends our previous work for N = 2 ( Cotar etal. in Commun Pure Appl Math 66:548-599, 2013). The correct limit problem has been derived in the physics literature by Seidl (Phys Rev A 60 4387-4395, 1999) and Seidl, Gorigiorgi and Savin (Phys Rev A 75:042511 1-12, 2007); in these papers the lack of a rigorous proofwas pointed out.We also give amathematical counterexample to this type of result, by replacing the constraint of given one-body density—an infinite dimensional quadratic expression in the wavefunction—by an infinite-dimensional quadratic expression in the wavefunction and its gradient. Connections with the Lawrentiev phenomenon in the calculus of variations are indicated.

  9. Decay of a linear pendulum in a collisional gas: Spatially one-dimensional case

    NASA Astrophysics Data System (ADS)

    Tsuji, Tetsuro; Aoki, Kazuo

    2014-05-01

    An infinitely wide plate, subject to an external force in its normal direction obeying Hooke's law, is placed in an infinite expanse of a rarefied gas. When the plate is displaced from its equilibrium position and released, it starts in general an oscillatory motion in its normal direction. This is the one-dimensional setting of a linear pendulum considered previously for a collisionless gas and a special Lorentz gas by the present authors [T. Tsuji and K. Aoki, J. Stat. Phys. 146, 620 (2012), 10.1007/s10955-011-0412-7]. The motion decays as time proceeds because of the drag force on the plate exerted by the surrounding gas. The long-time behavior of the unsteady motion of the gas caused by the motion of the plate is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation with special interest in the rate of the decay of the oscillatory motion of the plate. The result provides numerical evidence that the displacement of the plate decays in proportion to an inverse power of time for large time.

  10. Decay of a linear pendulum in a collisional gas: spatially one-dimensional case.

    PubMed

    Tsuji, Tetsuro; Aoki, Kazuo

    2014-05-01

    An infinitely wide plate, subject to an external force in its normal direction obeying Hooke's law, is placed in an infinite expanse of a rarefied gas. When the plate is displaced from its equilibrium position and released, it starts in general an oscillatory motion in its normal direction. This is the one-dimensional setting of a linear pendulum considered previously for a collisionless gas and a special Lorentz gas by the present authors [T. Tsuji and K. Aoki, J. Stat. Phys. 146, 620 (2012)]. The motion decays as time proceeds because of the drag force on the plate exerted by the surrounding gas. The long-time behavior of the unsteady motion of the gas caused by the motion of the plate is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation with special interest in the rate of the decay of the oscillatory motion of the plate. The result provides numerical evidence that the displacement of the plate decays in proportion to an inverse power of time for large time.

  11. Quantum heat waves in a one-dimensional condensate

    NASA Astrophysics Data System (ADS)

    Agarwal, Kartiek; Dalla Torre, Emanuele G.; Schmiedmayer, Jörg; Demler, Eugene

    2017-05-01

    We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a bi-directional, supersonic `unzipping' of a finite single condensate. We find that the system fractures into different extensive chunks of space-time, within which correlations appear thermal but correspond to different effective temperatures. Coherences between different eigen-modes are crucial for understanding the development of such thermal correlations; at no point in time can our system be described by a generalized Gibbs' ensemble despite nearly always appearing locally thermal. We rationalize a picture of propagating fronts of hot and cold sound waves, populated at effective, relativistically red- and blue-shifted temperatures to intuitively explain our findings. The disparity between these hot and cold temperatures vanishes for the case of instantaneous splitting but diverges in the limit where the splitting velocity approaches the speed of sound; in this limit, a sonic boom occurs wherein the system is excited only along an infinitely narrow, and infinitely hot beam. We expect our findings to apply generally to the study of superluminal perturbations in systems with emergent Lorentz symmetry.

  12. Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

    NASA Astrophysics Data System (ADS)

    Haitjema, Henk M.

    1985-10-01

    A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

  13. Modal Ring Method for the Scattering of Electromagnetic Waves

    NASA Technical Reports Server (NTRS)

    Baumeister, Kenneth J.; Kreider, Kevin L.

    1993-01-01

    The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.

  14. Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi

    1990-01-01

    In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.

  15. Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder

    NASA Astrophysics Data System (ADS)

    Nazarov, S. A.

    2014-08-01

    The Dirichlet problem is considered on the junction of thin quantum waveguides (of thickness h ≪ 1) in the shape of an infinite two-dimensional ladder. Passage to the limit as h → +0 is discussed. It is shown that the asymptotically correct transmission conditions at nodes of the corresponding one-dimensional quantum graph are Dirichlet conditions rather than the conventional Kirchhoff transmission conditions. The result is obtained by analyzing bounded solutions of a problem in the T-shaped waveguide that the boundary layer phenomenon.

  16. Solving time-dependent two-dimensional eddy current problems

    NASA Technical Reports Server (NTRS)

    Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

    1990-01-01

    Transient eddy current calculations are presented for an EM wave-scattering and field-penetrating case in which a two-dimensional transverse magnetic field is incident on a good (i.e., not perfect) and infinitely long conductor. The problem thus posed is of initial boundary-value interface type, where the boundary of the conductor constitutes the interface. A potential function is used for time-domain modeling of the situation, and finite difference-time domain techniques are used to march the potential function explicitly in time. Attention is given to the case of LF radiation conditions.

  17. Time-dependent reflection at the localization transition

    NASA Astrophysics Data System (ADS)

    Skipetrov, Sergey E.; Sinha, Aritra

    2018-03-01

    A short quasimonochromatic wave packet incident on a semi-infinite disordered medium gives rise to a reflected wave. The intensity of the latter decays as a power law, 1 /tα , in the long-time limit. Using the one-dimensional Aubry-André model, we show that in the vicinity of the critical point of Anderson localization transition, the decay slows down, and the power-law exponent α becomes smaller than both α =2 found in the Anderson localization regime and α =3 /2 expected for a one-dimensional random walk of classical particles.

  18. Thermographic Phosphor Measurements of Shock-Shock Interactions on a Swept Cylinder

    NASA Technical Reports Server (NTRS)

    Jones, Michelle L.; Berry, Scott A.

    2013-01-01

    The effects of fin leading-edge radius and sweep angle on peak heating rates due to shock-shock interactions were investigated in the NASA Langley Research Center 20-inch Mach 6 Air Tunnel. The fin model leading edges, which represent cylindrical leading edges or struts on hypersonic vehicles, were varied from 0.25 inches to 0.75 inches in radius. A 9deg wedge generated a planar oblique shock at 16.7deg to the flow that intersected the fin bow shock, producing a shock-shock interaction that impinged on the fin leading edge. The fin angle of attack was varied from 0deg (normal to the free-stream) to 15deg and 25deg swept forward. Global temperature data was obtained from the surface of the fused silica fins using phosphor thermography. Metal oil flow models with the same geometries as the fused silica models were used to visualize the streamline patterns for each angle of attack. High-speed zoom-schlieren videos were recorded to show the features and temporal unsteadiness of the shock-shock interactions. The temperature data were analyzed using one-dimensional semi-infinite as well as one- and two-dimensional finite-volume methods to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock interactions. The general trends in the leading-edge heat transfer behavior were similar for the three shock-shock interactions, respectively, between the test articles with varying leading-edge radius. The dimensional peak heat transfer coefficient augmentation increased with decreasing leading-edge radius. The dimensional peak heat transfer output from the two-dimensional code was about 20% higher than the value from a standard, semi-infinite onedimensional method.

  19. Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence

    NASA Astrophysics Data System (ADS)

    Grebenev, V. N.; Wacławczyk, M.; Oberlack, M.

    2017-10-01

    We study the statistical properties of the vorticity field in two-dimensional turbulence. The field is described in terms of the infinite Lundgren-Monin-Novikov (LMN) chain of equations for multi-point probability density functions (pdf’s) of vorticity. We perform a Lie group analysis of the first equation in this chain using the direct method based on the canonical Lie-Bäcklund transformations devised for integro-differential equations. We analytically show that the conformal group is broken for the first LMN equation i.e. for the 1-point pdf at least for the inviscid case but the equation is still conformally invariant on the associated characteristic with zero-vorticity. Then, we demonstrate that this characteristic is conformally transformed. We find this outcome coincides with the numerical results about the conformal invariance of the statistics of zero-vorticity isolines, see e.g. Falkovich (2007 Russian Math. Surv. 63 497-510). The conformal symmetry can be understood as a ‘local scaling’ and its traces in two-dimensional turbulence were already discussed in the literature, i.e. it was conjectured more than twenty years ago in Polyakov (1993 Nucl. Phys. B 396 367-85) and clearly validated experimentally in Bernard et al (2006 Nat. Phys. 2 124-8).

  20. The metric on field space, functional renormalization, and metric–torsion quantum gravity

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

    Reuter, Martin, E-mail: reuter@thep.physik.uni-mainz.de; Schollmeyer, Gregor M., E-mail: schollmeyer@thep.physik.uni-mainz.de

    Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modifiedmore » FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.« less

  1. On the Liouville Integrability of the Periodic Kostant-Toda Flow on Matrix Loops of Level k

    NASA Astrophysics Data System (ADS)

    Li, Luen-Chau; Nie, Zhaohu

    2017-06-01

    In this work, we consider the periodic Kostant-Toda flow on matrix loops in sl(n,C) of level k, which correspond to periodic infinite band matrices with period n with lower bandwidth equal to k and fixed upper bandwidth equal to 1 with 1's on the first superdiagonal. We show that the coadjoint orbits through the submanifold of such matrix loops can be identified with those of a finite-dimensional Lie group, which appears in the form of a semi-direct product. We then characterize the generic coadjoint orbits and obtain an explicit global cross-section for such orbits. We also establish the Liouville integrability of the periodic Kostant-Toda flow on such orbits via the construction of action-angle variables.

  2. Radiative transport equation for the Mittag-Leffler path length distribution

    NASA Astrophysics Data System (ADS)

    Liemert, André; Kienle, Alwin

    2017-05-01

    In this paper, we consider the radiative transport equation for infinitely extended scattering media that are characterized by the Mittag-Leffler path length distribution p (ℓ ) =-∂ℓEα(-σtℓα ) , which is a generalization of the usually assumed Lambert-Beer law p (ℓ ) =σtexp(-σtℓ ) . In this context, we derive the infinite-space Green's function of the underlying fractional transport equation for the spherically symmetric medium as well as for the one-dimensional string. Moreover, simple analytical solutions are presented for the prediction of the radiation field in the single-scattering approximation. The resulting equations are compared with Monte Carlo simulations in the steady-state and time domain showing, within the stochastic nature of the simulations, an excellent agreement.

  3. Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

    NASA Astrophysics Data System (ADS)

    Remizov, I. D.

    2012-07-01

    The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

  4. Exact solution for the Poisson field in a semi-infinite strip.

    PubMed

    Cohen, Yossi; Rothman, Daniel H

    2017-04-01

    The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

  5. Frozen into stripes: fate of the critical Ising model after a quench.

    PubMed

    Blanchard, T; Picco, M

    2013-09-01

    In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at T_{c}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.

  6. Limit of Kerr-de Sitter spacetime with infinite angular-momentum parameter a

    NASA Astrophysics Data System (ADS)

    Mars, Marc; Paetz, Tim-Torben; Senovilla, José M. M.

    2018-01-01

    We consider the limit a →∞ of the Kerr-de Sitter spacetime. The spacetime is a Petrov type-D solution of the vacuum Einstein field equations with a positive cosmological constant Λ , vanishing Mars-Simon tensor and conformally flat ℐ . It possesses an Abelian 2-dimensional group of symmetries whose orbits are spacelike or timelike in different regions, and it includes, as a particular case, de Sitter spacetime. The global structure of the solution is analyzed in detail, with particular attention to its Killing horizons: they are foliated by noncompact marginally trapped surfaces of finite area, and one of them "touches" the curvature singularity, which resembles a null 2-dimensional surface. Outside the region between these horizons there exist trapped surfaces that again are noncompact. The solution contains, apart from Λ , a unique free parameter which can be related to the angular momentum of the nonsingular horizon in a precise way. A maximal extension of the (axis of the) spacetime is explicitly built. We also analyze the structure of ℐ , whose topology is R3.

  7. Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

    NASA Astrophysics Data System (ADS)

    Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

    2015-03-01

    We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

  8. Structure and Electrical Conductivity of AgTaS 3

    NASA Astrophysics Data System (ADS)

    Kim, Changkeun; Yun, Hoseop; Lee, Youngju; Shin, Heekyoon; Liou, Kwangkyoung

    1997-09-01

    Single crystals of the compound AgTaS 3have been prepared through reactions of the elements with halide mixtures. The structure of AgTaS 3has been analyzed by single-crystal X-ray diffraction methods. AgTaS 3crystallizes in the space group D172h- Cmcmof the orthorhombic system with four formula units in a cell of dimensions a=3.378(2), b=14.070(5), c=7.756(3) Å. The structure of AgTaS 3consists of two-dimensional 2∞[TaS -3] layers separated by Ag +cations. The layer is composed of Ta-centered bicapped trigonal prisms stacked on top of each other by sharing triangular faces. These chains are linked to form the infinite two-dimensional 2∞[TaS -3] slabs. These layers are held together through van der Waals interactions, and Ag +ions reside in the distorted octahedral sites between the layers. The temperature dependence of the electrical conductivity along the needle axis of AgTaS 3shows the typical behavior of an extrinsic semiconductor.

  9. Chaos in quantum steering in high-dimensional systems

    NASA Astrophysics Data System (ADS)

    He, Guang Ping

    2018-04-01

    Quantum steering means that in some bipartite quantum systems the local measurements on one side can determine the state of the other side. Here we show that in high-dimensional systems there exists a specific entangled state which can display a kind of chaos effect when being adopted for steering. That is, a subtle difference in the measurement results on one side can steer the other side into completely orthogonal states. Moreover, by expanding the result to infinite-dimensional systems, we find two sets of states for which, contrary to common belief, even though their density matrices approach being identical, the steering between them is impossible. This property makes them very useful for quantum cryptography.

  10. Three-dimensional application of the Johnson-King turbulence model for a boundary-layer direct method

    NASA Technical Reports Server (NTRS)

    Kavsaoglu, Mehmet S.; Kaynak, Unver; Van Dalsem, William R.

    1989-01-01

    The Johnson-King turbulence model as extended to three-dimensional flows was evaluated using finite-difference boundary-layer direct method. Calculations were compared against the experimental data of the well-known Berg-Elsenaar incompressible flow over an infinite swept-wing. The Johnson-King model, which includes the nonequilibrium effects in a developing turbulent boundary-layer, was found to significantly improve the predictive quality of a direct boundary-layer method. The improvement was especially visible in the computations with increased three-dimensionality of the mean flow, larger integral parameters, and decreasing eddy-viscosity and shear stress magnitudes in the streamwise direction; all in better agreement with the experiment than simple mixing-length methods.

  11. The continuous spin representations of the Poincare and super-Poincare groups and their construction by the Inonu-Wigner group contraction

    NASA Astrophysics Data System (ADS)

    Khan, Abu M. A. S.

    We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is required to yield any CSR in four dimensions. The representation wavefunction is the Bessel function, as expected, but the scale factor is not the length of the light-cone vector. The amplitude and the scale factor are implicit functions of the parameter y which is a ratio of the internal and external coordinates. We also state under what conditions our solutions become identical to Wigner's solution.

  12. Infinite index extensions of local nets and defects

    NASA Astrophysics Data System (ADS)

    Del Vecchio, Simone; Giorgetti, Luca

    The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [62] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi-Longo-Popa [44] and Fidaleo-Isola [30], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [7].

  13. On the constrained classical capacity of infinite-dimensional covariant quantum channels

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

    Holevo, A. S.

    The additivity of the minimal output entropy and that of the χ-capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al., Commun. Math. Phys. 334(3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimodemore » generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111, 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. We also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.« less

  14. Symmetry algebra of a generalized anisotropic harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Castanos, O.; Lopez-Pena, R.

    1993-01-01

    It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

  15. Optimizing random searches on three-dimensional lattices

    NASA Astrophysics Data System (ADS)

    Yang, Benhao; Yang, Shunkun; Zhang, Jiaquan; Li, Daqing

    2018-07-01

    Search is a universal behavior related to many types of intelligent individuals. While most studies have focused on search in two or infinite-dimensional space, it is still missing how search can be optimized in three-dimensional space. Here we study random searches on three-dimensional (3d) square lattices with periodic boundary conditions, and explore the optimal search strategy with a power-law step length distribution, p(l) ∼l-μ, known as Lévy flights. We find that compared to random searches on two-dimensional (2d) lattices, the optimal exponent μopt on 3d lattices is relatively smaller in non-destructive case and remains similar in destructive case. We also find μopt decreases as the lattice length in z direction increases under high target density. Our findings may help us to understand the role of spatial dimension in search behaviors.

  16. Annual-ring-type quasi-phase-matching crystal for generation of narrowband high-dimensional entanglement

    NASA Astrophysics Data System (ADS)

    Hua, Yi-Lin; Zhou, Zong-Quan; Liu, Xiao; Yang, Tian-Shu; Li, Zong-Feng; Li, Pei-Yun; Chen, Geng; Xu, Xiao-Ye; Tang, Jian-Shun; Xu, Jin-Shi; Li, Chuan-Feng; Guo, Guang-Can

    2018-01-01

    A photon pair can be entangled in many degrees of freedom such as polarization, time bins, and orbital angular momentum (OAM). Among them, the OAM of photons can be entangled in an infinite-dimensional Hilbert space which enhances the channel capacity of sharing information in a network. Twisted photons generated by spontaneous parametric down-conversion offer an opportunity to create this high-dimensional entanglement, but a photon pair generated by this process is typically wideband, which makes it difficult to interface with the quantum memories in a network. Here we propose an annual-ring-type quasi-phase-matching (QPM) crystal for generation of the narrowband high-dimensional entanglement. The structure of the QPM crystal is designed by tracking the geometric divergences of the OAM modes that comprise the entangled state. The dimensionality and the quality of the entanglement can be greatly enhanced with the annual-ring-type QPM crystal.

  17. The Goertler vortex instability mechanism in three-dimensional boundary layers

    NASA Technical Reports Server (NTRS)

    Hall, P.

    1984-01-01

    The two dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

  18. A two-dimensional ZnII coordination polymer constructed from benzene-1,2,3-tricarboxylic acid and N,N'-bis[(pyridin-4-yl)methylidene]hydrazine.

    PubMed

    Wang, Xiangfei; Yang, Fang; Tang, Meng; Yuan, Limin; Liu, Wenlong

    2015-07-01

    The hydrothermal synthesis of the novel complex poly[aqua(μ4-benzene-1,2,3-tricarboxylato)[μ2-4,4'-(hydrazine-1,2-diylidenedimethanylylidene)dipyridine](μ3-hydroxido)dizinc(II)], [Zn(C9H3O6)(OH)(C12H10N4)(H2O)]n, is described. The benzene-1,2,3-tricarboxylate ligand connects neighbouring Zn4(OH)2 secondary building units (SBUs) producing an infinite one-dimensional chain. Adjacent one-dimensional chains are connected by the N,N'-bis[(pyridin-4-yl)methylidene]hydrazine ligand, forming a two-dimensional layered structure. Adjacent layers are stacked to generate a three-dimensional supramolecular architecture via O-H...O hydrogen-bond interactions. The thermal stability of this complex is described and the complex also appears to have potential for application as a luminescent material.

  19. Ideas of Flat and Curved Space in History of Physics

    NASA Astrophysics Data System (ADS)

    Berezin, Alexander A.

    2006-04-01

    Since ``everything which is not prohibited is compulsory'' (assigned to Gell-Mann) we can postulate infinite flat Cartesian N-dimensional (N: any integer) space-time (ST) as embedding for any curved ST. Ergodicity raises quest of whether total number of inflationary and/or Everett bubbles (mini-verses) is finite, countably infinite (aleph-zero) or uncountably infinite (aleph-one). Are these bubbles form Gaussian distribution or form some non-random subsetting? Perhaps, communication between mini-verses (idea of D.Deutsch) can be facilitated by a kind of minimax non-local dynamics akin to Fermat principle? (Minimax Principle in Bubble Cosmology). Even such classical effects as magnetism and polarization have some non-local features. Can we go below the Planck length to perhaps Compton wavelength of our ``Hubble's bubble'' (h/Mc = 10 to minus 95 m, if M = 10 to 54 kg)? When talking about time loops and ergodicity (eternal return paradigm) is there some hysterisis in the way quantum states are accessed in ``forward'' or ``reverse'' direction? (reverse direction implies backward causality of J.Wheeler and/or Aristotelian final causation).

  20. Fault-tolerant control of large space structures using the stable factorization approach

    NASA Technical Reports Server (NTRS)

    Razavi, H. C.; Mehra, R. K.; Vidyasagar, M.

    1986-01-01

    Large space structures are characterized by the following features: they are in general infinite-dimensional systems, and have large numbers of undamped or lightly damped poles. Any attempt to apply linear control theory to large space structures must therefore take into account these features. Phase I consisted of an attempt to apply the recently developed Stable Factorization (SF) design philosophy to problems of large space structures, with particular attention to the aspects of robustness and fault tolerance. The final report on the Phase I effort consists of four sections, each devoted to one task. The first three sections report theoretical results, while the last consists of a design example. Significant results were obtained in all four tasks of the project. More specifically, an innovative approach to order reduction was obtained, stabilizing controller structures for plants with an infinite number of unstable poles were determined under some conditions, conditions for simultaneous stabilizability of an infinite number of plants were explored, and a fault tolerance controller design that stabilizes a flexible structure model was obtained which is robust against one failure condition.

  1. Global Aeroheating Measurements of Shock-Shock Interactions on a Swept Cylinder

    NASA Technical Reports Server (NTRS)

    Mason, Michelle L.; Berry, Scott A.

    2015-01-01

    The effects of fin leading-edge radius and sweep angle on peak heating rates due to shock-shock interactions were investigated in the NASA Langley Research Center 20-Inch Mach 6 Air Tunnel. The cylindrical leading-edge fin models, with radii varied from 0.25 to 0.75 inches, represent wings or struts on hypersonic vehicles. A 9deg wedge generated a planar oblique shock at 16.7deg. to the flow that intersected the fin bow shock, producing a shock-shock interaction that impinged on the fin leading edge. The fin sweep angle was varied from 0deg (normal to the free-stream) to 15deg and 25deg swept forward. These cases were chosen to explore three characterized shock-shock interaction types. Global temperature data were obtained from the surface of the fused silica fins using phosphor thermography. Metal oil flow models with the same geometries as the fused silica models were used to visualize the streamline patterns for each angle of attack. High-speed zoom-schlieren videos were recorded to show the features and any temporal unsteadiness of the shock-shock interactions. The temperature data were analyzed using a one-dimensional semi-infinite method, as well as one- and two-dimensional finite-volume methods. These results were compared to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock interactions. The general trends in the leading-edge heat transfer behavior were similar for each explored shock-shock interaction type regardless of the leading-edge radius. However, the dimensional peak heat transfer coefficient augmentation increased with decreasing leading-edge radius. The dimensional peak heat transfer output from the two-dimensional code was about 20% higher than the value from a standard, semi-infinite one-dimensional method.

  2. K-theory of locally finite graph C∗-algebras

    NASA Astrophysics Data System (ADS)

    Iyudu, Natalia

    2013-09-01

    We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).

  3. Specific Language Impairment as a Period of Extended Optional Infinitive.

    ERIC Educational Resources Information Center

    Rice, Mabel L.; And Others

    1995-01-01

    This study evaluated an Extended Optional Infinitive theory of specific language impairment (SLI) in children, which suggests that SLI children omit finiteness markers longer than do normally developing children. Comparison of 18 SLI 5-year olds with 2 normally developing groups (ages 5 and 3) found that SLI subjects omitted finiteness markers…

  4. 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.

  5. The stochastic energy-Casimir method

    NASA Astrophysics Data System (ADS)

    Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

    2018-04-01

    In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

  6. On integrable boundaries in the 2 dimensional O(N) σ-models

    NASA Astrophysics Data System (ADS)

    Aniceto, Inês; Bajnok, Zoltán; Gombor, Tamás; Kim, Minkyoo; Palla, László

    2017-09-01

    We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) σ-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

  7. An obstacle to building a time machine

    NASA Astrophysics Data System (ADS)

    Carroll, Sean M.; Farhi, Edward; Guth, Alan H.

    1992-01-01

    Gott (1991) has shown that a spacetime with two infinite parallel cosmic strings passing each other with sufficient velocity contains closed timelike curves. An attempt to build such a time machine is discussed. Using the energy-momentum conservation laws in the equivalent (2 + 1)-dimensional theory, the spacetime representing the decay of one gravitating particle into two is explicitly constructed; there is never enough mass in an open universe to build the time machine from the products of decays of stationary particles. More generally, the Gott time machine cannot exist in any open (2 + 1)-dimensional universe for which the total momentum is timelike.

  8. 1+1 dimensional compactifications of string theory.

    PubMed

    Goheer, Naureen; Kleban, Matthew; Susskind, Leonard

    2004-05-14

    We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.

  9. BMS3 invariant fluid dynamics at null infinity

    NASA Astrophysics Data System (ADS)

    Penna, Robert F.

    2018-02-01

    We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

  10. The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

    NASA Technical Reports Server (NTRS)

    Reimers, J. R.; Heller, E. J.

    1985-01-01

    Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

  11. The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

    NASA Technical Reports Server (NTRS)

    Reimers, J. R.; Heller, E. J.

    1985-01-01

    The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

  12. Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Li, Lin-an; Wang, Teng; Wang, Yi

    2018-05-01

    We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.

  13. Many-body delocalization in a strongly disordered system with long-range interactions: Finite-size scaling

    NASA Astrophysics Data System (ADS)

    Burin, Alexander L.

    2015-03-01

    Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1 /Rα is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N . The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d -dimensional system including the absence of localization in the infinite system at α <2 d and a universal scaling of a critical energy disordering Wc∝N2/d -α d .

  14. On representations of U{sub q}osp(1{vert_bar}2) when q is a root of unity

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

    Chung, W.; Suzuki, T.

    1997-06-01

    The infinite dimensional highest weight representations of U{sub q}osp(1{vert_bar}2) for the deformation parameter q being a root of unity are investigated. As in the cases of q-deformed nongraded Lie algebras, we find that every irreducible representation is isomorphic to the tensor product of a highest weight representation of sl{sub 2}(R) and a finite dimensional one of U{sub q}osp(1{vert_bar}2). The structure is investigated in detail. {copyright} {ital 1997 American Institute of Physics.}

  15. Quantum Monte Carlo study of spin correlations in the one-dimensional Hubbard model

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

    Sandvik, A.W.; Scalapino, D.J.; Singh, C.

    1993-07-15

    The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding [ital T]=0 correlation function of the infinite system. For the [ital T][r arrow]0 divergence of the [ital q]=2[ital k][sub [ital F

  16. Three-dimensional volume containing multiple two-dimensional information patterns

    NASA Astrophysics Data System (ADS)

    Nakayama, Hirotaka; Shiraki, Atsushi; Hirayama, Ryuji; Masuda, Nobuyuki; Shimobaba, Tomoyoshi; Ito, Tomoyoshi

    2013-06-01

    We have developed an algorithm for recording multiple gradated two-dimensional projection patterns in a single three-dimensional object. When a single pattern is observed, information from the other patterns can be treated as background noise. The proposed algorithm has two important features: the number of patterns that can be recorded is theoretically infinite and no meaningful information can be seen outside of the projection directions. We confirmed the effectiveness of the proposed algorithm by performing numerical simulations of two laser crystals: an octagonal prism that contained four patterns in four projection directions and a dodecahedron that contained six patterns in six directions. We also fabricated and demonstrated an actual prototype laser crystal from a glass cube engraved by a laser beam. This algorithm has applications in various fields, including media art, digital signage, and encryption technology.

  17. Killing and Noether Symmetries of Plane Symmetric Spacetime

    NASA Astrophysics Data System (ADS)

    Shamir, M. Farasat; Jhangeer, Adil; Bhatti, Akhlaq Ahmad

    2013-09-01

    This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).

  18. On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

    NASA Astrophysics Data System (ADS)

    Karimi, Milad; Moradlou, Fridoun; Hajipour, Mojtaba

    2018-10-01

    This paper is concerned with a backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". This problem is drastically ill-posed which is caused by the amplified infinitely growth in the frequency components. A new regularization method based on the Meyer wavelet technique is developed to solve the considered problem. Using the Meyer wavelet technique, some new stable estimates are proposed in the Hölder and Logarithmic types which are optimal in the sense of given by Tautenhahn. The stability and convergence rate of the proposed regularization technique are proved. The good performance and the high-accuracy of this technique is demonstrated through various one and two dimensional examples. Numerical simulations and some comparative results are presented.

  19. A series of Cadmium(II) complexes with 2-substituted terephthalate building block and N-Donor co-ligands: Structural diversity and fluorescence properties

    NASA Astrophysics Data System (ADS)

    Ren, Yixia; Zhou, Shanhong; Wang, Zhixiang; Zhang, Meili; Wang, Jijiang; Cao, Jia

    2017-11-01

    Four new Cd(II) complexes have been prepared based on 1,2,4-trimellitic acid (H3tma) and monosodium 2-sulfoterephthalate (2-NaH2stp), formulated as [Cd2(Htma)2 (dpp)2(H2O)] (1), [Cd3 (tma)2 (2,4-bipy)4(H2O)2] (2), [Cd (2-Hstp) (2,2'-bipy)2]·2H2O (3) and [Cd (2-Hstp) (2,4-bipy) (H2O)2] (4) (dpp = dipyrido [3,2-a:2‧,3'-c] phenazine, 2,4-bipy = 2,4-bipyridine, 2,2'-bipy = 2,2'- bipyridine) by hydrothermal method. X-ray diffraction structural analyses show all these complexes crystallized in triclinic crystal system of Pī space group, but their structures are diverse. Complex 1 exhibits an infinite one-dimensional chain featuring the left- and right-handed stranded chains interweaved each other. For 2, the two-dimensional network is constructed by one-dimensional ladder-like chain linked by Cd2 ions. In complex 3, the cadmium ion is surrounded with one 2-Hstp2- anion and two 2,2'-bipy molecules. Complex 4 is also a discrete structure based on a metallic dimer unit. In all these complexes, the N-donor co-ligands take the important roles in the assembly of three-dimensional supramolecular structures. The fluorescence properties of complexes 1-4 could be assigned to the π - π* transition of organic ligands.

  20. Two-dimensional periodic structures in solid state laser resonator

    NASA Astrophysics Data System (ADS)

    Okulov, Alexey Y.

    1991-07-01

    Transverse effects in nonlinear optical devices are being widely investigated. Recently, synchronization of a laser set by means of the Talbot effect has been demonstrated experimentally. This paper considers a Talbot cavity formed by a solid-state amplifying laser separated from the output mirror by a free space interval. This approach involves the approximation of the nonlinear medium as a thin layer, within which the diffraction is negligible. The other part of a resonator is empty, and the wave field is transformed by the Fresnel-Kirchoff integral. As a result, the dynamics of the transverse (and temporal) structure is computed by a successively iterated nonlinear local map (one- or two-dimensional) and a linear nonlocal map (generally speaking, infinitely dimensional).

  1. A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Ito, K.

    1991-01-01

    A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

  2. A numerical algorithm for optimal feedback gains in high dimensional LQR problems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Ito, K.

    1986-01-01

    A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

  3. Dynamical decoupling of unbounded Hamiltonians

    NASA Astrophysics Data System (ADS)

    Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

    2018-03-01

    We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

  4. Exact edge, bulk, and bound states of finite topological systems

    NASA Astrophysics Data System (ADS)

    Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel

    2018-05-01

    Finite topologically nontrivial systems are characterized, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulk-edge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown previously [Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993), 10.1103/PhysRevLett.71.3697; D. Hügel and B. Paredes, Phys. Rev. A 89, 023619 (2014), 10.1103/PhysRevA.89.023619]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of nontopological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localized impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.

  5. Modelling of three dimensional equilibrium and stability of MAST plasmas with magnetic perturbations using VMEC and COBRA

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

    Ham, C. J., E-mail: christopher.ham@ccfe.ac.uk; Chapman, I. T.; Kirk, A.

    2014-10-15

    It is known that magnetic perturbations can mitigate edge localized modes (ELMs) in experiments, for example, MAST [Kirk et al., Nucl. Fusion 53, 043007 (2013)]. One hypothesis is that the magnetic perturbations cause a three dimensional corrugation of the plasma and this corrugated plasma has different stability properties to peeling-ballooning modes compared to an axisymmetric plasma. It has been shown in an up-down symmetric plasma that magnetic perturbations in tokamaks will break the usual axisymmetry of the plasma causing three dimensional displacements [Chapman et al., Plasma Phys. Controlled Fusion 54, 105013 (2012)]. We produce a free boundary three-dimensional equilibrium ofmore » a lower single null MAST relevant plasma using VMEC [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)]. The safety factor and pressure profiles used for the modelling are similar to those deduced from axisymmetric analysis of experimental data with ELMs. We focus on the effect of applying n = 3 and n = 6 magnetic perturbations using the resonant magnetic perturbation (RMP) coils. A midplane displacement of over ±1 cm is seen when the full current is applied. The current in the coils is scanned and a linear relationship between coil current and midplane displacement is found. The pressure gradient in real space in different toroidal locations is shown to change when RMPs are applied. This effect should be taken into account when diagnosing plasmas with RMPs applied. The helical Pfirsch-Schlüter currents which arise as a result of the assumption of nested flux surfaces are estimated for this equilibrium. The effect of this non-axisymmetric equilibrium on infinite n ballooning stability is investigated using COBRA [Sanchez et al., J. Comput. Phys. 161, 576–588 (2000)]. The infinite n ballooning stability is analysed for two reasons; it may give an indication of the effect of non-axisymmetry on finite n peeling-ballooning modes, responsible for ELMs; and infinite n ballooning modes are correlated to kinetic ballooning modes which are thought to limit the pressure gradient of the pedestal [Snyder et al., Phys. Plasmas 16, 056118 (2009)]. The ballooning mode growth rate gains a variation in toroidal angle. The equilibria with midplane displacements due to RMP coils have a higher ballooning mode growth rate than the axisymmetric case and the possible implications are discussed.« less

  6. A Zero-One Dichotomy Theorem for r-Semi-Stable Laws on Infinite Dimensional Linear Spaces.

    DTIC Science & Technology

    1978-10-01

    SEMISTABLE LAWS - LIKE STABLE ONES - ARE CONTINUOUS: i.e. THEY ASSIGN’ ZERO MASS TO SIIMGLETONS.. DD 172 1 1473 sov’ow as, IMail , 62 i 1 SOee..S $.M 0 102 LfP.Of 4 6601 1ECIuatY CLASSI’PICA1 130N 00 1 100 0449 (W%4 Dma rwer

  7. Chandrasekhar equations for infinite dimensional systems

    NASA Technical Reports Server (NTRS)

    Ito, K.; Powers, R.

    1985-01-01

    The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

  8. The effect of an infinite plane-wave approximation on calculations for second-harmonic generation in a one-dimensional nonlinear crystal

    NASA Astrophysics Data System (ADS)

    Zhao, Jing; Zhao, Li-Ming

    2012-05-01

    In this paper, the second-harmonic generation (SHG) in a one-dimensional nonlinear crystal that is embedded in air is investigated. Previously, the identical configuration was studied in Li Z. Y. et al., Phys. Rev. B, 60 (1999) 10644, without the use of the slowly varying amplitude approximation (SVAA), but by adopting the infinite plane-wave approximation (PWA), despite the fact that this approximation is not quite applicable to such a system. We calculate the SHG conversion efficiency without a PWA, and compare the results with those from the quoted reference. The investigation reveals that conversion efficiencies of SHG as calculated by the two methods appear to exhibit significant differences, and that the SHG may be modulated by the field of a fundamental wave (FW). The ratio between SHG conversion efficiencies as produced by the two methods shows a periodic variation, and this oscillatory behavior is fully consistent with the variation in transmittance of the FW. Quasi-phase matching (QPM) is also studied, and we find that the location of the peak for SHG conversion efficiency deviates from Δd=0, which differs from the conventional QPM results.

  9. On steady two-dimensional Carreau fluid flow over a wedge in the presence of infinite shear rate viscosity

    NASA Astrophysics Data System (ADS)

    Khan, Masood; Sardar, Humara

    2018-03-01

    This paper investigates the steady two-dimensional flow over a moving/static wedge in a Carreau viscosity model with infinite shear rate viscosity. Additionally, heat transfer analysis is performed. Using suitable transformations, nonlinear partial differential equations are transformed into ordinary differential equations and solved numerically using the Runge-Kutta Fehlberg method coupled with the shooting technique. The effects of various physical parameters on the velocity and temperature distributions are displayed graphically and discussed qualitatively. A comparison with the earlier reported results has been made with an excellent agreement. It is important to note that the increasing values of the wedge angle parameter enhance the fluid velocity while the opposite trend is observed for the temperature field for both shear thinning and thickening fluids. Generally, our results reveal that the velocity and temperature distributions are marginally influenced by the viscosity ratio parameter. Further, it is noted that augmented values of viscosity ratio parameter thin the momentum and thermal boundary layer thickness in shear thickening fluid and reverse is true for shear thinning fluid. Moreover, it is noticed that the velocity in case of moving wedge is higher than static wedge.

  10. Exactly solvable model of the two-dimensional electrical double layer.

    PubMed

    Samaj, L; Bajnok, Z

    2005-12-01

    We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

  11. Investigation on wide-band scattering of a 2-D target above 1-D randomly rough surface by FDTD method.

    PubMed

    Li, Juan; Guo, Li-Xin; Jiao, Yong-Chang; Li, Ke

    2011-01-17

    Finite-difference time-domain (FDTD) algorithm with a pulse wave excitation is used to investigate the wide-band composite scattering from a two-dimensional(2-D) infinitely long target with arbitrary cross section located above a one-dimensional(1-D) randomly rough surface. The FDTD calculation is performed with a pulse wave incidence, and the 2-D representative time-domain scattered field in the far zone is obtained directly by extrapolating the currently calculated data on the output boundary. Then the 2-D wide-band scattering result is acquired by transforming the representative time-domain field to the frequency domain with a Fourier transform. Taking the composite scattering of an infinitely long cylinder above rough surface as an example, the wide-band response in the far zone by FDTD with the pulsed excitation is computed and it shows a good agreement with the numerical result by FDTD with the sinusoidal illumination. Finally, the normalized radar cross section (NRCS) from a 2-D target above 1-D rough surface versus the incident frequency, and the representative scattered fields in the far zone versus the time are analyzed in detail.

  12. Modelling of Rail Vehicles and Track for Calculation of Ground-Vibration Transmission Into Buildings

    NASA Astrophysics Data System (ADS)

    Hunt, H. E. M.

    1996-05-01

    A methodology for the calculation of vibration transmission from railways into buildings is presented. The method permits existing models of railway vehicles and track to be incorporated and it has application to any model of vibration transmission through the ground. Special attention is paid to the relative phasing between adjacent axle-force inputs to the rail, so that vibration transmission may be calculated as a random process. The vehicle-track model is used in conjunction with a building model of infinite length. The tracking and building are infinite and parallel to each other and forces applied are statistically stationary in space so that vibration levels at any two points along the building are the same. The methodology is two-dimensional for the purpose of application of random process theory, but fully three-dimensional for calculation of vibration transmission from the track and through the ground into the foundations of the building. The computational efficiency of the method will interest engineers faced with the task of reducing vibration levels in buildings. It is possible to assess the relative merits of using rail pads, under-sleeper pads, ballast mats, floating-slab track or base isolation for particular applications.

  13. Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

    NASA Astrophysics Data System (ADS)

    Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

    2010-11-01

    Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

  14. Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

    NASA Astrophysics Data System (ADS)

    Gundry, James

    2017-03-01

    We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

  15. Mimicking glide symmetry dispersion with coupled slot metasurfaces

    NASA Astrophysics Data System (ADS)

    Camacho, Miguel; Mitchell-Thomas, Rhiannon C.; Hibbins, Alastair P.; Sambles, J. Roy; Quevedo-Teruel, Oscar

    2017-09-01

    In this letter, we demonstrate that the dispersion properties associated with glide symmetry can be achieved in systems that only possess reflection symmetry by balancing the influence of two sublattices. We apply this approach to a pair of coupled slots cut into an infinite perfectly conducting plane. Each slot is notched on either edge, with the complete two-slot system having only mirror symmetry. By modifying the relative size of the notches on either side of the slots, we show that a linear dispersion relation with a degeneracy with non-zero group velocity at the Brillouin zone boundary can be achieved. These properties, until now, only found in systems with glide symmetry are numerically and experimentally validated. We also show that these results can be used for the design of ultra-wideband one-dimensional leaky wave antennas in coplanar waveguide technology.

  16. Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map

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

    Kanakoglou, K.; School of Physics, Nuclear and Elementary Particle Physics Department, Aristotle University of Thessaloniki; Daskaloyannis, C.

    The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation-theoretic property of transferring invariably the super-Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, whilemore » the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.« less

  17. Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra

    NASA Astrophysics Data System (ADS)

    Grigorchuk, R.; Leemann, P.-H.; Nagnibeda, T.

    2016-05-01

    We study the infinite family of spider-web graphs \\{{{ S }}k,N,M\\}, k≥slant 2, N≥slant 0 and M≥slant 1, initiated in the 50s in the context of network theory. It was later shown in physical literature that these graphs have remarkable percolation and spectral properties. We provide a mathematical explanation of these properties by putting the spider-web graphs in the context of group theory and algebraic graph theory. Namely, we realize them as tensor products of the well-known de Bruijn graphs \\{{{ B }}k,N\\} with cyclic graphs \\{{C}M\\} and show that these graphs are described by the action of the lamplighter group {{ L }}k={Z}/k{Z}\\wr {Z} on the infinite binary tree. Our main result is the identification of the infinite limit of \\{{{ S }}k,N,M\\}, as N,M\\to ∞ , with the Cayley graph of the lamplighter group {{ L }}k which, in turn, is one of the famous Diestel-Leader graphs {{DL}}k,k. As an application we compute the spectra of all spider-web graphs and show their convergence to the discrete spectral distribution associated with the Laplacian on the lamplighter group.

  18. 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.

  19. The Interface between Neighborhood Density and Optional Infinitives: Normal Development and Specific Language Impairment

    ERIC Educational Resources Information Center

    Hoover, Jill R.; Storkel, Holly L.; Rice, Mabel L.

    2012-01-01

    The effect of neighborhood density on optional infinitives was evaluated for typically developing (TD) children and children with Specific Language Impairment (SLI). Forty children, twenty in each group, completed two production tasks that assessed third person singular production. Half of the sentences in each task presented a dense verb, and…

  20. Renormalization group flows and continual Lie algebras

    NASA Astrophysics Data System (ADS)

    Bakas, Ioannis

    2003-08-01

    We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

  1. A conceptual approach to approximate tree root architecture in infinite slope models

    NASA Astrophysics Data System (ADS)

    Schmaltz, Elmar; Glade, Thomas

    2016-04-01

    Vegetation-related properties - particularly tree root distribution and coherent hydrologic and mechanical effects on the underlying soil mantle - are commonly not considered in infinite slope models. Indeed, from a geotechnical point of view, these effects appear to be difficult to be reproduced reliably in a physically-based modelling approach. The growth of a tree and the expansion of its root architecture are directly connected with both intrinsic properties such as species and age, and extrinsic factors like topography, availability of nutrients, climate and soil type. These parameters control four main issues of the tree root architecture: 1) Type of rooting; 2) maximum growing distance to the tree stem (radius r); 3) maximum growing depth (height h); and 4) potential deformation of the root system. Geometric solids are able to approximate the distribution of a tree root system. The objective of this paper is to investigate whether it is possible to implement root systems and the connected hydrological and mechanical attributes sufficiently in a 3-dimensional slope stability model. Hereby, a spatio-dynamic vegetation module should cope with the demands of performance, computation time and significance. However, in this presentation, we focus only on the distribution of roots. The assumption is that the horizontal root distribution around a tree stem on a 2-dimensional plane can be described by a circle with the stem located at the centroid and a distinct radius r that is dependent on age and species. We classified three main types of tree root systems and reproduced the species-age-related root distribution with three respective mathematical solids in a synthetic 3-dimensional hillslope ambience. Thus, two solids in an Euclidian space were distinguished to represent the three root systems: i) cylinders with radius r and height h, whilst the dimension of latter defines the shape of a taproot-system or a shallow-root-system respectively; ii) elliptic paraboloids represent a cordate-root-system with radius r, height h and a constant, species-independent curvature. This procedure simplifies the classification of tree species into the three defined geometric solids. In this study we introduce a conceptual approach to estimate the 2- and 3-dimensional distribution of different tree root systems, and to implement it in a raster environment, as it is used in infinite slope models. Hereto we used the PCRaster extension in a python framework. The results show that root distribution and root growth are spatially reproducible in a simple raster framework. The outputs exhibit significant effects for a synthetically generated slope on local scale for equal time-steps. The preliminary results depict an initial step to develop a vegetation module that can be coupled with hydro-mechanical slope stability models. This approach is expected to yield a valuable contribution to the implementation of vegetation-related properties, in particular effects of root-reinforcement, into physically-based approaches using infinite slope models.

  2. Truly self-consistent solution of Kohn-Sham equations for extended systems with inhomogeneous electron gas

    NASA Astrophysics Data System (ADS)

    Shul'man, A. Ya; Posvyanskii, D. V.

    2014-05-01

    The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistent solution method for infinite systems involves iterations with alternate solutions of the Poisson and Schrödinger equations. One of problems with such an approach is that the charge distribution, updated by solving the Schrodinger equation, may be incompatible with the boundary conditions of the Poisson equation for Coulomb potential. The resulting instability or divergence manifests itself most appreciably in the case of infinitely extended systems because the corresponding boundary-value problem becomes singular. In this work the stable iterative scheme for solving the Kohn-Sham equations for infinite systems with inhomogeneous electron gas is described based on eliminating the long-range character of the Coulomb interaction, which causes the tight coupling of the charge distribution with the boundary conditions. This algorithm has been previously successfully implemented in the calculation of work function and surface energy of simple metals in the jellium model. Here it is used to calculate the energy spectrum of quasi-two-dimensional electron gas in the accumulation layer at the semiconductor surface n-InAs. The electrons in such a structure occupy states that belong to both discrete and continuous parts of the energy spectrum. This causes the problems of convergence in the usually used approaches, which do not exist in our case. Because of the narrow bandgap of InAs, it is necessary to take the nonparabolicity of the conduction band into account; this is done by means of a new effective mass method. The calculated quasi-two-dimensional energy bands correspond well to experimental data measured by the angle resolved photoelectron spectroscopy technique.

  3. An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

    NASA Astrophysics Data System (ADS)

    Re, B.; Dobrzynski, C.; Guardone, A.

    2017-07-01

    A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

  4. 1D helix, 2D brick-wall and herringbone, and 3D interpenetration d10 metal-organic framework structures assembled from pyridine-2,6-dicarboxylic acid N-oxide.

    PubMed

    Wen, Li-Li; Dang, Dong-Bin; Duan, Chun-Ying; Li, Yi-Zhi; Tian, Zheng-Fang; Meng, Qing-Jin

    2005-10-03

    Five novel interesting d(10) metal coordination polymers, [Zn(PDCO)(H2O)2]n (PDCO = pyridine-2,6-dicarboxylic acid N-oxide) (1), [Zn2(PDCO)2(4,4'-bpy)2(H2O)2.3H2O]n (bpy = bipyridine) (2), [Zn(PDCO)(bix)]n (bix = 1,4-bis(imidazol-1-ylmethyl)benzene) (3), [Zn(PDCO)(bbi).0.5H2O]n (bbi = 1,1'-(1,4-butanediyl)bis(imidazole)) (4), and [Cd(PDCO)(bix)(1.5).1.5H2O]n (5), have been synthesized under hydrothermal conditions and structurally characterized. Polymer 1 possesses a one-dimensional (1D) helical chainlike structure with 4(1) helices running along the c-axis with a pitch of 10.090 Angstroms. Polymer 2 has an infinite chiral two-dimensional (2D) brick-wall-like layer structure in the ac plane built from achiral components, while both 3 and 4 exhibit an infinite 2D herringbone architecture, respectively extended in the ac and ab plane. Polymer 5 features a most remarkable and unique three-dimensional (3D) porous framework with 2-fold interpenetration related by symmetry, which contains channels in the b and c directions, both distributed in a rectangular grid fashion. Compounds 1-5, with systematic variation in dimensionality from 1D to 2D to 3D, are the first examples of d(10) metal coordination polymers into which pyridinedicarboxylic acid N-oxide has been introduced. In addition, polymers 1, 4, and 5 display strong blue fluorescent emissions in the solid state. Polymer 3 exhibits a strong SHG response, estimated to be approximately 0.9 times that of urea.

  5. Active noise control: a review of the field.

    PubMed

    Gordon, R T; Vining, W D

    1992-11-01

    Active noise control (ANC) is the application of the principle of the superposition of waves to noise attenuation problems. Much progress has been made toward applying ANC to narrow-band, low-frequency noise in confined spaces. During this same period, the application of ANC to broad-band noise or noise in three-dimensional spaces has seen little progress because of the recent quantification of serious physical limitations, most importantly, noncausality, stability, spatial mismatch, and the infinite gain controller requirement. ANC employs superposition to induce destructive interference to affect the attenuation of noise. ANC was believed to utilize the mechanism of phase cancellation to achieve the desired attenuation. However, current literature points to other mechanisms that may be operating in ANC. Categories of ANC are one-dimensional field and duct noise, enclosed spaces and interior noise, noise in three-dimensional spaces, and personal hearing protection. Development of active noise control stems from potential advantages in cost, size, and effectiveness. There are two approaches to ANC. In the first, the original sound is processed and injected back into the sound field in antiphase. The second approach is to synthesize a cancelling waveform. ANC of turbulent flow in pipes and ducts is the largest area in the field. Much work into the actual mechanism involved and the causal versus noncausal aspects of system controllers has been done. Fan and propeller noise can be divided into two categories: noise generated directly as the blade passing tones and noise generated as a result of blade tip turbulence inducing vibration in structures. Three-dimensional spaces present a noise environment where physical limitations are magnified and the infinite gain controller requirement is confronted. Personal hearing protection has been shown to be best suited to the control of periodic, low-frequency noise.

  6. Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

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

    Klink, W.H.; Wickramasekara, S., E-mail: wickrama@grinnell.edu; Department of Physics, Grinnell College, Grinnell, IA 50112

    2014-01-15

    In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration canmore » equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle. -- Highlights: •A formulation of Galilean quantum mechanics in non-inertial reference frames is given. •The key concept is the Galilean line group, an infinite dimensional group. •A large class of general cocycle representations of the Galilean line group is constructed. •These representations show violations of the equivalence principle at the quantum level. •At the classical limit, no violations of the equivalence principle are detected.« less

  7. Advanced theoretical and experimental studies in automatic control and information systems. [including mathematical programming and game theory

    NASA Technical Reports Server (NTRS)

    Desoer, C. A.; Polak, E.; Zadeh, L. A.

    1974-01-01

    A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

  8. Geometric Methods for Infinite-Dimensional Dynamical Systems

    DTIC Science & Technology

    2012-08-27

    singular perturbation theory , nonlinear optic and traveling waves. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18...participants, but no registration fee was charged. The 14 (long) plenary talks and the eight (short) topical talks were held in the lecture hall of...afternoon about open problems and important mathematical techniques, as well as a reception Friday evening, both of which were attended by all

  9. Chandrasekhar equations for infinite dimensional systems

    NASA Technical Reports Server (NTRS)

    Ito, K.; Powers, R. K.

    1985-01-01

    Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

  10. Parsimonious description for predicting high-dimensional dynamics

    PubMed Central

    Hirata, Yoshito; Takeuchi, Tomoya; Horai, Shunsuke; Suzuki, Hideyuki; Aihara, Kazuyuki

    2015-01-01

    When we observe a system, we often cannot observe all its variables and may have some of its limited measurements. Under such a circumstance, delay coordinates, vectors made of successive measurements, are useful to reconstruct the states of the whole system. Although the method of delay coordinates is theoretically supported for high-dimensional dynamical systems, practically there is a limitation because the calculation for higher-dimensional delay coordinates becomes more expensive. Here, we propose a parsimonious description of virtually infinite-dimensional delay coordinates by evaluating their distances with exponentially decaying weights. This description enables us to predict the future values of the measurements faster because we can reuse the calculated distances, and more accurately because the description naturally reduces the bias of the classical delay coordinates toward the stable directions. We demonstrate the proposed method with toy models of the atmosphere and real datasets related to renewable energy. PMID:26510518

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

    Bena, Iosif; Bobev, Nikolay; Warner, Nicholas P.

    We discuss 'spectral-flow' coordinate transformations that take asymptotically four-dimensional solutions into other asymptotically four-dimensional solutions. We find that spectral flow can relate smooth three-charge solutions with a multicenter Taub-NUT base to solutions where one or several Taub-NUT centers are replaced by two-charge supertubes, and vice versa. We further show that multiparameter spectral flows can map such Taub-NUT centers to more singular centers that are either D2-D0 or pure D0-brane sources. Since supertubes can depend on arbitrary functions, we establish that the moduli space of smooth horizonless black-hole microstate solutions is classically of infinite dimension. We also use the physics ofmore » supertubes to argue that some multicenter solutions that appear to be bound states from a four-dimensional perspective are in fact not bound states when considered from a five- or six-dimensional perspective.« less

  12. Nonplanar wing load-line and slender wing theory

    NASA Technical Reports Server (NTRS)

    Deyoung, J.

    1977-01-01

    Nonplanar load line, slender wing, elliptic wing, and infinite aspect ratio limit loading theories are developed. These are quasi two dimensional theories but satisfy wing boundary conditions at all points along the nonplanar spanwise extent of the wing. These methods are applicable for generalized configurations such as the laterally nonplanar wing, multiple nonplanar wings, or wing with multiple winglets of arbitrary shape. Two dimensional theory infers simplicity which is practical when analyzing complicated configurations. The lateral spanwise distribution of angle of attack can be that due to winglet or control surface deflection, wing twist, or induced angles due to multiwings, multiwinglets, ground, walls, jet or fuselage. In quasi two dimensional theory the induced angles due to these extra conditions are likewise determined for two dimensional flow. Equations are developed for the normal to surface induced velocity due to a nonplanar trailing vorticity distribution. Application examples are made using these methods.

  13. Three dimensional radiation fields in free electron lasers using Lienard-Wiechert fields

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

    Elias, L.R.; Gallardo, J.

    1981-10-28

    In a free electron laser a relativistic electron beam is bunched under the action of the ponderomotive potential and is forced to radiate in close phase with the input wave. Until recently, most theories of the FEL have dealt solely with electron beams of infinite transverse dimension radiating only one-dimensional E.M. waves (plane waves). Although these theories describe accurately the dynamics of the electrons during the FEL interaction process, neither the three dimensional nature of the radiated fields nor its non-monochromatic features can be properly studied by them. As a result of this, very important practical issues such as themore » gain per gaussian-spherical optical mode in a free electron laser have not been well addressed, except through a one dimensional field model in which a filling factor describes crudely the coupling of the FEL induced field to the input field.« less

  14. Eigenstate Phase Transitions

    NASA Astrophysics Data System (ADS)

    Zhao, Bo

    Phase transitions are one of the most exciting physical phenomena ever discovered. The understanding of phase transitions has long been of interest. Recently eigenstate phase transitions have been discovered and studied; they are drastically different from traditional thermal phase transitions. In eigenstate phase transitions, a sharp change is exhibited in properties of the many-body eigenstates of the Hamiltonian of a quantum system, but not the thermal equilibrium properties of the same system. In this thesis, we study two different types of eigenstate phase transitions. The first is the eigenstate phase transition within the ferromagnetic phase of an infinite-range spin model. By studying the interplay of the eigenstate thermalization hypothesis and Ising symmetry breaking, we find two eigenstate phase transitions within the ferromagnetic phase: In the lowest-temperature phase the magnetization can macroscopically oscillate by quantum tunneling between up and down. The relaxation of the magnetization is always overdamped in the remainder of the ferromagnetic phase, which is further divided into phases where the system thermally activates itself over the barrier between the up and down states, and where it quantum tunnels. The second is the many-body localization phase transition. The eigenstates on one side of the transition obey the eigenstate thermalization hypothesis; the eigenstates on the other side are many-body localized, and thus thermal equilibrium need not be achieved for an initial state even after evolving for an arbitrary long time. We study this many-body localization phase transition in the strong disorder renormalization group framework. After setting up a set of coarse-graining rules for a general one dimensional chain, we get a simple "toy model'' and obtain an almost purely analytical solution to the infinite-randomness critical fixed point renormalization group equation. We also get an estimate of the correlation length critical exponent nu ≈ 2.5.

  15. Sinc-Galerkin estimation of diffusivity in parabolic problems

    NASA Technical Reports Server (NTRS)

    Smith, Ralph C.; Bowers, Kenneth L.

    1991-01-01

    A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

  16. Virial coefficients of anisotropic hard solids of revolution: The detailed influence of the particle geometry

    NASA Astrophysics Data System (ADS)

    Herold, Elisabeth; Hellmann, Robert; Wagner, Joachim

    2017-11-01

    We provide analytical expressions for the second virial coefficients of differently shaped hard solids of revolution in dependence on their aspect ratio. The second virial coefficients of convex hard solids, which are the orientational averages of the mutual excluded volume, are derived from volume, surface, and mean radii of curvature employing the Isihara-Hadwiger theorem. Virial coefficients of both prolate and oblate hard solids of revolution are investigated in dependence on their aspect ratio. The influence of one- and two-dimensional removable singularities of the surface curvature to the mutual excluded volume is analyzed. The virial coefficients of infinitely thin oblate and infinitely long prolate particles are compared, and analytical expressions for their ratios are derived. Beyond their dependence on the aspect ratio, the second virial coefficients are influenced by the detailed geometry of the particles.

  17. Virial coefficients of anisotropic hard solids of revolution: The detailed influence of the particle geometry.

    PubMed

    Herold, Elisabeth; Hellmann, Robert; Wagner, Joachim

    2017-11-28

    We provide analytical expressions for the second virial coefficients of differently shaped hard solids of revolution in dependence on their aspect ratio. The second virial coefficients of convex hard solids, which are the orientational averages of the mutual excluded volume, are derived from volume, surface, and mean radii of curvature employing the Isihara-Hadwiger theorem. Virial coefficients of both prolate and oblate hard solids of revolution are investigated in dependence on their aspect ratio. The influence of one- and two-dimensional removable singularities of the surface curvature to the mutual excluded volume is analyzed. The virial coefficients of infinitely thin oblate and infinitely long prolate particles are compared, and analytical expressions for their ratios are derived. Beyond their dependence on the aspect ratio, the second virial coefficients are influenced by the detailed geometry of the particles.

  18. Work distributions for random sudden quantum quenches

    NASA Astrophysics Data System (ADS)

    Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter

    2017-05-01

    The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

  19. Ultraviolet divergences in non-renormalizable supersymmetric theories

    NASA Astrophysics Data System (ADS)

    Smilga, A.

    2017-03-01

    We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4 D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.

  20. The generalization of the Mermin-Wagner theorem and the possibility of long-range order in the isotropic discrete one-dimensional quantum Heisenberg model

    NASA Astrophysics Data System (ADS)

    Rudoy, Yu. G.; Kotelnikova, O. A.

    2012-10-01

    The problem of existence of long-range order in the isotropic quantum Heisenberg model on the D=1 lattice is reconsidered in view of the possibility of sufficiently slow decaying exchange interaction with infinite effective radius. It is shown that the macrosopic arguments given by Landau and Lifshitz and then supported microscopically by Mermin and Wagner fail for this case so that the non-zero spontaneous magnetization may yet exist. This result was anticipated by Thouless on the grounds of phenomenological analysis, and we give its microscopic foundation, which amounts to the generalization of Mermin-Wagner theorem for the case of the infinite second moment of the exchange interaction. Two well known in lattice statistics models - i.e., Kac-I and Kac-II - illustrate our results.

  1. Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

    PubMed

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-10-10

    In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

  2. Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

    PubMed Central

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-01-01

    In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

  3. Heat and Mass Transfer on MHD Free convective flow of Second grade fluid through Porous medium over an infinite vertical plate

    NASA Astrophysics Data System (ADS)

    Dastagiri Babu, D.; Venkateswarlu, S.; Keshava Reddy, E.

    2017-08-01

    In this paper, we have considered the unsteady free convective two dimensional flow of a viscous incompressible electrically conducting second grade fluid over an infinite vertical porous plate under the influence of uniform transverse magnetic field with time dependent permeability, oscillatory suction. The governing equations of the flow field are solved by a regular perturbation method for small amplitude of the permeability. The closed form solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of profiles. The skin fiction on the boundary, the heat flux in terms of the Nusselt number and rate of mass transfer in terms of Sherwood number are also obtained and their behavior computationally discussed.

  4. Elastic guided waves in a layered plate with rectangular cross section.

    PubMed

    Mukdadi, O M; Desai, Y M; Datta, S K; Shah, A H; Niklasson, A J

    2002-11-01

    Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

  5. NMR shifts for polycyclic aromatic hydrocarbons from first-principles

    NASA Astrophysics Data System (ADS)

    Thonhauser, T.; Ceresoli, Davide; Marzari, Nicola

    We present first-principles, density-functional theory calculations of the NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene and increasing sizes up to the one- and two-dimensional infinite limits of graphene ribbons and sheets. Our calculations are performed using a combination of the recently developed theory of orbital magnetization in solids, and a novel approach to NMR calculations where chemical shifts are obtained from the derivative of the orbital magnetization with respect to a microscopic, localized magnetic dipole. Using these methods we study on equal footing the 1H and 13 shifts in benzene, pyrene, coronene, in naphthalene, anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and an infinite graphene ribbon. Our results show very good agreement with experiments and allow us to characterize the trends for the chemical shifts as a function of system size.

  6. The Existence of Steady Compressible Subsonic Impinging Jet Flows

    NASA Astrophysics Data System (ADS)

    Cheng, Jianfeng; Du, Lili; Wang, Yongfu

    2018-03-01

    In this paper, we investigate the compressible subsonic impinging jet flows through a semi-infinitely long nozzle and impacting on a solid wall. Firstly, it is shown that given a two-dimensional semi-infinitely long nozzle and a wall behind the nozzle, and an appropriate atmospheric pressure, then there exists a smooth global subsonic compressible impinging jet flow with two asymptotic directions. The subsonic impinging jet develops two free streamlines, which initiate smoothly at the end points of the semi-infinitely long nozzles. In particular, there exists a smooth curve which separates the fluids which go to different places downstream. Moreover, under some suitable asymptotic assumptions of the nozzle, the asymptotic behaviors of the compressible subsonic impinging jet flows in the inlet and the downstream are obtained by means of a blow-up argument. On the other hand, the non-existence of compressible subsonic impinging jet flows with only one asymptotic direction is also established. This main result in this paper solves the open problem (4) in Chapter 16.3 proposed by uc(Friedman) in his famous survey (uc(Friedman) in Mathematics in industrial problems, II, I.M.A. volumes in mathematics and its applications, vol 24, Springer, New York, 1989).

  7. Field patterns: A new type of wave with infinitely degenerate band structure

    NASA Astrophysics Data System (ADS)

    Mattei, Ornella; Milton, Graeme W.

    2017-12-01

    Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional-spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP-waves) (MILTON G. W. and MATTEI O., Proc. R. Soc. A, 473 (2017) 20160819; MATTEI O. and MILTON G. W., New J. Phys., 19 (2017) 093022). Specifically, due to the special periodic space-time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space-time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances: this is the field pattern. In this letter, by applying Bloch-Floquet theory, we show that the dispersion diagrams associated with these FP-materials are infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions. Each generalized function is concentrated on a specific field pattern, each parameterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation.

  8. Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results

    NASA Astrophysics Data System (ADS)

    El Hassouani, Y.; Aynaou, H.; El Boudouti, E. H.; Djafari-Rouhani, B.; Akjouj, A.; Velasco, V. R.

    2006-07-01

    We study theoretically and experimentally the existence and behavior of the localized surface modes in one-dimensional (1D) quasiperiodic photonic band gap structures. These structures are made of segments and loops arranged according to a Fibonacci sequence. The experiments are carried out by using coaxial cables in the frequency region of a few tens of MHz. We consider 1D periodic structures (superlattice) where each cell is a well-defined Fibonacci generation. In these structures, we generalize a theoretical rule on the surface modes, namely when one considers two semi-infinite superlattices obtained by the cleavage of an infinite superlattice, it exists exactly one surface mode in each gap. This mode is localized on the surface either of one or the other semi-infinite superlattice. We discuss the existence of various types of surface modes and their spatial localization. The experimental observation of these modes is carried out by measuring the transmission through a guide along which a finite superlattice (i.e., constituted of a finite number of quasiperiodic cells) is grafted vertically. The surface modes appear as maxima of the transmission spectrum. These experiments are in good agreement with the theoretical model based on the formalism of the Green function.

  9. On irregular singularity wave functions and superconformal indices

    NASA Astrophysics Data System (ADS)

    Buican, Matthew; Nishinaka, Takahiro

    2017-09-01

    We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU( N). As an application, we give closed-form expressions for the Schur indices of all ( A N - 1 , A N ( n - 1)-1) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the ( A N , A M ) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple "monopole vev RG" formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems.

  10. CellAtlasSearch: a scalable search engine for single cells.

    PubMed

    Srivastava, Divyanshu; Iyer, Arvind; Kumar, Vibhor; Sengupta, Debarka

    2018-05-21

    Owing to the advent of high throughput single cell transcriptomics, past few years have seen exponential growth in production of gene expression data. Recently efforts have been made by various research groups to homogenize and store single cell expression from a large number of studies. The true value of this ever increasing data deluge can be unlocked by making it searchable. To this end, we propose CellAtlasSearch, a novel search architecture for high dimensional expression data, which is massively parallel as well as light-weight, thus infinitely scalable. In CellAtlasSearch, we use a Graphical Processing Unit (GPU) friendly version of Locality Sensitive Hashing (LSH) for unmatched speedup in data processing and query. Currently, CellAtlasSearch features over 300 000 reference expression profiles including both bulk and single-cell data. It enables the user query individual single cell transcriptomes and finds matching samples from the database along with necessary meta information. CellAtlasSearch aims to assist researchers and clinicians in characterizing unannotated single cells. It also facilitates noise free, low dimensional representation of single-cell expression profiles by projecting them on a wide variety of reference samples. The web-server is accessible at: http://www.cellatlassearch.com.

  11. Methods for analysis of cracks in three-dimensional solids

    NASA Technical Reports Server (NTRS)

    Raju, I. S.; Newman, J. C., Jr.

    1984-01-01

    Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

  12. An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

    NASA Astrophysics Data System (ADS)

    Koga, Toshikatsu; Matsumoto, Shinya

    1985-06-01

    A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

  13. Perpetual motion of a mobile impurity in a one-dimensional quantum gas

    NASA Astrophysics Data System (ADS)

    Lychkovskiy, O.

    2014-03-01

    Consider an impurity particle injected in a degenerate one-dimensional gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum p0. We examine the infinite-time value of the momentum of the impurity, p∞, as a function of p0. A lower bound on |p∞(p0)| is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of the impurity in a one-dimensional gas of noninteracting fermions or Tonks-Girardeau bosons at zero temperature. The bound admits an especially simple and useful form when the interaction between the impurity and host particles is everywhere repulsive.

  14. On the applicability of low-dimensional models for convective flow reversals at extreme Prandtl numbers

    NASA Astrophysics Data System (ADS)

    Mannattil, Manu; Pandey, Ambrish; Verma, Mahendra K.; Chakraborty, Sagar

    2017-12-01

    Constructing simpler models, either stochastic or deterministic, for exploring the phenomenon of flow reversals in fluid systems is in vogue across disciplines. Using direct numerical simulations and nonlinear time series analysis, we illustrate that the basic nature of flow reversals in convecting fluids can depend on the dimensionless parameters describing the system. Specifically, we find evidence of low-dimensional behavior in flow reversals occurring at zero Prandtl number, whereas we fail to find such signatures for reversals at infinite Prandtl number. Thus, even in a single system, as one varies the system parameters, one can encounter reversals that are fundamentally different in nature. Consequently, we conclude that a single general low-dimensional deterministic model cannot faithfully characterize flow reversals for every set of parameter values.

  15. Non-equilibrium Phase Transitions: Activated Random Walks at Criticality

    NASA Astrophysics Data System (ADS)

    Cabezas, M.; Rolla, L. T.; Sidoravicius, V.

    2014-06-01

    In this paper we present rigorous results on the critical behavior of the Activated Random Walk model. We conjecture that on a general class of graphs, including , and under general initial conditions, the system at the critical point does not reach an absorbing state. We prove this for the case where the sleep rate is infinite. Moreover, for the one-dimensional asymmetric system, we identify the scaling limit of the flow through the origin at criticality. The case remains largely open, with the exception of the one-dimensional totally-asymmetric case, for which it is known that there is no fixation at criticality.

  16. Point force and point electric charge applied to the boundary of three-dimensional anisotropic piezoelectric solid

    DOE PAGES

    Borovikov, V. A.; Kalinin, S. V.; Khavin, Yu.; ...

    2015-08-19

    We derive the Green's functions for a three-dimensional semi-infinite fully anisotropic piezoelectric material using the plane wave theory method. The solution gives the complete set of electromechanical fields due to an arbitrarily oriented point force and a point electric charge applied to the boundary of the half-space. Moreover, the solution constitutes generalization of Boussinesq's and Cerruti's problems of elastic isotropy for the anisotropic piezoelectric materials. On the example of piezoceramics PZT-6B, the present results are compared with the previously obtained solution for the special case of transversely isotropic piezoelectric solid subjected to the same boundary condition.

  17. A numerical method for determination of source time functions for general three-dimensional rupture propagation

    NASA Technical Reports Server (NTRS)

    Das, S.

    1979-01-01

    A method to determine the displacement and the stress on the crack plane for a three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane is presented. The main idea of the method is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. As a test of the accuracy of the numerical technique, the results are compared with known solutions for two simple cases.

  18. Conformal Nets II: Conformal Blocks

    NASA Astrophysics Data System (ADS)

    Bartels, Arthur; Douglas, Christopher L.; Henriques, André

    2017-08-01

    Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

  19. Expandable space frames

    NASA Technical Reports Server (NTRS)

    Schoen, A. H. (Inventor)

    1973-01-01

    Expandable space frames having essentially infinite periodicity limited only by practical considerations, are described. Each expandable space frame comprises a plurality of hinge joint assemblies having arms that extend outwardly in predetermined symmetrically related directions from a central or vertex point. The outer ends of the arms form one part of a hinge point. The outer expandable space frame also comprises a plurality of struts. The outer ends of the struts from the other part of the hinged joint. The struts interconnect the plurality of hinge point in sychronism, the spaceframes can be expanded or collapsed. Three-dimensional as well as two-dimensional spaceframes of this general nature are described.

  20. A new characterization of three-dimensional conductivity backbone above and below the percolation threshold

    NASA Astrophysics Data System (ADS)

    Skal, Asya S.

    1996-08-01

    A new definition of three-dimensional conductivity backbone, obtained from a distribution function of Joule heat and the Hall coefficient is introduced. The fractal dimension d fB = d - ( {g}/{v}) = 2.25 of conductivity backbone for both sides of the threshold is obtained from a critical exponent of the Hall coefficient g = 0.6. This allows one to construct, below the threshold, a new order parameter of metal-conductor transition—the two-component infinite conductivity back-bone and tested scaling relation, proposed by Alexander and Orbach [ J. Phys. Rev. Lett.43, 1982, L625] for both sides of a threshold.

  1. Solving time-dependent two-dimensional eddy current problems

    NASA Technical Reports Server (NTRS)

    Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

    1988-01-01

    Results of transient eddy current calculations are reported. For simplicity, a two-dimensional transverse magnetic field which is incident on an infinitely long conductor is considered. The conductor is assumed to be a good but not perfect conductor. The resulting problem is an interface initial boundary value problem with the boundary of the conductor being the interface. A finite difference method is used to march the solution explicitly in time. The method is shown. Treatment of appropriate radiation conditions is given special consideration. Results are validated with approximate analytic solutions. Two stringent test cases of high and low frequency incident waves are considered to validate the results.

  2. One-loop β-function for an infinite-parameter family of gauge theories

    NASA Astrophysics Data System (ADS)

    Krasnov, Kirill

    2015-03-01

    We continue to study an infinite-parametric family of gauge theories with an arbitrary function of the self-dual part of the field strength as the Lagrangian. The arising one-loop divergences are computed using the background field method. We show that they can all be absorbed by a local redefinition of the gauge field, as well as multiplicative renormalisations of the couplings. Thus, this family of theories is one-loop renormalisable. The infinite set of β-functions for the couplings is compactly stored in a renormalisation group flow for a single function of the curvature. The flow is obtained explicitly.

  3. Quasi-periodic continuation along a continuous symmetry

    NASA Astrophysics Data System (ADS)

    Salomone, Matthew David

    Given a system of differential equations which admits a continuous group of symmetries and possesses a periodic solution, we show that under certain nondegeneracy assumptions there always exists a continuous family containing infinitely many periodic and quasi-periodic trajectories. This generalizes the continuation method of Poincaré to orbits which are not necessarily periodic. We apply these results in the setting of the Lagrangian N -body problem of homogeneous potential to characterize an infinite family of rotating nonplanar "hip-hop" orbits in the four-body problem of equal masses, and show how some other trajectories in the N -body theory may be extended to infinite families of periodic and quasi-periodic trajectories.

  4. Profinite Completions of Burnside-Type Quotients of Surface Groups

    NASA Astrophysics Data System (ADS)

    Funar, Louis; Lochak, Pierre

    2018-06-01

    Using quantum representations of mapping class groups, we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic quotients of surface groups.

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

    Han, Fei; Liu, Huimei; Malliakas, Christos D.

    The new bismuth chalcogenide LaBiS3 crystallizes in the monoclinic space group C2/m with a = 27.997(5) Å, b = 4.0663(4) Å, c = 14.747(3) Å, and β = 118.55(3)°. The structure of LaBiS3 is built up of NaCl-type Bi2S5 blocks, and BiS4 and LaS5 infinitely long chains forming a compact three-dimensional framework. Optical spectroscopy and resistivity measurements reveal a semiconducting behavior with a direct band gap of 1.08(2) eV and activation energy of 0.36(1) eV. Thermopower measurements suggest the majority carriers of LaBiS3 are electrons. Heat capacity measurement indicates no phase transition from 2 to 300 K. Band structure calculationsmore » at the density function level support the presence of a direct band gap in LaBiS3.« less

  6. Synthesis and Crystal Structure of a New Ruthenium Silicophosphate: RuP 3SiO 11

    NASA Astrophysics Data System (ADS)

    Fukuoka, Hiroshi; Imoto, Hideo; Saito, Taro

    1996-01-01

    A new ruthenium silicophosphate RuP3SiO11was obtained and the structure was determined by single-crystal X-ray diffraction. It crystallizes in the trigonal space groupR3cwitha= 8.253(3)Å,c= 39.317(4)Å,V= 2319(2)Å3,Z= 12,R= 0.029, andRW= 0.026. The structure is composed of RuO6, Si2O7, and P2O7units. The Si2O7unit shares the six oxygen atoms with six P2O7units, while the P2O7unit shares the six oxygen atoms with two Si2O7units and four RuO6octahedra. The anionic part forms an infinite three-dimensional network of silicophosphate. RuP3SiO11is isotypic with MoP3SiO11.

  7. On the Transition from Two-Dimensional to Three-Dimensional MHD Turbulence

    NASA Technical Reports Server (NTRS)

    Thess, A.; Zikanov, Oleg

    2004-01-01

    We report a theoretical investigation of the robustness of two-dimensional inviscid MHD flows at low magnetic Reynolds numbers with respect to three-dimensional perturbations. We analyze three model problems, namely flow in the interior of a triaxial ellipsoid, an unbounded vortex with elliptical streamlines, and a vortex sheet parallel to the magnetic field. We demonstrate that motion perpendicular to the magnetic field with elliptical streamlines becomes unstable with respect to the elliptical instability once the velocity has reached a critical magnitude whose value tends to zero as the eccentricity of the streamlines becomes large. Furthermore, vortex sheets parallel to the magnetic field, which are unstable for any velocity and any magnetic field, are found to emit eddies with vorticity perpendicular to the magnetic field and with an aspect ratio proportional to N(sup 1/2). The results suggest that purely two-dimensional motion without Joule energy dissipation is a singular type of flow which does not represent the asymptotic behaviour of three-dimensional MHD turbulence in the limit of infinitely strong magnetic fields.

  8. Transition to Complicated Behavior in Infinite Dimensional Dynamical Systems

    DTIC Science & Technology

    1990-03-01

    solitons in nonlinear refractive periodic media," Phys. Lett. A. 141 37 (1989). A.3. Dynamics of Free-Running and Injection- Locked Laser Diode Arrays...Fibers * Dynamics of Free-Running and Injection- Locked Laser Diode Arrays I Diffraction/Diffusion Mediated Instabilities in Self-focusing/Defocusing...optics, the interplay between the coherence of solitons and the scattering (Anderson localization) effects of randomness, and the value in looking at

  9. On Monotone Embedding in Information Geometry (Open Access)

    DTIC Science & Technology

    2015-06-25

    the non-parametric ( infinite - dimensional ) setting, as well [4,6], with the α-connection structure cast in a more general way. Theorem 1 of [4] gives... the weighting function for taking the expectation of random variables in calculating the Riemannian metric (G = 1 reduces to F - geometry , with the ...is a trivial rewriting of the convex function f used by [2]. This paper will start in Section 1

  10. Application of Time-Frequency Representations To Non-Stationary Radar Cross Section

    DTIC Science & Technology

    2009-03-01

    The three- dimensional plot produced by a TFR allows one to determine which spectral components of a signal vary with time [25... a range bin ( of width cT 2 ) from the stepped frequency waveform. 2. Cancel the clutter (stationary components) by zeroing out points associated with ...generating an infinite number of bilinear Time Frequency distributions based on a generalized equation and a change- able

  11. Stability analysis of unsteady ablation fronts

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

    Betti, R.; McCrory, R.L.; Verdon, C.P.

    1993-08-01

    The linear stability analysis of unsteady ablation fronts, is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

  12. Stability analysis of unsteady ablation fronts

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

    Betti, R.; McCrory, R.L.; Verdon, C.P.

    1993-11-08

    The linear stability analysis of unsteady ablation fronts is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

  13. Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Powers, Robert K.

    1987-01-01

    A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

  14. On representations of the filiform Lie superalgebra Lm,n

    NASA Astrophysics Data System (ADS)

    Wang, Qi; Chen, Hongjia; Liu, Wende

    2015-11-01

    In this paper, we study the representations for the filiform Lie superalgebras Lm,n, a particular class of nilpotent Lie superalgebras. We determine the minimal dimension of a faithful module over Lm,n using the theory of linear algebra. In addition, using the method of Feingold and Frenkel (1985), we construct some finite and infinite dimensional modules over Lm,n on the Grassmann algebra and the mixed Clifford-Weyl algebra.

  15. Combinatorial Market Processing for Multilateral Coordination

    DTIC Science & Technology

    2005-09-01

    8 In the classical auction theory literature, most of the attention is focused on one-sided, single-item auctions [86]. There is now a growing body of...Programming in Infinite-dimensional Spaces: Theory and Applications, Wiley, 1987. [3] K. J. Arrow, “An extension of the basic theorems of classical ...Commodities, Princeton University Press, 1969. [43] D. Friedman and J. Rust, The Double Auction Market: Institutions, Theories, and Evidence, Addison

  16. Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

    DTIC Science & Technology

    1980-05-01

    reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

  17. On power series representing solutions of the one-dimensional time-independent Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Trotsenko, N. P.

    2017-06-01

    For the equation χ″( x) = u( x)χ( x) with infinitely smooth u( x), the general solution χ( x) is found in the form of a power series. The coefficients of the series are expressed via all derivatives u ( m)( y) of the function u( x) at a fixed point y. Examples of solutions for particular functions u( x) are considered.

  18. Reconstruction and separation of vibratory field using structural holography

    NASA Astrophysics Data System (ADS)

    Chesnais, C.; Totaro, N.; Thomas, J.-H.; Guyader, J.-L.

    2017-02-01

    A method for reconstructing and separating vibratory field on a plate-like structure is presented. The method, called "Structural Holography" is derived from classical Near-field Acoustic Holography (NAH) but in the vibratory domain. In this case, the plate displacement is measured on one-dimensional lines (the holograms) and used to reconstruct the entire two-dimensional displacement field. As a consequence, remote measurements on non directly accessible zones are possible with Structural Holography. Moreover, as it is based on the decomposition of the field into forth and back waves, Structural Holography permits to separate forces in the case of multi-sources excitation. The theoretical background of the Structural Holography method is described first. Then, to illustrate the process and the possibilities of Structural Holography, the academic test case of an infinite plate excited by few point forces is presented. With the principle of vibratory field separation, the displacement fields produced by each point force separately is reconstructed. However, the displacement field is not always meaningful and some additional treatments are mandatory to localize the position of point forces for example. From the simple example of an infinite plate, a post-processing based on the reconstruction of the structural intensity field is thus proposed. Finally, Structural Holography is generalized to finite plates and applied to real experimental measurements

  19. Reliable Cellular Automata with Self-Organization

    NASA Astrophysics Data System (ADS)

    Gács, Peter

    2001-04-01

    In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in "software," it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary size and content. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of "self-organization." The latter means that unless a large amount of input information must be given, the initial configuration can be chosen homogeneous.

  20. Three-Dimensional Dynamic Analyses of Track-Embankment-Ground System Subjected to High Speed Train Loads

    PubMed Central

    2014-01-01

    A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed. PMID:24723838

  1. Three-dimensional dynamic analyses of track-embankment-ground system subjected to high speed train loads.

    PubMed

    Fu, Qiang; Zheng, Changjie

    2014-01-01

    A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed.

  2. Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

    NASA Astrophysics Data System (ADS)

    Schmitteckert, Peter

    2018-04-01

    We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

  3. Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.

    PubMed

    Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter

    2012-04-01

    This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

  4. Quantum information processing in phase space: A modular variables approach

    NASA Astrophysics Data System (ADS)

    Ketterer, A.; Keller, A.; Walborn, S. P.; Coudreau, T.; Milman, P.

    2016-08-01

    Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.

  5. On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

    NASA Technical Reports Server (NTRS)

    Brand, J. C.

    1985-01-01

    Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

  6. Feynman-Kac formula for stochastic hybrid systems.

    PubMed

    Bressloff, Paul C

    2017-01-01

    We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

  7. User's manual for CBS3DS, version 1.0

    NASA Astrophysics Data System (ADS)

    Reddy, C. J.; Deshpande, M. D.

    1995-10-01

    CBS3DS is a computer code written in FORTRAN 77 to compute the backscattering radar cross section of cavity backed apertures in infinite ground plane and slots in thick infinite ground plane. CBS3DS implements the hybrid Finite Element Method (FEM) and Method of Moments (MoM) techniques. This code uses the tetrahedral elements, with vector edge basis functions for FEM in the volume of the cavity/slot and the triangular elements with the basis functions for MoM at the apertures. By virtue of FEM, this code can handle any arbitrarily shaped three-dimensional cavities filled with inhomogeneous lossy materials; due to MoM, the apertures can be of any arbitrary shape. The User's Manual is written to make the user acquainted with the operation of the code. The user is assumed to be familiar with the FORTRAN 77 language and the operating environment of the computer the code is intended to run.

  8. Generalized conformal realizations of Kac-Moody algebras

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

    Palmkvist, Jakob

    2009-01-15

    We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3x3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f{sub 4}, e{sub 6}, e{sub 7}, e{sub 8} for n=2. Moreover, we obtain their infinite-dimensional extensions for n{>=}3. In the casemore » of 2x2 matrices, the resulting Lie algebras are of the form so(p+n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q)« less

  9. The calculation of a turbulent diffusion flame in a free shear flow with a statistical turbulence model

    NASA Astrophysics Data System (ADS)

    Bywater, R. J.

    1980-01-01

    Solutions are presented for the turbulent diffusion flame in a two-dimensional shear layer based upon a kinetic theory of turbulence (KTT). The fuel and oxidizer comprising the two streams are considered to react infinitely fast according to a one-step, irreversible kinetic mechanism. The solutions are obtained by direct numerical calculation of the transverse velocity probability density function (PDF) and the associated species distributions. The mean reactant profiles calculated from the solutions display the characteristic thick, turbulent flame zone. The phenomena result from the fact that in the context of the KTT, species react only when in the same velocity cell. This coincides with the known physical requirement that molecular mixing precedes reaction. The solutions demonstrate this behavior by showing how reactants can coexist in the mean, even when infinite reaction rates are enforced at each point (t,x,u) of velocity space.

  10. Detonation Failure Thickness Measurement in AN Annular Geometry

    NASA Astrophysics Data System (ADS)

    Mack, D. B.; Petel, O. E.; Higgins, A. J.

    2007-12-01

    The failure thickness of neat nitromethane in aluminum confinement was measured using a novel experimental technique. The thickness was approximated in an annular geometry by the gap between a concentric aluminum tube and rod. This technique was motivated by the desire to have a periodic boundary condition in the direction orthogonal to the annulus thickness, rather than a free surface occurring in typical rectangular geometry experiments. This results in a two-dimensional charge analogous to previous failure thickness setups but with infinite effective width (i.e. infinite aspect ratio). Detonation propagation or failure was determined by the observation of failure patterns engraved on the aluminum rod by the passing detonation. Analysis of these engraved patterns provides a statistical measurement of the spatial density of failure waves. Failure was observed as far as 180 thicknesses downstream. The failure thickness was measured to be 1.45 mm±0.15 mm.

  11. Syntheses, structures, and properties of two new zinc(II) metal-organic frameworks based on flexible 1,6-bis(2-methyl-imidazole-1-yl)hexane ligand

    NASA Astrophysics Data System (ADS)

    Jin, Jun-Cheng; Fu, Ai-Yun; Li, Dian; Chang, Wen-Gui; Wu, Ju; Yang, Mei; Xie, Cheng-Gen; Xu, Guang-Nian; Cai, An-Xing; Wu, Ai-Hua

    2014-11-01

    Two new zinc(II) metal-organic compounds of [Zn(ADC)(bimh)]n (1) and [Zn(ADA)(bimh)]n (2) (H2ADC = 1,3-adamantanedicarboxylic acid, H2ADA = 1,3-adamantanediacetic acid, bimh = 1,6-bis(2-methyl-imidazole-1-yl)-hexane, have been structurally characterized by X-ray diffraction analysis. In compound 1, the zinc(II) ions are bridged by ADC and bimh ligands to form a 1D looped chain. In compound 2, the ADA molecules alternately bridge Zn(II) atoms to form infinite chains, and then the 1D chain is connected through the bimh ligand resulting in an undulating infinite two-dimensional (2D) polymeric network. Additionally, TG analysis, XRPD and fluorescent properties for compounds 1 and 2 are also measured and discussed.

  12. Markov chain sampling of the O(n) loop models on the infinite plane

    NASA Astrophysics Data System (ADS)

    Herdeiro, Victor

    2017-07-01

    A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

  13. Three-dimensional elasticity solution of an infinite plate with a circular hole

    NASA Technical Reports Server (NTRS)

    Delale, F.; Erdogan, F.

    1982-01-01

    The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

  14. Universality of the Volume Bound in Slow-Roll Eternal Inflation

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

    Dubovsky, Sergei; Senatore, Leonardo; Villadoro, Giovanni

    2012-03-28

    It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e{sup S{sub dS}/2} without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic interpretation. As a spin-off we providemore » the formalism to compute the probability distribution of the volume after inflation for generic multi-field models, which might help to address questions about the population of vacua of the landscape during slow-roll inflation.« less

  15. Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

    NASA Astrophysics Data System (ADS)

    Rusin, Tomasz M.; Zawadzki, Wlodek

    2018-05-01

    Friedel oscillations (FO) of electron density caused by a deltalike neutral impurity in two-dimensional (2D) systems in a magnetic field are calculated. Three 2D cases are considered: free electron gas, monolayer graphene, and group-VI dichalcogenides. An exact form of the renormalized Green's function is used in the calculations, as obtained by a summation of the infinite Dyson series and regularization procedure. Final results are valid for large ranges of potential strengths V0, electron densities ne, magnetic fields B , and distances from the impurity r . Realistic models for the impurities are used. The first FO of induced density in WS2 are described by the relation Δ n (r ) ∝sin(2 π r /TFO) /r2 , where TFO∝1 /√{EF} . For weak impurity potentials, the amplitudes of FO are proportional to V0. For attractive potentials and high fields, the total electron density remains positive for all r . On the other hand, for low fields, repulsive potentials and small r , the total electron density may become negative, so that many-body effects should be taken into account.

  16. Ikeda-like chaos on a dynamically filtered supercontinuum light source

    NASA Astrophysics Data System (ADS)

    Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent

    2016-08-01

    We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

  17. An efficient high-frequency analysis of modal reflection and transmission coefficients for a class of waveguide discontinuities

    NASA Technical Reports Server (NTRS)

    Pathak, P. H.; Altintas, A.

    1988-01-01

    A high-frequency analysis of electromagnetic modal reflection and transmission coefficients is presented for waveguide discontinuities formed by joining different waveguide sections. The analysis uses an extended version of the concept of geometrical theory of diffraction based equivalent edge currents in conjunction with the reciprocity theorem to describe interior scattering effects. If the waveguide modes and their associated modal rays can be found explicitly, general two- and three-dimensional waveguide geometries can be analyzed. Expressions are developed for two-dimensional reflection and transmission coefficients. Numerical results are given for a flanged, semi-infinite parallel plate waveguide and for the junction between two linearly tapered waveguides.

  18. On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

  19. Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

  20. Quantum Machine Learning over Infinite Dimensions

    DOE PAGES

    Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George; ...

    2017-02-21

    Machine learning is a fascinating and exciting eld within computer science. Recently, this ex- citement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the nite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practi- cal, in nite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, we also map out an experi- mental implementation which can be used as amore » blueprint for future photonic demonstrations.« less

  1. On Born's Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal

    NASA Astrophysics Data System (ADS)

    Bétermin, Laurent; Knüpfer, Hans

    2018-04-01

    We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born's conjecture about the optimality of the rock salt alternate distribution of charges on a cubic lattice (and more generally on a d-dimensional orthorhombic lattice). Furthermore, we study this problem on the two-dimensional triangular lattice and we prove the optimality of a two-component honeycomb distribution of charges. The results hold for a class of completely monotone interaction potentials which includes Coulomb-type interactions for d≥3 . In a more general setting, we derive a connection between the optimal charge problem and a minimization problem for the translated lattice theta function.

  2. Vibroacoustic response of structures and perturbation Reynolds stress near structure-turbulence interface

    NASA Technical Reports Server (NTRS)

    Maekawa, S.; Lin, Y. K.

    1977-01-01

    The interaction between a turbulent flow and certain types of structures which respond to its excitation is investigated. One-dimensional models were used to develop the basic ideas applied to a second model resembling the fuselage construction of an aircraft. In the two-dimensional case a simple membrane, with a small random variation in the membrane tension, was used. A decaying turbulence was constructed by superposing infinitely many components, each of which is convected as a frozen pattern at a different velocity. Structure-turbulence interaction results are presented in terms of the spectral densities of the structural response and the perturbation Reynolds stress in the fluid at the vicinity of the interface.

  3. Quantum Machine Learning over Infinite Dimensions

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

    Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George

    Machine learning is a fascinating and exciting eld within computer science. Recently, this ex- citement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the nite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practi- cal, in nite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, we also map out an experi- mental implementation which can be used as amore » blueprint for future photonic demonstrations.« less

  4. Modeling and control of flexible space structures

    NASA Technical Reports Server (NTRS)

    Wie, B.; Bryson, A. E., Jr.

    1981-01-01

    The effects of actuator and sensor locations on transfer function zeros are investigated, using uniform bars and beams as generic models of flexible space structures. It is shown how finite element codes may be used directly to calculate transfer function zeros. The impulse response predicted by finite-dimensional models is compared with the exact impulse response predicted by the infinite dimensional models. It is shown that some flexible structures behave as if there were a direct transmission between actuator and sensor (equal numbers of zeros and poles in the transfer function). Finally, natural damping models for a vibrating beam are investigated since natural damping has a strong influence on the appropriate active control logic for a flexible structure.

  5. Difference equation state approximations for nonlinear hereditary control problems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1982-01-01

    Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

  6. 2 + 1 Toda chain. I. Inverse scattering method

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

    Lipovskii, V.D.; Shirokov, A.V.

    A formal scheme of the inverse scattering method is constructed for the2 + 1 Toda chain in the class of rapidly decreasing Cauchy data. Application of the inverse scattering method to the two-dimensional infinite Toda chain was made difficult by the circumstance that this system is a (2 + 1)-dimensional object, i.e., possesses time and two spatial variables, the role of one of these being played by the chain site number. Because of this, our information about the 2 + 1 Toda chain was limited to a rich set of particular solutions of soliton type obtained in the cycle ofmore » studies by the Darboux transformation method.« less

  7. Random Walks in a One-Dimensional Lévy Random Environment

    NASA Astrophysics Data System (ADS)

    Bianchi, Alessandra; Cristadoro, Giampaolo; Lenci, Marco; Ligabò, Marilena

    2016-04-01

    We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.

  8. Geometry of Spin and SPINc Structures in the M-Theory Partition Function

    NASA Astrophysics Data System (ADS)

    Sati, Hisham

    We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinc case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov-Lawson-Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.

  9. Newton-Cartan Gravity in Noninertial Reference Frames

    NASA Astrophysics Data System (ADS)

    Rodriguez, Leo; St. Germaine-Fuller, James; Wickramasekara, Sujeev

    2015-03-01

    We study Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. These transformations form an infinite dimensional Lie group, called the Galilean line group, which contains as a subgroup the Galilei group. The fictitious forces of noninertial reference frames are encoded in the Cartan connection transformed under the Galilean line group. These fictitious forces, which are coordinate effects, do not contribute to the Ricci tensor. Only the 00-component of the Ricci tensor is non-zero and equals (4 π times) the matter density in all reference frames. While the Ricci field equation and Gauss' law are fulfilled by the physical matter density in inertial and linearly accelerating reference frames, in rotating reference frames Gauss' law holds for an effective mass density that differs from the physical matter density. This effective density has its origin in the simulated magnetic field of rotating frames, highlighting a striking difference between linearly and rotationally accelerating frames. The equations governing the simulated fields have the same form as Maxwell's equations, a surprising result given that these equations obey special relativity (and U (1) -gauge symmetry), rather than Galilean symmetry. This work was supported in part by the HHMI Undergraduate Science Education Award 52006298 and the Grinnell College Academic Affairs' CSFS and MAP programs.

  10. Length-Two Representations of Quantum Affine Superalgebras and Baxter Operators

    NASA Astrophysics Data System (ADS)

    Zhang, Huafeng

    2018-03-01

    Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations; the extended T-systems of Kirillov-Reshetikhin modules. We make use of these representations over the full quantum affine superalgebra to define Baxter operators as transfer matrices for the quantum integrable model and to deduce Bethe Ansatz Equations, under genericity conditions.

  11. Ultra-Scalable Algorithms for Large-Scale Uncertainty Quantification in Inverse Wave Propagation

    DTIC Science & Technology

    2016-03-04

    53] N. Petra , J. Martin , G. Stadler, and O. Ghattas, A computational framework for infinite-dimensional Bayesian inverse problems: Part II...positions: Alen Alexanderian (NC State), Tan Bui-Thanh (UT-Austin), Carsten Burstedde (University of Bonn), Noemi Petra (UC Merced), Georg Stalder (NYU), Hari...Baltimore, MD, Nov. 2002. SC2002 Best Technical Paper Award. [3] A. Alexanderian, N. Petra , G. Stadler, and O. Ghattas, A-optimal design of exper

  12. Control optimization, stabilization and computer algorithms for aircraft applications

    NASA Technical Reports Server (NTRS)

    1975-01-01

    Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

  13. Seaworthy Quantum Key Distribution Design and Validation (SEAKEY)

    DTIC Science & Technology

    2015-08-07

    absorption and scattering using MODTRAN [ Berk et al.]. Thus, channel efficiency is expressed as follows: G=GT×exp[−αL], (10) where exp[−αL] is...34 New Journal of Physics 13, 013003 (2011). [Scarani et al.] Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J . Cerf, Miloslav Dušek, Norbert...050303 (2005). [Renner and Cirac] R. Renner and J . I. Cirac, de Finetti representation theorem for infinite-dimensional quantum systems and

  14. Loads Correlation of a Full-Scale UH-60A Airloads Rotor in a Wind Tunnel

    DTIC Science & Technology

    2012-05-01

    modeling in lifting line theory is unsteady, compressible, viscous flow about an infinite wing in a uniform flow consisting of a yawed freestream and...wake-induced velocity. This problem is modeled within CAMRAD II as two-dimensional, steady, compressible, viscous flow (airfoil tables), plus...and 21 aerodynamic panels. Detailed rotor control system geometry, stiffness, and lag damper were also incorporated. When not coupling to OVERFLOW, a

  15. Emergence of a confined state in a weakly bent wire

    NASA Astrophysics Data System (ADS)

    Granot, Er'El

    2002-06-01

    In this paper we use a simple straightforward technique to investigate the emergence of a bound state in a weakly bent wire. We show that the bend behaves like an infinitely shallow potential well, and in the limit of small bending angle (φ<<1) and low energy the bend can be presented by a simple one-dimensional δ-function potential, V(x)=-(2(cb)φ2)δ(x) where cb≅2.1.

  16. Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Huang, Zhi-Xiang; Wu, Xian-Liang

    Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

  17. Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems

    DTIC Science & Technology

    2007-03-01

    mathematical frame- 1-6 work of linear algebra and functional analysis [122, 33], while Kalman-Bucy filtering [96, 32] is an especially important...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, March 2002. 85. Hoffman, Kenneth and Ray Kunze. Linear Algebra (Second Edition...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, December 1989. 189. Strang, Gilbert. Linear Algebra and Its Applications

  18. Water-Stable In(III)-Based Metal-Organic Frameworks with Rod-Shaped Secondary Building Units: Single-Crystal to Single-Crystal Transformation and Selective Sorption of C2H2 over CO2 and CH4.

    PubMed

    Guo, Zhen-Ji; Yu, Jiamei; Zhang, Yong-Zheng; Zhang, Jian; Chen, Ya; Wu, Yufeng; Xie, Lin-Hua; Li, Jian-Rong

    2017-02-20

    Three new water-stable In(III)-based metal-organic frameworks, namely, [In 3 (TTTA) 2 (OH) 3 (H 2 O)]·(DMA) 3 (BUT-70, DMA = N,N-dimethylacetamide), [In 3 (TTTA) 2 (CH 3 O) 3 ] (BUT-70A), and [In 3 (TTTA) 2 (OH) 3 ] (BUT-70B), with rod-shaped secondary building units (SBUs) and an new acrylate-based ligand, (2E,2'E,2″E)-3,3',3″-(2,4,6-trimethylbenzene-1,3,5-triyl)-triacrylate (TTTA 3- ) were obtained and structurally characterized. BUT-70A and -70B were generated in a single-crystal to single-crystal transformation fashion from BUT-70 through guest exchange followed by their removal. The solvents used for guest exchange were methanol and dichloromethane, respectively. Single-crystal structure analyses show that the guest exchange and removal process is accompanied by the substitution of coordinated water molecules of In(III) centers with uncoordinated carboxylate O atoms of TTTA 3- ligands. Moreover, hydroxyl groups bridging two In(III) centers are also replaced by methoxyl groups in the transformation from BUT-70 to -70A. Overall, three metal-organic frameworks (MOFs) are constructed by infinite chains consisting of corner-sharing InO 4 (OR) 2 (R = H or Me) octahedral entities, which are interconnected by TTTA 3- ligands to form three-dimensional frameworks. Unlike most reported MOFs with infinite chains as SBUs, such as well-known MIL-53 and M-MOF-74, which have one-dimensional channels along the chain direction, the BUT-70 series contain two-dimensional intersecting channels. The Brunauer-Emmett-Teller surface area and pore volume of BUT-70A were estimated to be 460 m 2 g -1 and 0.18 cm 3 g -1 , respectively, which are obviously lower than those of BUT-70B (695 m 2 g -1 and 0.29 cm 3 g -1 ). Gas adsorption experiments demonstrated that BUT-70A and -70B are able to selectively adsorb C 2 H 2 over CO 2 and CH 4 . At 1 atm and 298 K, BUT-70A uptakes 3.1 mmol g -1 C 2 H 2 , which is 3.6 times that of the CO 2 uptake and 7.2 times that of the CH 4 uptake. Compared with BUT-70A, BUT-70B presents an even higher C 2 H 2 uptake of 3.9 mmol g -1 at the same conditions, but slightly lower Ideal Adsorbed Solution Theory C 2 H 2 /CO 2 and C 2 H 2 /CH 4 selectivities.

  19. Multi-Dimensional Shallow Landslide Stability Analysis Suitable for Application at the Watershed Scale

    NASA Astrophysics Data System (ADS)

    Milledge, D.; Bellugi, D.; McKean, J. A.; Dietrich, W.

    2012-12-01

    The infinite slope model is the basis for almost all watershed scale slope stability models. However, it assumes that a potential landslide is infinitely long and wide. As a result, it cannot represent resistance at the margins of a potential landslide (e.g. from lateral roots), and is unable to predict the size of a potential landslide. Existing three-dimensional models generally require computationally expensive numerical solutions and have previously been applied only at the hillslope scale. Here we derive an alternative analytical treatment that accounts for lateral resistance by representing the forces acting on each margin of an unstable block. We apply 'at rest' earth pressure on the lateral sides, and 'active' and 'passive' pressure using a log-spiral method on the upslope and downslope margins. We represent root reinforcement on each margin assuming that root cohesion is an exponential function of soil depth. We benchmark this treatment against other more complete approaches (Finite Element (FE) and closed form solutions) and find that our model: 1) converges on the infinite slope predictions as length / depth and width / depth ratios become large; 2) agrees with the predictions from state-of-the-art FE models to within +/- 30% error, for the specific cases in which these can be applied. We then test our model's ability to predict failure of an actual (mapped) landslide where the relevant parameters are relatively well constrained. We find that our model predicts failure at the observed location with a nearly identical shape and predicts that larger or smaller shapes conformal to the observed shape are indeed more stable. Finally, we perform a sensitivity analysis using our model to show that lateral reinforcement sets a minimum landslide size, while the additional strength at the downslope boundary means that the optimum shape for a given size is longer in a downslope direction. However, reinforcement effects cannot fully explain the size or shape distributions of observed landslides, highlighting the importance of spatial patterns of key parameters (e.g. pore water pressure) and motivating the model's watershed scale application. This watershed scale application requires an efficient method to find the least stable shapes among an almost infinite set. However, when applied in this context, it allows a more complete examination of the controls on landslide size, shape and location.

  20. Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems

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

    Adesso, Gerardo; CNR-INFM Coherentia , Naples; Grup d'Informacio Quantica, Universitat Autonoma de Barcelona, E-08193 Bellaterra

    2007-08-15

    Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N{>=}4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantummore » correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.« less

  1. Measuring acoustic impedances using a semi-infinite waveguide reference: Applications to wind instruments and vocal tracts

    NASA Astrophysics Data System (ADS)

    Wolfe, Joe; Smith, John; Tann, John; France, Ryan

    2002-11-01

    Acoustic pressures may generally be measured with much greater sensitivity, dynamic range, and frequency response than acoustic currents. Consequently, most measurements of acoustic impedance consist of comparison with standard impedances. The method reported here uses a semi-infinite waveguide as the reference because its impedance is purely resistive, frequency independent and accurately known, independent of theories of the boundary layer. Waveguides are effectively infinite for pulses shorter than the echo return time, or if the attenuation due to wall losses (typically 80 dB) exceeds the dynamic range of the experiment. The measurement signal from a high output impedance source is calibrated to have Fourier components proportional to fn, where n may be 1 for convenience or chosen to improve the signal:noise ratio. The method has been used on diverse systems over the range 50 Hz to 13 kHz. When applied to systems with simple geometries, the technique yields results with a little higher wall losses than those expected from the calculations of Rayleigh and Benade. Discontinuities introduce further losses as well as the expected departures from simple one-dimensional models. Measurements on musical wind instruments and on the human vocal tract are reported. [Work supported by the Australian Research Council.

  2. Filtration of the classical knot concordance group and Casson-Gordon invariants

    NASA Astrophysics Data System (ADS)

    Kim, Taehee

    2004-09-01

    It is known that if every prime power branched cyclic cover of a knot in S(3) is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in S(3) whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of scrf_{(1.0)}/scrf_{(1.5)} for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot concordance group. As a corollary, it follows that Casson-Gordon invariants are not a complete set of obstructions to a second layer of Whitney disks.

  3. Squeezing the Efimov effect

    NASA Astrophysics Data System (ADS)

    Sandoval, J. H.; Bellotti, F. F.; Yamashita, M. T.; Frederico, T.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.

    2018-03-01

    The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.

  4. Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

    NASA Technical Reports Server (NTRS)

    Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

    2003-01-01

    The use of multi-dimensional finite volume numerical techniques with finite thickness models for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the one-dimensional semi -infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody were investigated. An array of streamwise orientated heating striations were generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients due to the striation patterns two-dimensional heat transfer techniques were necessary to obtain accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates because it did not account for lateral heat conduction in the model.

  5. Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories

    NASA Astrophysics Data System (ADS)

    Zemba, Guillermo Raul

    A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

  6. Phonon thermal conductivity of monolayer MoS{sub 2}

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

    Wang, Xiaonan; Tabarraei, Alireza, E-mail: atabarra@uncc.edu

    We use nonequilibrium molecular dynamics modeling using Stillinger–Weber interatomic potential to investigate the thermal properties of monolayer molybdenum disulfide (MoS{sub 2}) nanoribbons. We study the impact of factors such as length, edge chirality, monovacancies, and uniaxial stretching on the thermal conductivity of MoS{sub 2} nanoribbons. Our results show that longer ribbons have a higher thermal conductivity, and the thermal conductivity of infinitely long zigzag and armchair MoS{sub 2} nanoribbons is, respectively, 54 W/mK and 33 W/mK. This is significantly lower than the thermal conductivity of some other graphene-like two-dimensional materials such as graphene and boron nitride. While the presence of molybdenum ormore » sulfur vacancies reduces the thermal conductivity of ribbons, molybdenum vacancies have a more deteriorating effect on thermal conductivities. We also have studied the impact of uniaxial stretching on the thermal conductivity of MoS{sub 2} nanoribbons. The results show that in contrast to three dimensional materials, thermal conductivity of MoS{sub 2} is fairly insensitive to stretching. We have used the phonon dispersion curves and group velocities to investigate the mechanism of this unexpected behavior. Our results show that tensile strain does not alter the phonon dispersion curves and hence the thermal conductivity does not change.« less

  7. A boundary element alternating method for two-dimensional mixed-mode fracture problems

    NASA Technical Reports Server (NTRS)

    Raju, I. S.; Krishnamurthy, T.

    1992-01-01

    A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

  8. Three-Dimensional Dynamic Deformation Measurements Using Stereoscopic Imaging and Digital Speckle Photography

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

    Prentice, H. J.; Proud, W. G.

    2006-07-28

    A technique has been developed to determine experimentally the three-dimensional displacement field on the rear surface of a dynamically deforming plate. The technique combines speckle analysis with stereoscopy, using a modified angular-lens method: this incorporates split-frame photography and a simple method by which the effective lens separation can be adjusted and calibrated in situ. Whilst several analytical models exist to predict deformation in extended or semi-infinite targets, the non-trivial nature of the wave interactions complicates the generation and development of analytical models for targets of finite depth. By interrogating specimens experimentally to acquire three-dimensional strain data points, both analytical andmore » numerical model predictions can be verified more rigorously. The technique is applied to the quasi-static deformation of a rubber sheet and dynamically to Mild Steel sheets of various thicknesses.« less

  9. A Dissimilarity Measure for Clustering High- and Infinite Dimensional Data that Satisfies the Triangle Inequality

    NASA Technical Reports Server (NTRS)

    Socolovsky, Eduardo A.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    The cosine or correlation measures of similarity used to cluster high dimensional data are interpreted as projections, and the orthogonal components are used to define a complementary dissimilarity measure to form a similarity-dissimilarity measure pair. Using a geometrical approach, a number of properties of this pair is established. This approach is also extended to general inner-product spaces of any dimension. These properties include the triangle inequality for the defined dissimilarity measure, error estimates for the triangle inequality and bounds on both measures that can be obtained with a few floating-point operations from previously computed values of the measures. The bounds and error estimates for the similarity and dissimilarity measures can be used to reduce the computational complexity of clustering algorithms and enhance their scalability, and the triangle inequality allows the design of clustering algorithms for high dimensional distributed data.

  10. Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

    NASA Astrophysics Data System (ADS)

    Gavrilov, S. N.; Krivtsov, A. M.; Tsvetkov, D. V.

    2018-05-01

    We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.

  11. Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

    NASA Astrophysics Data System (ADS)

    Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

    2015-11-01

    Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

  12. Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Ta'asan, Shlomo

    1996-01-01

    In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

  13. An approximation theory for the identification of linear thermoelastic systems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.; Su, Chien-Hua Frank

    1990-01-01

    An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

  14. The canonical quantization of chaotic maps on the torus

    NASA Astrophysics Data System (ADS)

    Rubin, Ron Shai

    In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

  15. Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

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

    MacGregor, B.R.; McCoy, A.E.; Wickramasekara, S., E-mail: wickrama@grinnell.edu

    2012-09-15

    We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertialmore » reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantum mechanics in non-inertial reference frames is given. Black-Right-Pointing-Pointer The key concept is the Galilean line group, an infinite dimensional group. Black-Right-Pointing-Pointer Unitary, cocycle representations of the Galilean line group are constructed. Black-Right-Pointing-Pointer A non-central extension of the group underlies these representations. Black-Right-Pointing-Pointer Quantum equivalence principle and gravity emerge from these representations.« less

  16. Remarks on a New Possible Discretization Scheme for Gauge Theories

    NASA Astrophysics Data System (ADS)

    Magnot, Jean-Pierre

    2018-03-01

    We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

  17. Problems of interaction longitudinal shear waves with V-shape tunnels defect

    NASA Astrophysics Data System (ADS)

    Popov, V. G.

    2018-04-01

    The problem of determining the two-dimensional dynamic stress state near a tunnel defect of V-shaped cross-section is solved. The defect is located in an infinite elastic medium, where harmonic longitudinal shear waves are propagating. The initial problem is reduced to a system of two singular integral or integro-differential equations with fixed singularities. A numerical method for solving these systems with regard to the true asymptotics of the unknown functions is developed.

  18. Remarks on a New Possible Discretization Scheme for Gauge Theories

    NASA Astrophysics Data System (ADS)

    Magnot, Jean-Pierre

    2018-07-01

    We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

  19. Diagnostics for Intelligent Control of MPD Engines

    DTIC Science & Technology

    1988-11-15

    Comparison of finite and infinite dimensional systems. -29- V r eAtvo which satisfies - ( eAtv ,,) =AeAtvo -Av where eAt is the transition matrix defined by, eA...Bu (6-1) and v(o) =v o where vER’, ueRm, Ae2(Rn,R’), and Bei(Rm,Ra). The solution of this equation at time t is t v(t) = eAtv + f eA(t-S)Bu(s) ds (6-2

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

    Aslangul, C.; Bouchaud, J.; Georges, A.

    The authors present new exact results for a one-dimensional asymmetric disordered hopping model. The lattice is taken infinite from the start and they do not resort to the periodization scheme used by Derrida. An explicit resummation allows for the calculation of the velocity V and the diffusion constant D (which are found to coincide with those given by Derrida) and for demonstrating that V is indeed a self-averaging quantity; the same property is established for D in the limiting case of a directed walk.

  1. Bound eigenstate dynamics under a sudden shift of the well's wall

    NASA Astrophysics Data System (ADS)

    Granot, Er'El; Marchewka, Avi

    2010-03-01

    We investigate the dynamics of the eigenstate of an infinite well under an abrupt shift of the well’s wall. It is shown that when the shift is small compared to the initial well’s dimensions, the short-time behavior changes from the well-known t3/2 behavior to t1/2. It is also shown that the complete dynamical picture converges to a universal function, which has fractal structure with dimensionality D=1.25.

  2. The forced vibration of one-dimensional multi-coupled periodic structures: An application to finite element analysis

    NASA Astrophysics Data System (ADS)

    Mead, Denys J.

    2009-01-01

    A general theory for the forced vibration of multi-coupled one-dimensional periodic structures is presented as a sequel to a much earlier general theory for free vibration. Starting from the dynamic stiffness matrix of a single multi-coupled periodic element, it derives matrix equations for the magnitudes of the characteristic free waves excited in the whole structure by prescribed harmonic forces and/or displacements acting at a single periodic junction. The semi-infinite periodic system excited at its end is first analysed to provide the basis for analysing doubly infinite and finite periodic systems. In each case, total responses are found by considering just one periodic element. An already-known method of reducing the size of the computational problem is reexamined, expanded and extended in detail, involving reduction of the dynamic stiffness matrix of the periodic element through a wave-coordinate transformation. Use of the theory is illustrated in a combined periodic structure+finite element analysis of the forced harmonic in-plane motion of a uniform flat plate. Excellent agreement between the computed low-frequency responses and those predicted by simple engineering theories validates the detailed formulations of the paper. The primary purpose of the paper is not towards a specific application but to present a systematic and coherent forced vibration theory, carefully linked with the existing free-wave theory.

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

    Hua, Xiu-Ni; Qin, Lan; Yan, Xiao-Zhi

    Hydrothermal reactions of N-auxiliary flexible exo-bidentate ligand 1,3-bis(4-pyridyl)propane (bpp) and carboxylates ligands naphthalene-2,6-dicarboxylic acid (2,6-H{sub 2}ndc) or 4,4′-(hydroxymethylene)dibenzoic acid (H{sub 2}hmdb), in the presence of cadmium(II) salts have given rise to two novel metal-organic frameworks based on flexible ligands (FL-MOFs), namely, [Cd{sub 2}(2,6-ndc){sub 2}(bpp)(DMF)]·2DMF (1) and [Cd{sub 3}(hmdb){sub 3}(bpp)]·2DMF·2EtOH (2) (DMF=N,N-Dimethylformamide). Single-crystal X-ray diffraction analyses revealed that compound 1 exhibits a three-dimensional self-penetrating 6-connected framework based on dinuclear cluster second building unit. Compound 2 displays an infinite three-dimensional ‘Lucky Clover’ shape (2,10)-connected network based on the trinuclear cluster and V-shaped organic linkers. The flexible bpp ligand displays different conformations inmore » 1 and 2, which are successfully controlled by size-matching mixed ligands during the self-assembly process. - Graphical abstract: Compound 1 exhibits a 3D self-penetrating 6-connected framework based on dinuclear cluster, and 2 displays an infinite 3D ‘Lucky Clover’ shape (2,10)-connected network based on the trinuclear cluster. The flexible 1,3-bis(4-pyridyl)propane ligand displays different conformations in 1 and 2, which successfully controlled by size-matching mixed ligands during the self-assembly process.« less

  4. Construction and optical properties of infinite Cd and finite Cu molecules stairs

    NASA Astrophysics Data System (ADS)

    Zhao, Qiang; Mao, Wutao; Shen, Zhi; Wang, Qinghong; Zhou, Qian

    2017-02-01

    Two coordination complexes, namely [(hpdq)(pta)Cd]n (1) and [(pptp)(pta)Cu2Cl] (2) have been synthesized by solvothermal method based on two polypyridyl ligands, 2,3,6,7,10,11-hexakis- (2-pyridyl)dipyrazino[2,3-f:2‧,3‧-h]quinoxaline) (hpdq), 4‧-(4- (3H-pyrrol-3-yl)phenyl)- 2,2‧:6‧,2″- terpyridine (pptp) and auxiliary ligand p-phthalic acid (pta), respectively. Single crystal x-ray diffraction analyses reveal that complexes 1 and 2 assembled based on distinct asymmetric unit comprising one and two respective polypyridyl ligands but one Cd(II) and two Cu(I)ions, respectively. Among them, The asymmetric units in 1 was extended to one dimensional chain via the link of auxiliary ligand pta, just like infinite layers of stairs that connected by cadmium ions as the node. While that in 2 to Zero dimensional tetranuclear structure via the link of auxiliary ligand pta, just like finite four layers of stairs that Copper ion as the node connection. Furthermore, solid fluorescence spectra properties of two complexes were also investigated, and the result shows the fluorescence intensity of complex 1 is stronger than that of the hpdq ligand, but the fluorescence intensity of complex 2 is weaker than that of the pptp ligand. CCDC number of 1and 2 are 1483301 and 1483302.

  5. Crystal structures of 4-meth-oxy-N-(4-methyl-phenyl)benzene-sulfonamide and N-(4-fluoro-phenyl)-4-meth-oxy-benzene-sulfonamide.

    PubMed

    Rodrigues, Vinola Z; Preema, C P; Naveen, S; Lokanath, N K; Suchetan, P A

    2015-11-01

    Crystal structures of two N-(ar-yl)aryl-sulfonamides, namely, 4-meth-oxy-N-(4-methyl-phen-yl)benzene-sulfonamide, C14H15NO3S, (I), and N-(4-fluoro-phen-yl)-4-meth-oxy-benzene-sulfonamide, C13H12FNO3S, (II), were determined and analyzed. In (I), the benzene-sulfonamide ring is disordered over two orientations, in a 0.516 (7):0.484 (7) ratio, which are inclined to each other at 28.0 (1)°. In (I), the major component of the sulfonyl benzene ring and the aniline ring form a dihedral angle of 63.36 (19)°, while in (II), the planes of the two benzene rings form a dihedral angle of 44.26 (13)°. In the crystal structure of (I), N-H⋯O hydrogen bonds form infinite C(4) chains extended in [010], and inter-molecular C-H⋯πar-yl inter-actions link these chains into layers parallel to the ab plane. The crystal structure of (II) features N-H⋯O hydrogen bonds forming infinite one dimensional C(4) chains along [001]. Further, a pair of C-H⋯O inter-molecular inter-actions consolidate the crystal packing of (II) into a three-dimensional supra-molecular architecture.

  6. The Edge States of the BF System and the London Equations

    NASA Astrophysics Data System (ADS)

    Balachandran, A. P.; Teotonio-Sobrinho, P.

    It is known that the 3D Chern-Simons interaction describes the scaling limit of a quantum Hall system and predicts edge currents in a sample with boundary, the currents generating a chiral U(1) Kac-Moody algebra. It is no doubt also recognized that, in a somewhat similar way, the 4D BF interaction (with B a two-form, dB the dual *j of the electromagnetic current, and F the electromagnetic field form) describes the scaling limit of a superconductor. We show in this paper that there are edge excitations in this model as well for manifolds with boundaries. They are the modes of a scalar field with invariance under the group of diffeomorphisms (diffeos) of the bounding spatial two-manifold. Not all diffeos of this group seem implementable by operators in quantum theory, the implementable group being a subgroup of volume-preserving diffeos. The BF system in this manner can lead to the w1+∞ algebra and its variants. Lagrangians for fields on the bounding manifold which account for the edge observables on quantization are also presented. They are the analogs of the (1+1)-dimensional massless scalar field Lagrangian describing the edge modes of an Abelian Chern-Simons theory with a disk as the spatial manifold. We argue that the addition of “Maxwell” terms constructed from F∧*F and dB∧*dB does not affect the edge states, and that the augmented Lagrangian has an infinite number of conserved charges—the aforementioned scalar field modes—localized at the edges. This Lagrangian is known to describe London equations and a massive vector field. A (3+1)-dimensional generalization of the Hall effect involving vortices coupled to B is also proposed.

  7. Copula based flexible modeling of associations between clustered event times.

    PubMed

    Geerdens, Candida; Claeskens, Gerda; Janssen, Paul

    2016-07-01

    Multivariate survival data are characterized by the presence of correlation between event times within the same cluster. First, we build multi-dimensional copulas with flexible and possibly symmetric dependence structures for such data. In particular, clustered right-censored survival data are modeled using mixtures of max-infinitely divisible bivariate copulas. Second, these copulas are fit by a likelihood approach where the vast amount of copula derivatives present in the likelihood is approximated by finite differences. Third, we formulate conditions for clustered right-censored survival data under which an information criterion for model selection is either weakly consistent or consistent. Several of the familiar selection criteria are included. A set of four-dimensional data on time-to-mastitis is used to demonstrate the developed methodology.

  8. Difference equation state approximations for nonlinear hereditary control problems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1984-01-01

    Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

  9. Wave radiation and diffraction by a two-dimensional floating body with an opening near a side wall

    NASA Astrophysics Data System (ADS)

    Zhang, Hong-sheng; Zhou, Hua-wei

    2013-08-01

    The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi-infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.

  10. Neuronal models in infinite-dimensional spaces and their finite-dimensional projections: Part II.

    PubMed

    Brzychczy, S; Leszczyński, H; Poznanski, R R

    2012-09-01

    Application of comparison theorem is used to examine the validitiy of the "lumped parameter assumption" in describing the behavior of solutions of the continuous cable equation U(t) = DU(xx)+f(U) with the discrete cable equation dV(n)/dt = d*(V(n+1) - 2V(n) + V(n-1)) + f(V(n)), where f is a nonlinear functional describing the internal diffusion of electrical potential in single neurons. While the discrete cable equation looks like a finite difference approximation of the continuous cable equation, solutions of the two reveal significantly different behavior which imply that the compartmental models (spiking neurons) are poor quantifiers of neurons, contrary to what is commonly accepted in computational neuroscience.

  11. 8-Hy­droxy­quinolin-1-ium hydrogen sulfate monohydrate

    PubMed Central

    Damous, Maamar; Dénès, George; Bouacida, Sofiane; Hamlaoui, Meriem; Merazig, Hocine; Daran, Jean-Claude

    2013-01-01

    In the crystal structure of the title salt hydrate, C9H8NO+·HSO4 −·H2O, the quinoline N—H atoms are hydrogen bonded to the bis­ulfate anions. The bis­ulfate anions and water mol­ecules are linked together by O—H⋯O hydrogen-bonding inter­actions. The cations and anions form separate layers alternating along the c axis, which are linked by N—H⋯O and O—H⋯O hydrogen bonds into a two-dimensional network parallel to (100). Further O—H⋯O contacts connect these layers, forming a three-dimensional network, in which two R 4 4(12) rings and C 2 2(13) infinite chains can be identified. PMID:24427083

  12. Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1987-01-01

    The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

  13. Metriplectic integrators for the Landau collision operator

    DOE PAGES

    Kraus, Michael; Hirvijoki, Eero

    2017-10-02

    Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

  14. Host-guest capability of a three-dimensional heterometallic macrocycle.

    PubMed

    Fan, Qi-Jia; Lin, Yue-Jian; Hahn, F Ekkehardt; Jin, Guo-Xin

    2018-02-13

    A three-dimensional heterometallic coordination macrocycle is found to be capable of encapsulating planar pyrene (G1), coronene (G4) and non-planar corannulene (G2) guest molecules in high yields, giving rise to 1 : 1 host-guest complexes. The bowl-shaped guest corannulene is found to be significantly flattened upon inclusion within the cavity. However, macrocyclic compounds with larger cavity sizes, which form 1 : 1 stoichiometry assemblies with a naphthalene bisimide planar molecule (G3), are more inclined to form infinite sandwich structures. Furthermore, these heterometallic coordination macrocycles can be destroyed in the presence of a soft base to form hexanuclear triangular prism complexes. These structures are unambiguously revealed by single-crystal X-ray analysis.

  15. A large deviations principle for stochastic flows of viscous fluids

    NASA Astrophysics Data System (ADS)

    Cipriano, Fernanda; Costa, Tiago

    2018-04-01

    We study the well-posedness of a stochastic differential equation on the two dimensional torus T2, driven by an infinite dimensional Wiener process with drift in the Sobolev space L2 (0 , T ;H1 (T2)) . The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier-Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.

  16. Local entanglement entropy of fermions as a marker of quantum phase transition in the one-dimensional Hubbard model

    NASA Astrophysics Data System (ADS)

    Cha, Min-Chul; Chung, Myung-Hoon

    2018-05-01

    We study quantum phase transition of interacting fermions by measuring the local entanglement entropy in the one-dimensional Hubbard model. The reduced density matrices for blocks of a few sites are constructed from the ground state wave function in infinite systems by adopting the matrix product state representation where time-evolving block decimations are performed to obtain the lowest energy states. The local entanglement entropy, constructed from the reduced density matrices, as a function of the chemical potential shows clear signatures of the Mott transition. The value of the central charge, numerically determined from the universal properties of the local entanglement entropy, confirms that the transition is caused by the suppression of the charge degrees of freedom.

  17. Global Culture: A Noise Induced Transition in Finite Systems

    NASA Astrophysics Data System (ADS)

    Klemm, Konstantin; Eguíluz, Victor M.; Toral, Raúl; San Miguel, Maxi

    2003-04-01

    We analyze Axelrod's model for the unbiased transmission of culture in the presence of noise. In a one-dimensional lattice, the dynamics is described in terms of a Lyapunov potential, where the disordered configurations are metastable states of the dynamics. In a two-dimensional lattice the dynamics is governed by the average relaxation time T for perturbations to the homogeneous configuration. If the noise rate is smaller than 1/T, the perturbations drive the system to a completely ordered configuration, whereas the system remains disordered for larger noise rates. Based on a mean-field approximation we obtain the average relaxation time T(N) = Nln(N) for system size N. Thus in the limit of infinite system size the system is disordered for any finite noise rate.

  18. Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

    NASA Astrophysics Data System (ADS)

    Luther, K.; Haitjema, H. M.

    2000-04-01

    We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

  19. 2-(3-Chloro­phen­yl)-4,5-dihydro-1H-imidazole

    PubMed Central

    Kia, Reza; Fun, Hoong-Kun; Kargar, Hadi

    2009-01-01

    In the title compound, C9H9ClN2, a substituted imidazoline, the six- and five-membered rings are twisted from each other, making a dihedral angle of 17.07 (5)°. In the crystal structure, a short Cl⋯Cl [3.3540 (3) Å] inter­action is observed. Neighbouring mol­ecules are linked together by inter­molecular N—H⋯N hydrogen bonds into a one-dimensional infinite chain along the [101] direction and short Cl⋯Cl contacts link the chains into a three-dimensional network. There is also a significant π-stacking inter­action between the planar sections of the six- and five-membered rings. PMID:21581940

  20. Correlations of RMT characteristic polynomials and integrability: Hermitean matrices

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

    Osipov, Vladimir Al., E-mail: Vladimir.Osipov@uni-due.d; Kanzieper, Eugene, E-mail: Eugene.Kanzieper@hit.ac.i; Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100

    Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of {tau} functions, we (i) identify a zoo of hierarchical relations satisfied by {tau} functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasismore » is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.« less

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