WorldWideScience

Sample records for two-dimensional hilbert space

  1. Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence

    CERN Document Server

    Tan, H S; Meng, Jianping

    2014-01-01

    In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed $\\omega(x,y)$ in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang Transform, to a vorticity field obtained from a $8192^2$ grid-points direct numerical simulation of the 2D turbulence with a forcing scale $k_f=100$ and an Ekman friction. The measured joint probability density function $p(C,k)$ of mode $C_i(x)$ of the vorticity $\\omega$ and instantaneous wavenumber $k(x)$ is separated by the forcing scale $k_f$ into two parts, which corresponding to the inverse energy cascade and the forward enstrophy cascade. It is found that all conditional pdf $p(C\\vert k)$ at given wavenumber $k$ has an exponential tail. In the inverse energy cascade, the shape of $p(C\\vert k)$ does collapse with each other, indicating a nonintermittent cascade. The measured scaling exponent $\\zeta_{\\omega}^I(q)$ is linear with the statistical ord...

  2. Tomography in Hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Marmo, G; Simoni, A; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)

    2007-11-15

    We present a method of constructing the tomographic probability distributions describing quantum states in parallel with density operators in abstract Hilbert spaces. After the study of an infinite dimensional example, the well known Husimi-Kano quasi-distribution is reconsidered in the new setting and a new tomographic scheme based on coherent states is suggested. Starting from the Sudarshan's diagonal coherent state representation, the associated identity decomposition providing Gram-Schmidt operators is explicitly given.

  3. Operators on Hilbert space

    CERN Document Server

    Sunder, V S

    2016-01-01

    The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators. .

  4. Quantitative interferometric microscopy with two dimensional Hilbert transform based phase retrieval method

    Science.gov (United States)

    Wang, Shouyu; Yan, Keding; Xue, Liang

    2017-01-01

    In order to obtain high contrast images and detailed descriptions of label free samples, quantitative interferometric microscopy combining with phase retrieval is designed to obtain sample phase distributions from fringes. As accuracy and efficiency of recovered phases are affected by phase retrieval methods, thus approaches owning higher precision and faster processing speed are still in demand. Here, two dimensional Hilbert transform based phase retrieval method is adopted in cellular phase imaging, it not only reserves more sample specifics compared to classical fast Fourier transform based method, but also overcomes disadvantages of traditional algorithm according to Hilbert transform which is a one dimensional processing causing phase ambiguities. Both simulations and experiments are provided, proving the proposed phase retrieval approach can acquire quantitative sample phases with high accuracy and fast speed.

  5. EXTENSION OF THE PROJECTION THEOREM ON HILBERT SPACE TO FUZZY HILBERT SPACE OVER FUZZY NUMBER SPACE

    OpenAIRE

    K. P. DEEPA; Dr.S.Chenthur Pandian

    2012-01-01

    In this paper, we extend the projection theorem on Hilbert space to its fuzzy version over fuzzy number space embedded with fuzzy number mapping. To prove this we discuss the concepts of fuzzy Hilbert space over fuzzy number space with fuzzy number mapping. The fuzzy orthogonality, fuzzy orthonormality, fuzzy complemented subset property etc. of fuzzy Hilbert space over fuzzy number space using fuzzy number mapping also been discussed.

  6. Hilbert-Schmidt Geometry of n-Level Jakobczyk-Siennicki Two-Dimensional Quantum Systems

    CERN Document Server

    Slater, P B

    2005-01-01

    Jakobczyk and Siennicki studied two-dimensional sections of a set of Bloch vectors corresponding to n x n density matrices of two-qubit systems (that is, the case n=4). They found essentially five different types of (nontrivial) separability regimes. We compute the Euclidean/Hilbert-Schmidt (HS) separability probabilities assigned to these regimes, and conduct parallel two-dimensional section analyses for the cases n=6,8,9 and 10. We obtain a very wide variety of exact HS-probabilities. For n>6, the probabilities are those of having a partial positive transpose (PPT). For the n=6 case, we also obtain biseparability probabilities; in the n=8,9 instances, bi-PPT probabilities; and for n=8, tri-PPT probabilities. By far, the most frequently recorded probability for n>4 is Pi/4 = 0.785398$. We also conduct a number of related analyses, pertaining to the (one-dimensional) boundaries (both exterior and interior) of the separability and PPT domains, and discuss some exact calculations pertaining to the 9-dimensional...

  7. Structure of Hilbert space operators

    CERN Document Server

    Jiang, Chunlan

    2006-01-01

    This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K -theory, complex geometry and operator algebra tools. Sample Chapter(s). Chapter 1: Background (153 KB). Contents: Jordan Standard Theorem and K 0 -Group; Approximate Jordan Theorem of Opera

  8. Linear systems and operators in Hilbert space

    CERN Document Server

    Fuhrmann, Paul A

    2014-01-01

    A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.

  9. Geometrical Underpinning of Finite Dimensional Hilbert space

    CERN Document Server

    Revzen, M

    2011-01-01

    Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of Hilbert space operators that form mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among them revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.

  10. Radon Transform for Finite Dimensional Hilbert Space

    CERN Document Server

    Revzen, M

    2012-01-01

    Finite dimensional, d, Hilbert space operators are underpinned with ?nite geometry. The analysis emphasizes a central role for mutual unbiased bases (MUB) states projectors. Interrelation among the Hilbert space operators revealed via their (?nite) dual a?ne plane geometry (DAPG) underpin- ning is studied and utilized in formulating a ?nite dimensional Radon transformation. The ?nite geometry required for our study is outlines.

  11. Geometrical Underpinning of Finite Dimensional Hilbert space

    OpenAIRE

    Revzen, M.

    2011-01-01

    Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.

  12. Rigged Hilbert spaces for chaotic dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Suchanecki, Z. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels (Belgium)]|[Hugo Steinhaus Center and Institute of Mathematics, Wrocl/aw Technical University, ul. Wybrzeze Wyspianskiego 27, 50-370 Wroclaw (Poland); Antoniou, I. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels (Belgium)]|[Theoretische Natuurkunde Free University of Brussels; Tasaki, S. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels, Belgium and]|[Institute for Fundamental Chemistry 34-4 Takano Nishihiraki-cho Kyoto 606 (Japan); Bandtlow, O.F. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels (Belgium)]|[Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB30HE (United Kingdom)

    1996-11-01

    We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. {copyright} {ital 1996 American Institute of Physics.}

  13. Introduction to spectral theory in Hilbert space

    CERN Document Server

    Helmberg, Gilbert; Koiter, W T

    1969-01-01

    North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of lin

  14. Hilbert space methods in partial differential equations

    CERN Document Server

    Showalter, Ralph E

    1994-01-01

    This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

  15. Theory of linear operators in Hilbert space

    CERN Document Server

    Akhiezer, N I

    1993-01-01

    This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

  16. Radon Transform in Finite Dimensional Hilbert Space

    OpenAIRE

    Revzen, M.

    2012-01-01

    Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechani...

  17. Hilbert space theory of classical electrodynamics

    Indian Academy of Sciences (India)

    RAJAGOPAL A K; GHOSE PARTHA

    2016-06-01

    Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, {\\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.

  18. Frames and Bases in Tensor Products of Hilbert Spaces and Hilbert *-Modules

    Indian Academy of Sciences (India)

    Amir Khosravi; Behrooz Khosravi

    2007-02-01

    In this article, we study tensor product of Hilbert *-modules and Hilbert spaces. We show that if is a Hilbert -module and is a Hilbert -module, then tensor product of frames (orthonormal bases) for and produce frames (orthonormal bases) for Hilbert $A \\otimes B$-module $E \\otimes F$, and we get more results. For Hilbert spaces and , we study tensor product of frames of subspaces for and , tensor product of resolutions of the identities of and , and tensor product of frame representations for and .

  19. Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

    Energy Technology Data Exchange (ETDEWEB)

    Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)

    2014-10-15

    We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

  20. Coherent states in projected Hilbert spaces

    Science.gov (United States)

    Drummond, P. D.; Reid, M. D.

    2016-12-01

    Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with postselected measurement results. In these cases, only a part of the Hilbert space needs to be represented, and one can define this restriction by way of a projection operator. Here coherent state bases and normally ordered phase-space representations are introduced for treating such projected Hilbert spaces, including existence theorems and dynamical equations. These techniques are very useful in studying novel optical or microwave integrated photonic quantum technologies, such as boson sampling or Josephson quantum computers. In these cases, states become strongly restricted due to inputs, nonlinearities, or conditional measurements. This paper focuses on coherent phase states, which have especially simple properties. Practical applications are reported on calculating recurrences in anharmonic oscillators, the effects of arbitrary phase noise on Schrödinger cat fringe visibility, and on boson sampling interferometry for large numbers of modes.

  1. More on (,-Normal Operators in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Rasoul Eskandari

    2012-01-01

    Full Text Available We study some properties of (,-normal operators and we present various inequalities between the operator norm and the numerical radius of (,-normal operators on Banach algebra ℬ(ℋ of all bounded linear operators ∶ℋ→ℋ, where ℋ is Hilbert space.

  2. Invariant Hilbert spaces of holomorphic functions

    NARCIS (Netherlands)

    Faraut, J; Thomas, EGF

    1999-01-01

    A Hilbert space of holomorphic functions on a complex manifold Z, which is invariant under a group G of holomorphic automorphisms of Z, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on Z and G which implies that this decomposition is multiplicity

  3. Quantum mechanics in finite dimensional Hilbert space

    CERN Document Server

    de la Torre, A C

    2002-01-01

    The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.

  4. Hilbert space for quantum mechanics on superspace

    CERN Document Server

    Coulembier, Kevin

    2011-01-01

    In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed.

  5. Hilbert space for quantum mechanics on superspace

    Science.gov (United States)

    Coulembier, K.; De Bie, H.

    2011-06-01

    In superspace a realization of {sl}_2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the {sl}_2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

  6. Elements of Hilbert spaces and operator theory

    CERN Document Server

    Vasudeva, Harkrishan Lal

    2017-01-01

    The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...

  7. Basis-neutral Hilbert-space analyzers

    CERN Document Server

    Martin, Lane; Kondakci, H Esat; Larson, Walker D; Shabahang, Soroush; Jahromi, Ali K; Malhotra, Tanya; Vamivakas, A Nick; Atia, George K; Abouraddy, Ayman F

    2016-01-01

    Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes -- a critical task for spatial-mode multiplexing and quantum communication -- basis-specific principles are invoked that are altogether distinct from that of `delay.' Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis -- exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a `delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, rec...

  8. Penalty Algorithms in Hilbert Spaces

    Institute of Scientific and Technical Information of China (English)

    Jean Pierre DUSSAULT; Hai SHEN; André BANDRAUK

    2007-01-01

    We analyze the classical penalty algorithm for nonlinear programming in HUbert spaces and obtain global convergence results, as well as asymptotic superlinear convergence order. These convergence results generalize similar results obtained for finite-dimensional problems. Moreover, the nature of the algorithms allows us to solve the unconstrained subproblems in finite-dimensional spaces.

  9. Functional Analysis: Entering Hilbert Space

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded...... of the new material on normed vector spaces and their operators, the book can hopefully serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them....... in a new chapter on Fredholm theory (Chapter 6). Fredholm theory originates in pioneering work of the Swedish mathematician Erik Ivar Fred-holm on integral equations, which inspired the study of a new class of bounded linear operators, known as Fredholm operators. Chapter 6 presents the basic elements...

  10. STATIONARY CONNECTED CURVES IN HILBERT SPACES

    Directory of Open Access Journals (Sweden)

    Raed Hatamleh

    2014-01-01

    Full Text Available In this article the structure of non-stationary curves which are stationary connected in Hilbert space is studied using triangular models of non-self-adjoint operator. The concept of evolutionary representability plays here an important role. It is proved that if one of two curves in Hilbert space is evolutionary representable and the curves are stationary connected, then another curve is evolutionary representable too. These curves are studied firstly. The structure of a cross-correlation function in the case when operator, defining the evolutionary representation, has one-dimensional non-Hermitian subspace (the spectrum is discreet and situated in the upper complex half-plane or has infinite multiplicity at zero (Volterra operator is studied.

  11. Rigidity of contractions on Hilbert spaces

    CERN Document Server

    Eisner, Tanja

    2009-01-01

    We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times the identity operator in the strong limit set of its powers, while $T^{n_j}$ converges weakly to zero along a sequence $\\{n_j\\}$ with density one. The continuous analogue is presented for isometric ang unitary $C_0$-(semi)groups.

  12. Sparse Signal Recovery in Hilbert Spaces

    CERN Document Server

    Pope, Graeme

    2012-01-01

    This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the number of (possibly infinite-dimensional) subspaces participating in the signal's representation. Our general results recover uncertainty relations and coherence-based recovery thresholds for sparse signals, block-sparse signals, multi-band signals, signals in shift-invariant spaces, and signals in finite unions of (possibly infinite-dimensional) subspaces. Moreover, we improve upon and generalize several of the existing results and, in many cases, we find shortened and simplified proofs.

  13. Quantum Holonomy Theory and Hilbert Space Representations

    CERN Document Server

    Aastrup, Johannes

    2016-01-01

    We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state exist is left for later publications.

  14. Quantum mechanics in an evolving Hilbert space

    CERN Document Server

    Artacho, Emilio

    2016-01-01

    Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalisation, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fibre bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge imp...

  15. A distribution space for Hilbert transform and its applications

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, a new distribution space DH is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that DH is the biggest subspace of D on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in DH. Finally, the applications of the extended Hilbert transform are discussed.

  16. A distribution space for Hilbert transform and its applications

    Institute of Scientific and Technical Information of China (English)

    YANG LiHua

    2008-01-01

    In this paper, a new distribution space D'H is constructed and the definition of the classical Hilbert transform is extended to it, It is shown that D'H is the biggest subspace of D' on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in D'H. Finally, the applications of the extended Hilbert transform are discussed.

  17. SpaceTime from Hilbert Space: Decompositions of Hilbert Space as Instances of Time

    CERN Document Server

    Noorbala, Mahdiyar

    2016-01-01

    There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting geometry looks like. We then propose that time may be regarded as a variable that parameterizes a family of such decompositions, thus giving rise to a family of spatial geometries. As a proof of concept, this idea is demonstrated in two toy models based on Kitaev's toric code, which feature a dynamical change of dimension and topology.

  18. Eigenfunction expansions and scattering theory in rigged Hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es

    2008-08-15

    The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.

  19. Quantum mechanics in an evolving Hilbert space

    Science.gov (United States)

    Artacho, Emilio; O'Regan, David D.

    2017-03-01

    Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.

  20. Kinks in two-dimensional Anti-de Sitter Space

    CERN Document Server

    Barnes, J L; ter Veldhuis, T; Webster, M J

    2009-01-01

    Soliton solutions in scalar field theory defined on a two-dimensional Anti-de Sitter background space-time are investigated. It is shown that the lowest soliton excitation generically has frequency equal to the inverse radius of the space-time. Analytic and numerical soliton solutions are determined in "phi to the fourth" scalar field theory with a negative mass-squared. The classical soliton mass is calculated as a function of the ratio of the square of the mass scale of the field theory over the curvature of the space-time. For the case that this ratio equals unity, the soliton excitation spectrum is determined algebraically and the one-loop radiative correction to the soliton mass is computed in the semi-classical approximation.

  1. Quantum holonomy theory and Hilbert space representations

    Energy Technology Data Exchange (ETDEWEB)

    Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)

    2016-11-15

    We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  2. Relations between Stochastic and Partial Differential Equations in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    I. V. Melnikova

    2012-01-01

    Full Text Available The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation and solutions to the deterministic partial differential (with derivatives in Hilbert spaces equation for the probability characteristic is proved. Interpretation of objects in the equations is given.

  3. Contributions to the extension theory in Hilbert spaces

    NARCIS (Netherlands)

    Sandovici, Valerica Adrian; Sandovici, 27740

    2006-01-01

    This thesis presents solutions to certain problems in the extension theory in Hilbert spaces. Basically there are three main parts of the thesis corresponding to three objects which are studied. The first part consists of chapter 3 and deals with Lagrangian pairs in a pair of Hilbert spaces. In the

  4. Tools for analysis of Dirac structures on Hilbert spaces

    NARCIS (Netherlands)

    Golo, G.; Iftime, O.V.; Zwart, Heiko J.; van der Schaft, Arjan

    2004-01-01

    In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are presented. The theory is illustrated on the example of the ideal transmission line.

  5. Random diffusion and cooperation in continuous two-dimensional space.

    Science.gov (United States)

    Antonioni, Alberto; Tomassini, Marco; Buesser, Pierre

    2014-03-07

    This work presents a systematic study of population games of the Prisoner's Dilemma, Hawk-Dove, and Stag Hunt types in two-dimensional Euclidean space under two-person, one-shot game-theoretic interactions, and in the presence of agent random mobility. The goal is to investigate whether cooperation can evolve and be stable when agents can move randomly in continuous space. When the agents all have the same constant velocity cooperation may evolve if the agents update their strategies imitating the most successful neighbor. If a fitness difference proportional is used instead, cooperation does not improve with respect to the static random geometric graph case. When viscosity effects set-in and agent velocity becomes a quickly decreasing function of the number of neighbors they have, one observes the formation of monomorphic stable clusters of cooperators or defectors in the Prisoner's Dilemma. However, cooperation does not spread in the population as in the constant velocity case.

  6. Hilbert Space Operators in Quantum Physics

    CERN Document Server

    Blank, Jiří; Havlíček, Miloslav

    2008-01-01

    The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs. Some praise for the previous edition: "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands...

  7. Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincar\\'e symmetry

    CERN Document Server

    Oppio, Marco

    2016-01-01

    As established by Sol\\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this issue from another viewpoint, we argue that there is a fundamental reason why elementary quantum systems are not described in real Hilbert spaces: their symmetry group. We consider an elementary relativistic system within Wigner's approach defined as a faithful irreducible continuous unitary representation of the Poincar\\'e group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincar\\'e invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation. All that leads to a physically equivalent formulation in a complex Hilbert space. Differently from what happens in the real picture, here all selfadjoint operators are observables in accor...

  8. Hilbert space, Poincare dodecahedron and golden mean transfiniteness

    Energy Technology Data Exchange (ETDEWEB)

    El Naschie, M.S. [Department of Physics, University of Alexandria, Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)

    2007-02-15

    A rather direct connection between Hilbert space and E-infinity theory is established via an irrational-transfinite golden mean topological probability. Subsequently the ramifications for Kleinian modular spaces and the cosmological Poincare Dodecahedron proposals are considered.

  9. Partial Differential Equations A unified Hilbert Space Approach

    CERN Document Server

    Picard, Rainer

    2011-01-01

    This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. Thefocus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations.This global point of view is takenby focussing on the issues involved in determining the appropriate func

  10. Some remarks about interpolating sequences in reproducing kernel Hilbert spaces

    CERN Document Server

    Raghupathi, Mrinal

    2011-01-01

    In this paper we study two separate problems on interpolation. We first give a new proof of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence for the multiplier algebra and for an associated Hilbert space. We next turn our attention to the question of interpolation for reproducing kernel Hilbert spaces on the polydisc and provide a collection of equivalent statements about when it is possible to interpolation in the Schur-Agler class of the associated reproducing kernel Hilbert space.

  11. Analytic Characterization for Hilbert-Schmidt Operators on Fock Space

    Institute of Scientific and Technical Information of China (English)

    Cai Shi WANG; Zhi Yuan HUANG; Xiang Jun WANG

    2005-01-01

    In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.

  12. Isometric Reflection Vectors and Characterizations of Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Donghai Ji

    2014-01-01

    Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.

  13. Space from Hilbert space: Recovering geometry from bulk entanglement

    Science.gov (United States)

    Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon

    2017-01-01

    We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of "redundancy-constrained states" in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER =EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.

  14. Space from Hilbert Space: Recovering Geometry from Bulk Entanglement

    CERN Document Server

    Cao, ChunJun

    2016-01-01

    We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\\mathcal{H}$ into a tensor product of factors, we consider a class of "redundancy-constrained states" in $\\mathcal{H}$ that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of...

  15. Hilbert space renormalization for the many-electron problem

    CERN Document Server

    Li, Zhendong

    2015-01-01

    Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the 'physical indices' or the coupling rules in the HS-MPS. Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to a family of size-extensive wav...

  16. The 2-Hilbert Space of a Prequantum Bundle Gerbe

    CERN Document Server

    Bunk, Severin; Szabo, Richard J

    2016-01-01

    We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantisation, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantisation. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantisation in this setting, including its dimensional reductio...

  17. Automorphisms of Hilbert space effect algebras

    Science.gov (United States)

    Šemrl, Peter

    2015-05-01

    Let H be a Hilbert space and E (H) the effect algebra on H. A bijective map φ :E(H)\\to E(H) is called an ortho-order automorphism of E (H) if for every A,B\\in E(H) we have A≤slant B \\Longleftrightarrow φ (A)≤slant φ (B) and φ ({{A}\\bot })=φ {{(A)}\\bot }. The classical theorem of Ludwig states that every such ϕ is of the form φ (A)=UA{{U}*}, A\\in E(H), for some unitary or antiunitary operator U. It is also known that each bijective map on E (H) preserving order and coexistency in both directions is of the same form. Can we improve these two theorems by relaxing the bijectivity assumption and/or replacing the above preserving properties by the weaker assumptions of preserving above relations in one direction only and still get the same conclusion? For both characterizations of automorphisms of effect algebras we will prove the optimal versions and give counterexamples showing the optimality of the obtained results. This research was supported by a grant from ARRS, Slovenia.

  18. Snakes and articulated arms in an Hilbert space

    CERN Document Server

    Pelletier, Fernand

    2011-01-01

    The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space

  19. The Hilbert Inequality in Banach Spaces%Banach空间上的Hilbert不等式

    Institute of Scientific and Technical Information of China (English)

    华柳斌; 黎永锦

    2011-01-01

    Some Hilbert's inequalities in Hilbert spaces and Banach spaces were discussed by inner and functional. The Hilbert spaces and Banach space version of Hilbert's inequalities were established.%利用内积和泛函,在Hilbert空间和Banach空间中讨论Hilbert不等式,建立了抽象空间的Hilbert不等式.

  20. A primer on Hilbert space theory linear spaces, topological spaces, metric spaces, normed spaces, and topological groups

    CERN Document Server

    Alabiso, Carlo

    2015-01-01

    This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...

  1. Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces

    Science.gov (United States)

    Simon, David S.; Fitzpatrick, Casey A.; Sergienko, Alexander V.

    2015-04-01

    We propose an interferometric method for statistically discriminating between nonorthogonal states in high-dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital angular momentum (OAM) states. These states belong to pairs of bases that are mutually unbiased on a sequence of two-dimensional subspaces of the full Hilbert space, but the vectors within the same basis are not necessarily orthogonal to each other. Over multiple trials, this method allows distinguishing OAM eigenstates from superpositions of multiple such eigenstates. Variations of the same method are then shown to be capable of preparing and detecting arbitrary linear combinations of states in Hilbert space. One further variation allows the construction of chains of states obeying recurrence relations on the Hilbert space itself, opening a new range of possibilities for more abstract information-coding algorithms to be carried out experimentally in a simple manner. Among other applications, we show that this approach provides a simplified means of switching between pairs of high-dimensional mutually unbiased OAM bases.

  2. On the Inclusion Relation of Reproducing Kernel Hilbert Spaces

    OpenAIRE

    Zhang, Haizhang; Zhao, Liang

    2011-01-01

    To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of ...

  3. Hilbert Space of Probability Density Functions Based on Aitchison Geometry

    Institute of Scientific and Technical Information of China (English)

    J. J. EGOZCUE; J. L. D(I)AZ-BARRERO; V. PAWLOWSKY-GLAHN

    2006-01-01

    The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison's ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.

  4. Securing QKD Li01nks in the Full Hilbert Space

    CERN Document Server

    Jackson, David J

    2004-01-01

    Many quantum key distribution analyses examine the link security in a subset of the full Hilbert space that is available to describe the system. In reality, information about the photon state can be embedded in correlations between the polarization space and other dimensions of the Hilbert space in such a way that Eve can determine the polarization of a photon without affecting it. This paper uses the concept of suitability to quantify the available information for Eve, and then describe a systematic way to calculate and measure these possibilities.

  5. Two-dimensional imaginary lobachevsky space. Separation of variables and contractions

    Energy Technology Data Exchange (ETDEWEB)

    Pogosyan, G. S., E-mail: pogosyan@theor.jinr.ru; Yakhno, A. [Universidad de Guadalajara, Departamento de Matematicas, CUCEI (Mexico)

    2011-07-15

    The Inoenue-Wigner contraction from the SO(2, 1) group to the E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the corresponding two-dimensional homogeneous spaces: two-dimensional one sheeted hyperboloid and two-dimensional pseudo-Euclidean space. Here we consider the contraction limits of some basis functions for the subgroup coordinates only.

  6. ON APPROXIMATION BY SPHERICAL REPRODUCING KERNEL HILBERT SPACES

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given.

  7. Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras

    Directory of Open Access Journals (Sweden)

    Qing Yuan

    2014-01-01

    Full Text Available Let ℰ(H be the Hilbert space effect algebra on a Hilbert space H with dim⁡H≥3, α,β two positive numbers with 2α+β≠1 and Φ:ℰ(H→ℰ(H a bijective map. We show that if Φ(AαBβAα=Φ(AαΦ(BβΦ(Aα holds for all A,B∈ℰ(H, then there exists a unitary or an antiunitary operator U on H such that Φ(A=UAU* for every A∈ℰ(H.

  8. Coarsely Invariant Hilbert Spaces over Infinite Connected Graphs

    Institute of Scientific and Technical Information of China (English)

    WANG Qin

    2002-01-01

    We study in this paper a Hilbert space HV associated with the coarse geometry of an infinite connected graph X(V, E) with vertex set V and edge set E. We show that X(V,E) is uniformly expanding if and only ifl2(V)can be continuously included in HV as a closed subspace,and that the inner product structure of HV is topologically invariant under uniform coarsening of the graph. We also discuss the functorial properties of these Hilbert spaces.

  9. Hilbert space renormalization for the many-electron problem.

    Science.gov (United States)

    Li, Zhendong; Chan, Garnet Kin-Lic

    2016-02-28

    Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.

  10. On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space

    Directory of Open Access Journals (Sweden)

    Hamdy M. Ahmed

    2009-01-01

    Full Text Available We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.

  11. Perturbation for Frames for a Subspace of a Hilbert Space

    DEFF Research Database (Denmark)

    Christensen, Ole; deFlicht, C.; Lennard, C.

    1997-01-01

    We extend a classical result stating that a sufficiently small perturbation$\\{ g_i \\}$ of a Riesz sequence $\\{ f_i \\}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very...

  12. Approximate controllability of semilinear neutral systems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    N. I. Mahmudov

    2003-01-01

    Full Text Available The approximate controllability of semilinear neutral systems in Hilbert spaces is studied using the Schauder fixed point theorem. It is shown that the approximate controllability of the semilinear system under some conditions is implied by the approximate controllability of its linear part.

  13. Canonical analysis of scalar fields in two-dimensional curved space

    Science.gov (United States)

    McKeon, D. G. C.; Patrushev, Alexander

    2011-12-01

    Scalar fields on a two-dimensional curved surface are considered and the canonical structure of this theory analyzed. Both the first- and second-order forms of the Einstein-Hilbert (EH) action for the metric are used (these being inequivalent in two dimensions). The Dirac constraint formalism is used to find the generator of the gauge transformation, using the formalisms of Henneaux, Teitelboim and Zanelli (HTZ) and of Castellani (C). The HTZ formalism is slightly modified in the case of the first-order EH action to accommodate the gauge transformation of the metric; this gauge transformation is unusual as it mixes the affine connection with the scalar field.

  14. A geometric approach to quantum control in projective hilbert spaces

    Science.gov (United States)

    Pastorello, Davide

    2017-02-01

    A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper geometric Hamiltonian theory as explained in [2, 3, 7, 9]. From this point of view a quantum system can be described within a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by a projective Hilbert space. This paper is devoted to investigating how the notion of an accessibility algebra from classical control theory can be applied within the geometric Hamiltonian formulation of quantum mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. the Fubini-Study metric on projective space is also discussed.

  15. On Space Efficient Two Dimensional Range Minimum Data Structures

    DEFF Research Database (Denmark)

    Davoodi, Pooya; Brodal, Gerth Stølting; Rao, S. Srinivasa

    2010-01-01

    , the lower bound is tight up to a constant factor. In two dimensions, we complement the lower bound with an indexing data structure of size O(N/c) bits additional space which can be preprocessed in O(N) time and achieves O(clog2 c) query time. For c = O(1), this is the first O(1) query time algorithm using...... optimal O(N) bits additional space. For the case where queries can not probe A, we give a data structure of size O(N· min {m,logn}) bits with O(1) query time, assuming m ≤ n. This leaves a gap to the lower bound of Ω(Nlogm) bits for this version of the problem....

  16. On Space Efficient Two Dimensional Range Minimum Data Structures

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Davoodi, Pooya; Rao, S. Srinivasa

    2012-01-01

    the space and query time of the problem. We show that every algorithm enabled to access A during the query and using a data structure of size O(N/c) bits requires Ω(c) query time, for any c where 1≤c≤N. This lower bound holds for arrays of any dimension. In particular, for the one dimensional version...... of the problem, the lower bound is tight up to a constant factor. In two dimensions, we complement the lower bound with an indexing data structure of size O(N/c) bits which can be preprocessed in O(N) time to support O(clog 2 c) query time. For c=O(1), this is the first O(1) query time algorithm using a data...... structure of optimal size O(N) bits. For the case where queries can not probe A, we give a data structure of size O(N⋅min {m,log n}) bits with O(1) query time, assuming m≤n. This leaves a gap to the space lower bound of Ω(Nlog m) bits for this version of the problem...

  17. Observables and density matrices embedded in dual Hilbert spaces

    Science.gov (United States)

    Prosen, T.; Martignon, L.; Seligman, T. H.

    2015-06-01

    The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between {{L}}2({{R}}) and the Bargmann-Hilbert space. We pursue this line of thinking one step further and discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

  18. Hörmander multipliers on two-dimensional dyadic Hardy spaces

    Science.gov (United States)

    Daly, J.; Fridli, S.

    2008-12-01

    In this paper we are interested in conditions on the coefficients of a two-dimensional Walsh multiplier operator that imply the operator is bounded on certain of the Hardy type spaces Hp, 0Dokl. Akad. Nauk SSSR 109 (1956) 701-703; S.G. Mihlin, Multidimensional Singular Integrals and Integral Equations, Pergamon Press, 1965]. In this paper we extend these results to the two-dimensional dyadic Hardy spaces.

  19. The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces

    NARCIS (Netherlands)

    Ćurgus, Branko; Dijksma, Aad; Read, Tom

    2001-01-01

    The boundary eigenvalue problems for the adjoint of a symmetric relation S in a Hilbert space with finite, not necessarily equal, defect numbers, which are related to the selfadjoint Hilbert space extensions of S are characterized in terms of boundary coefficients and the reproducing kernel Hilbert

  20. Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Zoryana Mozhyrovska

    2015-01-01

    Full Text Available We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.

  1. Precise Asymptotics for Complete Moment Convergence in Hilbert Spaces

    Indian Academy of Sciences (India)

    Keang Fu; Juan Chen

    2012-02-01

    Let $\\{X, X_n;n≥ 1\\}$ be a sequence of i.i.d. random variables taking values in a real separable Hilbert space $(H,\\|\\cdot p\\|)$ with covariance operator $\\sum$. Set $S_n=\\sum^n_{i=1}X_i,n≥ 1$. We prove that for 1 < < 2 and $r>1+p/2$, \\begin{multline*}\\lim\\limits_{\\searrow 0}^{(2r-p-2)/(2-p)}\\sum\\limits^∞_{n=1}n^{r/p-2-1/p}E\\{\\|S_n\\|- n^{1/p}\\}+\\\\ =^{-(2r-2-p)/(2-p)}\\frac{p(2-p)}{(r-p)(2r-p-2)}E\\|Y\\|^{2(r-p)/(2-p)},\\end{multline*} where is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator , and 2 is the largest eigenvalue of .

  2. Hilbert space structure in quantum gravity: an algebraic perspective

    CERN Document Server

    Giddings, Steven B

    2015-01-01

    If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of...

  3. Finite-part singular integral approximations in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    E. G. Ladopoulos

    2004-01-01

    Full Text Available Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.

  4. Separability criteria with angular and Hilbert space averages

    Science.gov (United States)

    Fujikawa, Kazuo; Oh, C. H.; Umetsu, Koichiro; Yu, Sixia

    2016-05-01

    The practically useful criteria of separable states ρ =∑kwkρk in d = 2 × 2 are discussed. The equality G(a , b) = 4 [ - ] = 0 for any two projection operators P(a) and P(b) provides a necessary and sufficient separability criterion in the case of a separable pure state ρ = | ψ > Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average.

  5. A construction of full qed using finite dimensional Hilbert space

    OpenAIRE

    Francis, Charles

    2006-01-01

    While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I present a rigorous construction of quantum and classical electrodynamics from fundamental principles of quantum theory. Hilbert space of dimension N is justified from statements about measurements with finite range and resolution. Using linear combinations o...

  6. Differential representations of dynamical oscillator symmetries in discrete Hilbert space

    Directory of Open Access Journals (Sweden)

    Andreas Ruffing

    2000-01-01

    Full Text Available As a very important example for dynamical symmetries in the context of q-generalized quantum mechanics the algebra aa†−q−2a†a=1 is investigated. It represents the oscillator symmetry SUq(1,1 and is regarded as a commutation phenomenon of the q-Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert space structure. Generalized q-Hermite functions and systems of creation and annihilation operators are derived. The classical limit q→1 is investigated. Finally the SUq(1,1 algebra is represented by the dynamical variables of the q-Heisenberg algebra.

  7. Cantorian spacetime and Hilbert space: Part I-Foundations

    Energy Technology Data Exchange (ETDEWEB)

    Iovane, G. [Dipartimento di Ingegneria dell' Informazione e Matematica Applicata, Universita di Salerno, Via Ponte Don Melillo, 84084 Fisicano, SA (Italy)]. E-mail: iovane@diima.unisa.it

    2006-05-15

    We are going to show the link between the {epsilon} {sup ({infinity})} Cantorian space and the Hilbert spaces H {sup ({infinity})}. In particular, El Naschie's {epsilon} {sup ({infinity})} is a physical spacetime, i.e. an infinite dimensional fractal space, where time is spacialized and the transfinite nature manifests itself. El Naschie's Cantorian spacetime is an arena where the physics laws appear at each scale in a self-similar way linked to the resolution of the act of observation. By contrast the Hilbert space H {sup ({infinity})} is a mathematical support, which describes the interaction between the observer and the dynamical system under measurement. The present formulation, which is based on the non-classical Cantorian geometry and topology of spacetime, automatically solves the paradoxical outcome of the two-slit experiment and the so-called particle-wave duality. In particular, measurement (i.e. the observation) is equivalent to a projection of {epsilon} {sup ({infinity})} in the Hilbert space built on 3 + 1 Euclidean spacetime. Consequently, the wave-particle duality becomes a mere natural consequence of conducting an experiment in a spacetime with non-classical topological and geometrical structures, while observing and taking measurements in a classical smooth 3 + 1 Euclidean spacetime. In other words, the experimental fact that a wave-particle duality exists is an indirect confirmation of the existence of {epsilon} {sup ({infinity})} and a property of the quantum-classical interface. Another direct consequence of the fact that real spacetime is infinite dimensional hierarchical {epsilon} {sup ({infinity})} is the existence of scaling law R(N), introduced by the author, which generalizes the Compton wavelength. It gives an answer to the problem of segregation of matter at different scales, and shows the role of fundamental constants such as the speed of light and Plank's constant h in the fundamental lengths scale without invoking the

  8. Explicit signal to noise ratio in reproducing kernel Hilbert spaces

    DEFF Research Database (Denmark)

    Gomez-Chova, Luis; Nielsen, Allan Aasbjerg; Camps-Valls, Gustavo

    2011-01-01

    This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose...... an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted...

  9. Real analysis measure theory, integration, and Hilbert spaces

    CERN Document Server

    Stein, Elias M

    2005-01-01

    Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After

  10. 3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries

    DEFF Research Database (Denmark)

    Ujang, Uznir; Antón Castro, Francesc/François; Azri, Suhaibah;

    2014-01-01

    are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a sub-interval of the ([0,1]) interval to the corresponding...... method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban...... web standards. However, these 3D city models consume much more storage compared to two dimensional (2 D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access...

  11. Divide and conquer the Hilbert space of translation-symmetric spin systems.

    Science.gov (United States)

    Weisse, Alexander

    2013-04-01

    Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin [Phys. Rev. B 42, 6561 (1990)]. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^{11} become accessible.

  12. Invitation to linear operators from matrices to bounded linear operators on a Hilbert space

    CERN Document Server

    Furuta, Takayuki

    2014-01-01

    Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developm

  13. Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time

    Institute of Scientific and Technical Information of China (English)

    YAN Jun

    2005-01-01

    The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.

  14. Hilbert space structure in quantum gravity: an algebraic perspective

    Science.gov (United States)

    Giddings, Steven B.

    2015-12-01

    If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.

  15. Two-dimensional relativistic space charge limited current flow in the drift space

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Y. L.; Chen, S. H., E-mail: chensh@ncu.edu.tw [Department of Physics, National Central University, Jhongli 32001, Taiwan (China); Koh, W. S. [A-STAR Institute of High Performance Computing, Singapore 138632 (Singapore); Ang, L. K. [Engineering Product Development, Singapore University of Technology and Design, Singapore 138682 (Singapore)

    2014-04-15

    Relativistic two-dimensional (2D) electrostatic (ES) formulations have been derived for studying the steady-state space charge limited (SCL) current flow of a finite width W in a drift space with a gap distance D. The theoretical analyses show that the 2D SCL current density in terms of the 1D SCL current density monotonically increases with D/W, and the theory recovers the 1D classical Child-Langmuir law in the drift space under the approximation of uniform charge density in the transverse direction. A 2D static model has also been constructed to study the dynamical behaviors of the current flow with current density exceeding the SCL current density, and the static theory for evaluating the transmitted current fraction and minimum potential position have been verified by using 2D ES particle-in-cell simulation. The results show the 2D SCL current density is mainly determined by the geometrical effects, but the dynamical behaviors of the current flow are mainly determined by the relativistic effect at the current density exceeding the SCL current density.

  16. New Characterizations of Fusion Bases and Riesz Fusion Bases in Hilbert Spaces

    OpenAIRE

    Asgari, Mohammad Sadegh

    2012-01-01

    In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we define the fusion biorthogonal sequence, Bessel fusion basis, Hilbert fusion basis and obtain some characterizations of them. we study orthonormal fusion systems...

  17. Energy Spectrum of Helium Confined to a Two-Dimensional Space

    Institute of Scientific and Technical Information of China (English)

    XIEWen-Fang

    2005-01-01

    Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional helium in a magnetic field. The results show that the ground and low-excited states of helium in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.

  18. Convex analysis and monotone operator theory in Hilbert spaces

    CERN Document Server

    Bauschke, Heinz H

    2017-01-01

    This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...

  19. Finite-dimensional Hilbert space and frame quantization

    Energy Technology Data Exchange (ETDEWEB)

    Cotfas, Nicolae [Faculty of Physics, University of Bucharest, PO Box 76-54, Post Office 76, Bucharest (Romania); Gazeau, Jean Pierre [Laboratoire APC, Universite Paris Diderot, 10, rue A Domon et L Duquet, 75205 Paris Cedex 13 (France); Vourdas, Apostol, E-mail: ncotfas@yahoo.com, E-mail: gazeau@apc.univ-paris7.fr, E-mail: A.Vourdas@bradford.ac.uk [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)

    2011-04-29

    The quantum observables used in the case of quantum systems with finite-dimensional Hilbert space are defined either algebraically in terms of an orthonormal basis and discrete Fourier transformation or by using a continuous system of coherent states. We present an alternative approach to these important quantum systems based on the finite frame quantization. Finite systems of coherent states, usually called finite tight frames, can be defined in a natural way in the case of finite quantum systems. Novel examples of such tight frames are presented. The quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system. They are obtained by using a finite frame and a Klauder-Berezin-Toeplitz-type quantization. Semi-classical aspects of tight frames are studied through lower symbols of basic classical observables.

  20. Construction and coupling of frames in Hilbert spaces with W-metrics

    Directory of Open Access Journals (Sweden)

    German Escobar

    2016-05-01

    Full Text Available A definition of frames unitarily equivalent in Hilbert spaces with W-metric is stated, and a characterization is given in terms of their respective analysis operators. From a Hilbert space with a frame we construct a Hilbert space with W-metric and a frame unitarily equivalent to the given one. Finally, we prove that the coupling of two frames is a frame. Resumen. Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.

  1. Corner-Space Renormalization Method for Driven-Dissipative Two-Dimensional Correlated Systems.

    Science.gov (United States)

    Finazzi, S; Le Boité, A; Storme, F; Baksic, A; Ciuti, C

    2015-08-21

    We present a theoretical method to study driven-dissipative correlated quantum systems on lattices with two spatial dimensions (2D). The steady-state density matrix of the lattice is obtained by solving the master equation in a corner of the Hilbert space. The states spanning the corner space are determined through an iterative procedure, using eigenvectors of the density matrix of smaller lattice systems, merging in real space two lattices at each iteration and selecting M pairs of states by maximizing their joint probability. The accuracy of the results is then improved by increasing the dimension M of the corner space until convergence is reached. We demonstrate the efficiency of such an approach by applying it to the driven-dissipative 2D Bose-Hubbard model, describing lattices of coupled cavities with quantum optical nonlinearities.

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

    Science.gov (United States)

    Fath, Elaine

    2015-03-01

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

  3. Area integral functions and $H^{\\8}$ functional calculus for sectorial operators on Hilbert spaces

    OpenAIRE

    Chen, Zeqian; Sun, Mu

    2012-01-01

    Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi's results on $H^{\\8}$ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.

  4. Recursive estimation of the conditional geometric median in Hilbert spaces

    CERN Document Server

    Cardot, Hervé; Zitt, Pierre-André

    2012-01-01

    A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirms the interest of this new and fast algorithm when the sample sizes are large. Finally, the ability of these recursive algorithms to deal with very high-dimensional data is illustrated on the robust estimation of television audience profiles conditional on the total time spent watching television over a period of 24 hours.

  5. Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mickael D. Chekroun

    2017-07-01

    Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

  6. Hamiltonian and physical Hilbert space in polymer quantum mechanics

    CERN Document Server

    Corichi, A; Zapata, R J A; Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.

    2006-01-01

    In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so called polymer representation of the Heisenberg-Weyl (H-W) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.

  7. Simulating strongly correlated multiparticle systems in a truncated Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Ernst, Thomas; Hallwood, David W.; Gulliksen, Jake; Brand, Joachim [New Zealand Institute for Advanced Study and Centre for Theoretical Chemistry and Physics, Massey University, Private Bag 102904, North Shore, Auckland 0745 (New Zealand); Meyer, Hans-Dieter [Theoretische Chemie, Physikalisch-Chemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)

    2011-08-15

    Representing a strongly interacting multiparticle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. A detailed comparison between finite Hilbert space calculations and exact results for up to five particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground-state energies, the low-lying excitation spectrum, density profile, and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.

  8. Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space

    CERN Document Server

    Setter, Ophir

    2009-05-01

    We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional parametric surfaces in $R^3$. The computation of the diagrams is carried out through the construction of envelopes of surfaces in 3-space provided by CGAL (the Computational Geometry Algorithm Library). The construction of the envelopes follows a divide-and-conquer approach. A straightforward application of the divide-and-conquer approach for computing Voronoi diagrams yields algorithms that are inefficient in the worst case. We prove that through randomization the expected running time becomes near-optimal in the worst case. We show how to employ our framework to realize various types of Voronoi diagrams with different properties by providing implementations for a vast collection of commonly used Voronoi diagrams. We also show how to apply the new framework and other exist...

  9. On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

    Science.gov (United States)

    Falomir, H.; Pisani, P. A. G.; Vega, F.; Cárcamo, D.; Méndez, F.; Loewe, M.

    2016-02-01

    We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras {sl}(2,{{R}}) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.

  10. On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

    CERN Document Server

    Falomir, H; Vega, F; Cárcamo, D; Méndez, F; Loewe, M

    2015-01-01

    We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters. From this perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.

  11. A Two-Dimensional Signal Space for Intensity-Modulated Channels

    CERN Document Server

    Karout, Johnny; Kschischang, Frank R; Agrell, Erik

    2012-01-01

    A two-dimensional signal space for intensity- modulated channels is presented. Modulation formats using this signal space are designed to maximize the minimum distance between signal points while satisfying average and peak power constraints. The uncoded, high-signal-to-noise ratio, power and spectral efficiencies are compared to those of the best known formats. The new formats are simpler than existing subcarrier formats, and are superior if the bandwidth is measured as 90% in-band power. Existing subcarrier formats are better if the bandwidth is measured as 99% in-band power.

  12. The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains

    OpenAIRE

    Chandran, A.; Schulz, M. D.; Burnell, F. J.

    2016-01-01

    Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this article, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned ...

  13. A Hilbert Space setting for higher spin interactions which replaces Gauge Theory

    CERN Document Server

    Schroer, Bert

    2014-01-01

    The recently discovered Hilbert space description of renormalizable interactions of higher spin (equal or bigger than 1) fields requires to replace the pointlocal s=1 vectorpotentials of indefinite metric (Krein space) BRST gauge theory by their stringlike counterpart in Hilbert space. It is shown that the Hilbert space positivity leads to new properties outside the conceptual range of the gauge theoretic description: topological aspects of Wilson loops, induced normalization terms (in particular Mexican hat type potentials for massive vectormesons coupled to Hermitian scalar field) and a possible role of string-localization in confinerment and "darkness".

  14. Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

    Science.gov (United States)

    Ehlers, G.; White, S. R.; Noack, R. M.

    2017-03-01

    The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

  15. THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The multiplier bimodule of Hilbert bimodule is introduced in a way similar to [1],and its realization on a quotient of bidual space and Tietze extension theorem are obtained similar to that in C*-algebra case. As a result,the multiplier bimodule here is also a Hilbert bimodule.

  16. Errors in using two dimensional methods for ergonomic assessment of motion in three dimensional space

    Energy Technology Data Exchange (ETDEWEB)

    Hollerbach, K.; Van Vorhis, R.L. [Lawrence Livermore National Lab., CA (United States); Hollister, A. [Louisiana State Univ., Shreveport, LA (United States)

    1996-03-01

    Wrist posture and rapid wrist movements are risk factors for work related musculoskeletal disorders. Measurement studies frequently involve optoelectronic methods in which markers are placed on the subject`s hand and wrist and the trajectories of the markers are tracked in three dimensional space. A goal of wrist posture measurements is to quantitatively establish wrist posture orientation. Accuracy and fidelity of the measurement data with respect to kinematic mechanisms are essential in wrist motion studies. Fidelity with the physical kinematic mechanism can be limited by the choice of kinematic modeling techniques and the representation of motion. Frequently, ergonomic studies involving wrist kinematics make use of two dimensional measurement and analysis techniques. Two dimensional measurement of human joint motion involves the analysis of three dimensional displacements in an obersver selected measurement plane. Accurate marker placement and alignment of joint motion plane with the observer plane are difficult. In nature, joint axes can exist at any orientation and location relative to an arbitrarily chosen global reference frame. An arbitrary axis is any axis that is not coincident with a reference coordinate. We calculate the errors that result from measuring joint motion about an arbitrary axis using two dimensional methods.

  17. Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators

    CERN Document Server

    Dittrich, Bianca; Kaminski, Wojciech

    2012-01-01

    In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space. These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.

  18. Relating Berkovits and $A_\\infty$ Superstring Field Theories; Large Hilbert Space Perspective

    CERN Document Server

    Erler, Theodore

    2015-01-01

    We lift the dynamical field of the $A_\\infty$ superstring field theory to the large Hilbert space by introducing a trivial gauge invariance associated with the eta zero mode. We then provide a field redefinition which relates to the lifted field to the dynamical field of Berkovits' superstring field theory in the large Hilbert space. This generalizes the field redefinition in the small Hilbert space described in earlier works, and is useful for understanding the relation between the gauge symmetries of the theories.

  19. Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators

    Directory of Open Access Journals (Sweden)

    Banan Maayah

    2014-01-01

    Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.

  20. The role of sleep in forming a memory representation of a two-dimensional space.

    Science.gov (United States)

    Coutanche, Marc N; Gianessi, Carol A; Chanales, Avi J H; Willison, Kate W; Thompson-Schill, Sharon L

    2013-12-01

    There is ample evidence from human and animal models that sleep contributes to the consolidation of newly learned information. The precise role of sleep for integrating information into interconnected memory representations is less well understood. Building on prior findings that following sleep (as compared to wakefulness) people are better able to draw inferences across learned associations in a simple hierarchy, we ask how sleep helps consolidate relationships in a more complex representational space. We taught 60 subjects spatial relationships between pairs of buildings, which (unknown to participants) formed a two-dimensional grid. Critically, participants were only taught a subset of the many possible spatial relations, which allowed them to potentially infer the remainder. After a 12 h period that either did or did not include a normal period of sleep, participants returned to the lab. We examined the quality of each participant's map of the two-dimensional space, and their knowledge of relative distances between buildings. After 12 h with sleep, subjects could more accurately map the full space than subjects who experienced only wakefulness. The incorporation of untaught, but inferable, associations was particularly improved. We further found that participants' distance judgment performance related to self-reported navigational style, but only after sleep. These findings demonstrate that consolidation over a night of sleep begins to integrate relations into an interconnected complex representation, in a way that supports spatial relational inference.

  1. Mild solutions of semilinear elliptic equations in Hilbert spaces

    Science.gov (United States)

    Federico, Salvatore; Gozzi, Fausto

    2017-03-01

    This paper extends the theory of regular solutions (C1 in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of G-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into G-differentiable ones. The validity of this smoothing assumption is fully discussed for the case of the Ornstein-Uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature. It is shown that the results apply to Hamilton-Jacobi-Bellman (HJB) equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that, in particular, they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now.

  2. Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces

    Directory of Open Access Journals (Sweden)

    Hacer Bozkurt

    2014-01-01

    Full Text Available Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986. Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005, Talo and Başar (2010, and Nikol'skiĭ (1993. His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.

  3. Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160

    Institute of Scientific and Technical Information of China (English)

    WANG Gong-bao

    2001-01-01

    In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160are presented at the end of the paper.

  4. Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order

    OpenAIRE

    Balashov, Maxim V.; Repovš, Dušan,

    2011-01-01

    We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.

  5. On the minimizers of calculus of variations problems in Hilbert spaces

    KAUST Repository

    Gomes, Diogo A.

    2014-01-19

    The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.

  6. Singularly perturbed Cauchy problem for abstract linear differential equations of second order in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Andrei Perjan

    2009-07-01

    Full Text Available We study the behavior of solutions to perturbed second order abstract evolution equations in Hilbert spaces, when the small parameter, multiplying the second order time derivative, converges to zero.

  7. Nonlocality Proof for Two-Particle Systems in 3 3 Hilbert Space

    Institute of Scientific and Technical Information of China (English)

    WU Xiao-Hua; ZONG Hong-Shi; PANG Hou-Rong; WANG Fan

    2001-01-01

    For a two-particle system in 3 3 Hilbert space, we derive a new type of inequality for local hidden variable model. Using an entangled state, we give a realizable experiment whose joint probabilities violate the inequality.``

  8. Positioning with stationary emitters in a two-dimensional space-time

    CERN Document Server

    Coll, B; Morales, J A; Coll, Bartolom\\'{e}; Ferrando, Joan Josep; Morales, Juan Antonio

    2006-01-01

    The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called {\\em emission coordinates}, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, absence and presence of a gravitational field, are identical. The interesting...

  9. A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Kaplitskii, V M [Southern Federal University, Rostov-on-Don (Russian Federation)

    2014-08-01

    The function Ψ(x,y,s)=e{sup iy}Φ(−e{sup iy},s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L{sub 2}(Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles.

  10. Digital chaos-masked optical encryption scheme enhanced by two-dimensional key space

    Science.gov (United States)

    Liu, Ling; Xiao, Shilin; Zhang, Lu; Bi, Meihua; Zhang, Yunhao; Fang, Jiafei; Hu, Weisheng

    2017-09-01

    A digital chaos-masked optical encryption scheme is proposed and demonstrated. The transmitted signal is completely masked by interference chaotic noise in both bandwidth and amplitude with analog method via dual-drive Mach-Zehnder modulator (DDMZM), making the encrypted signal analog, noise-like and unrecoverable by post-processing techniques. The decryption process requires precise matches of both the amplitude and phase between the cancellation and interference chaotic noises, which provide a large two-dimensional key space with the help of optical interference cancellation technology. For 10-Gb/s 16-quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) signal over the maximum transmission distance of 80 km without dispersion compensation or inline amplifier, the tolerable mismatch ranges of amplitude and phase/delay at the forward error correction (FEC) threshold of 3.8×10-3 are 0.44 dB and 0.08 ns respectively.

  11. Detecting dimensional crossover and finite Hilbert space through entanglement entropies

    OpenAIRE

    Garagiola, Mariano; Cuestas, Eloisa; Pont, Federico M.; Serra, Pablo; Osenda, Omar

    2016-01-01

    The information content of the two-particle one- and two-dimensional Calogero model is studied using the von Neumann and R\\'enyi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large interaction strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confine...

  12. The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time

    Science.gov (United States)

    Matsyuk, Roman Ya.

    2008-02-01

    The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.

  13. The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time

    CERN Document Server

    Matsyuk, Roman Ya

    2008-01-01

    The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.

  14. The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time

    Directory of Open Access Journals (Sweden)

    Roman Ya. Matsyuk

    2008-02-01

    Full Text Available The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo-Euclidean geometry.

  15. Two-dimensional inversion of spectral induced polarization data using MPI parallel algorithm in data space

    Institute of Scientific and Technical Information of China (English)

    Zhang Zhi-Yong; Tan Han-Dong; Wang Kun-Peng; Lin Chang-Hong; Zhang Bin; Xie Mao-Bi

    2016-01-01

    Traditional two-dimensional (2D) complex resistivity forward modeling is based on Poisson’s equation but spectral induced polarization (SIP) data are the coprod-ucts of the induced polarization (IP) and the electromagnetic induction (EMI) effects. This is especially true under high frequencies, where the EMI effect can exceed the IP effect. 2D inversion that only considers the IP effect reduces the reliability of the inver-sion data. In this paper, we derive differential equations using Maxwell’s equations. With the introduction of the Cole–Cole model, we use thefi nite-element method to conduct 2D SIP forward modeling that considers the EMI and IP effects simultaneously. The data-space Occam method, in which different constraints to the model smoothness and parametric boundaries are introduced, is then used to simultaneously obtain the four parameters of the Cole–Cole model using multi-array electricfi eld data. This approach not only improves the stability of the inversion but also signifi cantly reduces the solution ambiguity. To improve the computational effi ciency, message passing interface program-ming was used to accelerate the 2D SIP forward modeling and inversion. Synthetic da-tasets were tested using both serial and parallel algorithms, and the tests suggest that the proposed parallel algorithm is robust and effi cient.

  16. Two-dimensional inversion of spectral induced polarization data using MPI parallel algorithm in data space

    Science.gov (United States)

    Zhang, Zhi-Yong; Tan, Han-Dong; Wang, Kun-Peng; Lin, Chang-Hong; Zhang, Bin; Xie, Mao-Bi

    2016-03-01

    Traditional two-dimensional (2D) complex resistivity forward modeling is based on Poisson's equation but spectral induced polarization (SIP) data are the coproducts of the induced polarization (IP) and the electromagnetic induction (EMI) effects. This is especially true under high frequencies, where the EMI effect can exceed the IP effect. 2D inversion that only considers the IP effect reduces the reliability of the inversion data. In this paper, we derive differential equations using Maxwell's equations. With the introduction of the Cole-Cole model, we use the finite-element method to conduct 2D SIP forward modeling that considers the EMI and IP effects simultaneously. The data-space Occam method, in which different constraints to the model smoothness and parametric boundaries are introduced, is then used to simultaneously obtain the four parameters of the Cole—Cole model using multi-array electric field data. This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity. To improve the computational efficiency, message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion. Synthetic datasets were tested using both serial and parallel algorithms, and the tests suggest that the proposed parallel algorithm is robust and efficient.

  17. Positioning in a flat two-dimensional space-time: the delay master equation

    CERN Document Server

    Coll, Bartolomé; Morales-Lladosa, Juan Antonio

    2010-01-01

    The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\\bf 73}, 084017 (2006); {\\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. We illustrate these result...

  18. Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource

    Science.gov (United States)

    Silva, Ralph; Manzano, Gonzalo; Skrzypczyk, Paul; Brunner, Nicolas

    2016-09-01

    Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

  19. Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

    Directory of Open Access Journals (Sweden)

    M. Znojil

    2010-01-01

    Full Text Available A few recent innovations of the applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by models using apparently non-Hermitian (often called “crypto-Hermitian” Hamiltonians with real spectra. The formalism (originally inspired by the topical need for a mathematically consistent description of tobogganic quantum models is shown to admit even certain unusual nonlocal and/or “moving-frame” representations H(S of the standard physical Hilbert space of wave functions.

  20. How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms

    CERN Document Server

    D'Ariano, G M

    2006-01-01

    In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper quant-ph/0506034. Pivotal roles are played by the "local observability principle", which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of "informationally complete observables" and of a "symmetric faithful state". This last notion allows one to introduce an operational definition for the real version of the "adjoint"--i. e. the transposition--from which one can derive a real Hilbert-space structure via either the Mackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze in detail only the Gelfand-Naimark-Segal construction, which leads to a real Hilbert space structure analogous to that...

  1. Characterizations of g-Frames and g-Riesz Bases in Hilbert Spaces

    Institute of Scientific and Technical Information of China (English)

    Yu Can ZHU

    2008-01-01

    In this paper,we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space,which will play a key role in studying g-frames and g-Riesz bases etc.Using the pre-frame operator Q,we give some necessary and sufficient conditions for a g-Bessel sequence,a g-frame,and a g-Riesz basis in a complex Hilbert space,which have properties similar to those of the Bessel sequence, frame,and Riesz basis respectively.We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis.Lastly,we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.

  2. Hofstadter butterfly evolution in the space of two-dimensional Bravais lattices

    Science.gov (United States)

    Yılmaz, F.; Oktel, M. Ö.

    2017-06-01

    The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold-atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work [F. Yılmaz et al., Phys. Rev. A 91, 063628 (2015), 10.1103/PhysRevA.91.063628], we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit-cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point-symmetry groups. We model the optical lattice with a sinusoidal real-space potential and obtain the tight-binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e., the triangular and the square lattices, displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transitions from the square to rectangular lattice and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.

  3. Asymptotic behaviour of a family of gradient algorithms in R^d and Hilbert spaces

    CERN Document Server

    Pronzato, Luc; Zhigljavsky, Anatoly A

    2008-01-01

    The asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in R^d and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.

  4. Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Subalakshmi, R. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: suba.ab.bu@gmail.com; Balachandran, K. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: balachandran_k@lycos.com

    2009-11-30

    Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.

  5. The Interaction of Vision and Audition in Two-Dimensional Space

    Directory of Open Access Journals (Sweden)

    Martine eGodfroy-Cooper

    2015-09-01

    Full Text Available Using a mouse-driven visual pointer, ten participants made repeated open loop egocentric localizations of memorized visual, auditory and combined visual-auditory targets projected randomly across the two-dimensional frontal field (2D. The results are reported in terms of variable error, constant error and local distortion. The results confirmed that auditory and visual maps of the egocentric space differ in their precision (variable error and accuracy (constant error, both from one another, and as a function of eccentricity and direction within a given modality. These differences were used, in turn, to make predictions about the precision and accuracy within which spatially and temporally congruent bimodal visual-auditory targets are localized. Overall, the improvement in precision for bimodal relative to the best unimodal target revealed the presence of optimal integration well predicted by the Maximum Likelihood Estimation (MLE model. Conversely, the hypothesis that accuracy in localizing the bimodal visual-auditory targets would represent a compromise between auditory and visual performance in favor of the most precise modality was rejected. Instead, the bimodal accuracy was found to be equivalent to or to exceed that of the best unimodal condition. Finally, we described how the different types of errors could be used to identify properties of the internal representations and coordinate transformations within the central nervous system (CNS. The results provide some insight into the structure of the underlying sensorimotor processes employed by the brain. This result confirms the usefulness of capitalizing on naturally occurring differences between vision and audition to better understand their interaction and their contribution to multimodal perception.

  6. Resistive MHD reconstruction of two-dimensional coherent structures in space

    Directory of Open Access Journals (Sweden)

    W.-L. Teh

    2010-11-01

    Full Text Available We present a reconstruction technique to solve the steady resistive MHD equations in two dimensions with initial inputs of field and plasma data from a single spacecraft as it passes through a coherent structure in space. At least two components of directly measured electric fields (the spacecraft spin-plane components are required for the reconstruction, to produce two-dimensional (2-D field and plasma maps of the cross section of the structure. For convenience, the resistivity tensor η is assumed diagonal in the reconstruction coordinates, which allows its values to be estimated from Ohm's law, E+v×B=η·j. In the present paper, all three components of the electric field are used. We benchmark our numerical code by use of an exact, axi-symmetric solution of the resistive MHD equations and then apply it to synthetic data from a 3-D, resistive, MHD numerical simulation of reconnection in the geomagnetic tail, in a phase of the event where time dependence and deviations from 2-D are both weak. The resistivity used in the simulation is time-independent and localized around the reconnection site in an ellipsoidal region. For the magnetic field, plasma density, and pressure, we find very good agreement between the reconstruction results and the simulation, but the electric field and plasma velocity are not predicted with the same high accuracy.

  7. The Construction of Hilbert Spaces over the Non-Newtonian Field

    Directory of Open Access Journals (Sweden)

    Uğur Kadak

    2014-01-01

    the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of *-calculus. Furthermore, as an example of Hilbert spaces, first we introduce the non-Cartesian plane which is a nonlinear model for plane Euclidean geometry. Secondly, we give Euclidean, unitary, and sequence spaces via corresponding norms which are induced by an inner product. Finally, by using the *-norm properties of complex structures, we examine Cauchy-Schwarz and triangle inequalities.

  8. Nonlinear sigma model in the case of N x. cap alpha. N rectangular matrices in two-dimensional euclidean space

    Energy Technology Data Exchange (ETDEWEB)

    Chekhov, L.O.

    1985-12-01

    Matrix nonlinear sigma models are discussed and the matrix nonlinear sigma model in the case of N x ..cap alpha..N rectangular matrices is considered. The authors show that in two-dimensional Euclidean space, the model is renormalizable with respect to ..cap alpha.. and 1/N. The fulfillment of the chirality identity is demonstrated in the operator expansion for the renormalized theory.

  9. Nonlinear sigma-model in the case of rectangular Nx. alpha. N matrices in two-dimensional euclidean space

    Energy Technology Data Exchange (ETDEWEB)

    Chekhov, L.O.

    1985-06-01

    Matrix nonlinear sigma-model is considered in the case of rectangular matrices of the dimension Nx..alpha..N. Renormalizability of the model with respect to ..alpha.. and 1/N is demonstrated for the case of two-dimensional Euclidean space. Validity of the chiral identity is proved in the operator expansion for the renormalized theory.

  10. Further two-dimensional code development for Stirling space engine components

    Science.gov (United States)

    Ibrahim, Mounir; Tew, Roy C.; Dudenhoefer, James E.

    1990-01-01

    The development of multidimensional models of Stirling engine components is described. Two-dimensional parallel plate models of an engine regenerator and a cooler were used to study heat transfer under conditions of laminar, incompressible oscillating flow. Substantial differences in the nature of the temperature variations in time over the cycle were observed for the cooler as contrasted with the regenerator. When the two-dimensional cooler model was used to calculate a heat transfer coefficient, it yields a very different result from that calculated using steady-flow correlations. Simulation results for the regenerator and the cooler are presented.

  11. Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces

    Science.gov (United States)

    Cho, Yeol Je; Qin, Xiaolong

    2009-06-01

    In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others.

  12. On the quasiuniqueness of solutions of degenerate equations in Hilbert space

    Directory of Open Access Journals (Sweden)

    Vladimir Schuchman

    1988-01-01

    Full Text Available In this paper, we study the quasiuniqueness (i.e., f1≐f2 if f1−f2 is flat, the function f(t being called flat if, for any K>0, t−kf(t→0 as t→0 for ordinary differential equations in Hilbert space. The case of inequalities is studied, too.

  13. On the physical Hilbert space of $QCD_2$ in the decoupled formulation

    CERN Document Server

    Cabra, D C

    1997-01-01

    We consider the QCD$_2$ partition function in the non-local, decoupled formulation and systematically establish which subset of the nilpotent Noether charges is required to vanish on the physical states. The implications for the Hilbert space structure are also examined.

  14. Growth estimates for $\\exp(A^{-1}t)$ on a Hilbert space

    NARCIS (Netherlands)

    Zwart, H.J.

    2007-01-01

    Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by

  15. Existence Results for Impulsive Neutral Stochastic Evolution Inclusions in Hilbert Space

    Institute of Scientific and Technical Information of China (English)

    Han Wen NING; Bin LIU

    2011-01-01

    This paper is concerned with the existence of mild solutions of a class of impulsive neutral stochastic evolution inclusions in Hilbert space in the case where the right hand side is convex or nonconvex-valued.The results are obtained by using two fixed point theorems for multivalued mappings and evolution system theory.

  16. Approximation of Besov vectors by Paley-Wiener vectors in Hilbert spaces

    CERN Document Server

    Pesenson, Isaac Z

    2011-01-01

    We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data representation, compression, denoising and visualization. These tasks are of great importance to machine learning, complex data analysis and computer vision.

  17. Approximately dual frames in Hilbert spaces and applications to Gabor frames

    DEFF Research Database (Denmark)

    Christensen, Ole; Laugesen, Richard S.

    2011-01-01

    Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames cons...

  18. New Hybrid Iterative Schemes for an Infinite Family of Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Guo Baohua

    2010-01-01

    Full Text Available We propose some new iterative schemes for finding common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove the strong convergence of the proposed schemes. Our results extend and improve ones of Nakajo and Takahashi (2003.

  19. A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Singthong Urailuk

    2010-01-01

    Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.

  20. Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

    Directory of Open Access Journals (Sweden)

    Alma García

    2015-01-01

    Full Text Available We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.

  1. Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space

    OpenAIRE

    Bracken, A. J.

    2002-01-01

    Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.

  2. Beyond gauge theory: Hilbert space positivity and causal localization in the presence of vector mesons

    CERN Document Server

    Schroer, Bert

    2016-01-01

    The Hilbert space formulation of interacting spin 1 vector-potentials stands in an interesting contrast with the point-local Krein space setting.of gauge theory. Already in the absence of interactions the Wilson loop in a Hilbert space setting has a topological property which is missing in the gauge theoretic description (Haag duality, Aharonov-Bohm effect); the conceptual differences increase in the presence of interactions. The Hilbert space positivity weakens the causal localization properties if interacting fields from point- to string-like, but it also improves the short distance properties in that the scale dimensions of string-local fields fields is independent of spin. This makes it possible to find interaction densities within the power-counting bound of renormalizability for any spin, But for string-local interacting fields there is a new requirement (existence of a L,V pair) which has no analog for point-local fields.It insures the preservation of string-localization in higher orders and secures th...

  3. The Construction of Hilbert Spaces over the Non-Newtonian Field

    OpenAIRE

    Uğur Kadak; Hakan Efe

    2014-01-01

    Although there are many excellent ways to present the principle of the classical calculus, the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complet...

  4. A Quantitative Version of the Bishop-Phelps Theorem for Operators in Hilbert Spaces

    Institute of Scientific and Technical Information of China (English)

    Li Xin CHENG; Yun Bai DONG

    2012-01-01

    In this paper,with the help of spectral integral,we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces.Precisely,let H be a complex Hilbert space and 0 < ε < 1/2. Then for every bounded linear operator T:H → H and x0 ∈ H with ‖T‖ =1 =‖x0‖ such that ‖Txo‖ > 1 -ε,there exist xε ∈ H and a bounded linear operator S:H → Hwith ‖S‖ =1 =‖xε‖ such that ‖Sxε‖=1,‖xε-x0‖≤√2ε+4√2ε,‖S-T‖≤√2ε.

  5. Corrections to nucleon capture cross sections computed in truncated Hilbert spaces

    Science.gov (United States)

    Acharya, B.; Ekström, A.; Odell, D.; Papenbrock, T.; Platter, L.

    2017-03-01

    Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of ab initio many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.

  6. Precise asymptotics in the law of the logarithm for random fields in Hilbert space

    Institute of Scientific and Technical Information of China (English)

    FU Ke-ang; ZHANG Li-xin

    2007-01-01

    Consider the positive d-dimensional lattice Zd+ (d≥2) with partial ordering ≤, let {XK; K∈Zd+} be i.i.d. random variables taking values in a real separable Hilbert space (H, ‖·‖) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K, N ∈ Zd+. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↘0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).

  7. Vacuum GR in Chang--Soo variables: Hilbert space structure in anisotropic minisuperspace

    CERN Document Server

    Ita, Eyo

    2009-01-01

    In this paper we address the major criticism of the pure Kodama state, namely its normalizability and its existence within a genuine Hilbert space of states, by recasting Ashtekar's general relativity into set of new variables attributed to Chang--Soo/CDJ. While our results have been shown for anisotropic minisuperspace, we reserve a treatment of the full theory for a following paper which it is hoped should finally bring this issue to a close. We have performed a canonical treatment of these new variables from the level of the classical/quantum algebra of constraints, all the way to the construction of the Hilbert space of states, and have demonstrated their relevance to the principle of the semiclassical-quantum correspondence. It is hoped that these new variables and their physical interpretation should provide a new starting point for investigations in classical and quantum GR and in the construction of a consistent quantum theory.

  8. Band alignment of two-dimensional semiconductors for designing heterostructures with momentum space matching

    Science.gov (United States)

    Özçelik, V. Ongun; Azadani, Javad G.; Yang, Ce; Koester, Steven J.; Low, Tony

    2016-07-01

    We present a comprehensive study of the band alignments of two-dimensional (2D) semiconducting materials and highlight the possibilities of forming momentum-matched type I, II, and III heterostructures, an enticing possibility being atomic heterostructures where the constituent monolayers have band edges at the zone center, i.e., Γ valley. Our study, which includes the group IV and III-V compound monolayer materials, group V elemental monolayer materials, transition-metal dichalcogenides, and transition-metal trichalcogenides, reveals that almost half of these materials have conduction and/or valence band edges residing at the zone center. Using first-principles density functional calculations, we present the type of the heterostructure for 903 different possible combinations of these 2D materials which establishes a periodic table of heterostructures.

  9. Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space

    CERN Document Server

    Maldacena, Juan; Yang, Zhenbin

    2016-01-01

    We study a two dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near extremal black holes, or more generally, nearly $AdS_2$ spacetimes. The asymptotic symmetries of $AdS_2$ are all the time reparametrizations of the boundary. These symmetries are spontaneously broken by the $AdS_2$ geometry and they are explicitly broken by the small deformation away from $AdS_2$. This pattern of spontaneous plus explicit symmetry breaking governs the gravitational backreaction of the system. It determines several gravitational properties such as the linear in temperature dependence of the near extremal entropy as well as the gravitational corrections to correlation functions. These corrections include the ones determining the growth of out of time order correlators that is indicative of chaos. These gravitational aspects can be described in terms of a Schwarzian derivative effective action for a reparametrization.

  10. High-temperature superconductivity in space-charge regions of lanthanum cuprate induced by two-dimensional doping

    Science.gov (United States)

    Baiutti, F.; Logvenov, G.; Gregori, G.; Cristiani, G.; Wang, Y.; Sigle, W.; van Aken, P. A.; Maier, J.

    2015-10-01

    The exploitation of interface effects turned out to be a powerful tool for generating exciting material properties. Such properties include magnetism, electronic and ionic transport and even superconductivity. Here, instead of using conventional homogeneous doping to enhance the hole concentration in lanthanum cuprate and achieve superconductivity, we replace single LaO planes with SrO dopant planes using atomic-layer-by-layer molecular beam epitaxy (two-dimensional doping). Electron spectroscopy and microscopy, conductivity measurements and zinc tomography reveal such negatively charged interfaces to induce layer-dependent superconductivity (Tc up to 35 K) in the space-charge zone at the side of the planes facing the substrate, where the strontium (Sr) profile is abrupt. Owing to the growth conditions, the other side exhibits instead a Sr redistribution resulting in superconductivity due to conventional doping. The present study represents a successful example of two-dimensional doping of superconducting oxide systems and demonstrates its power in this field.

  11. Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Arnon Ploymukda

    2016-01-01

    Full Text Available We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.

  12. Relating Berkovits and $A_\\infty$ Superstring Field Theories; Small Hilbert Space Perspective

    CERN Document Server

    Erler, Theodore

    2015-01-01

    In a previous paper it was shown that the recently constructed action for open superstring field theory based on $A_\\infty$ algebras can be re-written in Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits' open superstring field theory. In this paper we explain the relation between these two theories from a different perspective which emphasizes the small Hilbert space, and in particular the relation between the $A_\\infty$ structures on both sides.

  13. On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Yeol Je Cho

    2010-01-01

    Full Text Available We use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE in Hilbert spaces. The algorithm for finding a solution of the problem (SMIE is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.

  14. Multiple-Set Split Feasibility Problems for κ-Strictly Pseudononspreading Mapping in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Jing Quan

    2013-01-01

    Full Text Available The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems for κ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006, of Osilike et al. (2011, and of many other authors.

  15. On Nyman, Beurling and Baez-Duarte's Hilbert Space Reformulation of the Riemann Hypothesis

    Indian Academy of Sciences (India)

    Bhaskar Bagchi

    2006-05-01

    There has been a surge of interest of late in an old result of Nyman and Beurling giving a Hilbert space formulation of the Riemann hypothesis. Many authors have contributed to this circle of ideas, culminating in a beautiful refinement due to Baez-Duarte. The purpose of this little survey is to dis-entangle the resulting web of complications, and reveal the essential simplicity of the main results.

  16. H\\"{o}lder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces

    CERN Document Server

    Wiśnicki, Andrzej

    2012-01-01

    Suppose that S is a left amenable semitopological semigroup. We prove that if $\\{T_{t}: t \\in S \\}$ is a uniformly k-Lipschitzian semigroup on a bounded closed and convex subset C of a Hilbert space and $k<\\sqrt{2}$, then the set of fixed points of this semigroup is a H\\"{o}lder continuous retract of C. This gives a qualitative complement to the Ishihara-Takahashi fixed point existence theorem.

  17. Beta-gamma system, pure spinors and Hilbert series of arc spaces

    Energy Technology Data Exchange (ETDEWEB)

    Bhamidipati, Chandrasekhar [School of Basic Sciences, Indian Institute of Technology Bhubaneswar,Bhubaneswar 751 007 (India); Ray, Koushik [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Calcutta 700 032 (India)

    2015-01-14

    Algorithms are presented for calculating the partition function of constrained beta-gamma systems in terms of the generating functions of the individual fields of the theory, the latter obtained as the Hilbert series of the arc space of the algebraic variety defined by the constraint. Examples of a beta-gamma system on a complex surface with an A{sub 1} singularity and pure spinors are worked out and compared with existing results.

  18. A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Samia Bushnaq

    2014-01-01

    Full Text Available We present a new version of the reproducing kernel Hilbert space method (RKHSM for the solution of systems of fractional integrodifferential equations. In this approach, the solution is obtained as a convergent series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method. The method described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.

  19. Fast-forward scaling in a finite-dimensional Hilbert space

    OpenAIRE

    TAKAHASHI, Kazutaka

    2014-01-01

    Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential. We also use our formulation to accelerate the adiabatic dynamics. Applying the method to the transitionless quantum driving, we find that the fast-forward potential can be understood as a counterdiabatic term.

  20. Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))

    1993-11-29

    Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)

  1. Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces

    Institute of Scientific and Technical Information of China (English)

    Shi Sheng ZHANG; H. W. JOSEPH LEE; Chi Kin CHAN

    2007-01-01

    The purpose of this paper is to study the convergence problem of the iteration schemexn+1=λn+1y + (1-λn+1)Tn+1Xn for a family of infinitely many nonexpansive mappings T1, T2,…ina Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly tothe nearest common fixed point of this family of nonexpansive mappings. The results presented in thispaper extend and improve some recent results.

  2. A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

    Directory of Open Access Journals (Sweden)

    Mustafa Inc

    2013-01-01

    Full Text Available We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.

  3. Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Krishnan Balachandran

    2008-12-01

    Full Text Available In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.

  4. Applications of rigged Hilbert spaces in quantum mechanics and signal processing

    Science.gov (United States)

    Celeghini, E.; Gadella, M.; del Olmo, M. A.

    2016-07-01

    Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su(1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them is obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.

  5. The Born rule from a consistency requirement on hidden measurements in complex Hilbert space

    CERN Document Server

    Aerts, S

    2002-01-01

    We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming the state space of a physical entity is a complex Hilbert space and introduce the principle of consistent interaction which effectively partitions the space of apparatus states. The normalized measure of the set of apparatus states that interact with a pure state giving rise to a fixed outcome is shown to be in accordance with the probability obtained using the Born rule.

  6. Protein folding: complex potential for the driving force in a two-dimensional space of collective variables.

    Science.gov (United States)

    Chekmarev, Sergei F

    2013-10-14

    Using the Helmholtz decomposition of the vector field of folding fluxes in a two-dimensional space of collective variables, a potential of the driving force for protein folding is introduced. The potential has two components. One component is responsible for the source and sink of the folding flows, which represent respectively, the unfolded states and the native state of the protein, and the other, which accounts for the flow vorticity inherently generated at the periphery of the flow field, is responsible for the canalization of the flow between the source and sink. The theoretical consideration is illustrated by calculations for a model β-hairpin protein.

  7. Moduli Structures, Separability of the Kinematic Hilbert Space and Frames in Loop Quantum Gravity

    CERN Document Server

    Carvalho, Bruno

    2016-01-01

    We reassess the problem of separability of the kinematic Hilbert space in loop quantum gravity under a new mathematical point of view. We use the formalism of frames, a tool used in signal analysis, in order to remove the redundancy of the moduli structures in high valence graphs, without resorting to set extension of diffeomorphism group. For this, we introduce a local redundancy which encodes the concentration of frame vectors on the tangent spaces $T_pM$ around points of intersections $p$ of smooth loops $\\alpha$ in $\\mathbb{R}^{3}$.

  8. Truncated Hilbert space approach to the 2d $\\phi^{4}$ theory

    CERN Document Server

    Bajnok, Z

    2015-01-01

    We apply the massive analogue of the truncated conformal space approach to study the two dimensional $\\phi^{4}$ theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We compare these results against semi-classical analysis and the Bethe-Yang spectrum.

  9. An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations

    CERN Document Server

    Wang, Bei; Colella, Phil

    2012-01-01

    The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.

  10. Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space

    Institute of Scientific and Technical Information of China (English)

    Ma Jun; Ying He-Ping; Liu Yong; Li Shi-Rong

    2009-01-01

    The dynamics and the transition of spiral waves in the couplcd Hindmarsh-Rose (H-R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient DI, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.

  11. Two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity: a numerical study.

    Science.gov (United States)

    Küchler, Sebastian; Meurer, Thomas; Jacobs, Laurence J; Qu, Jianmin

    2009-03-01

    This study investigates two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity. The problem is formulated as a hyperbolic system of conservation laws, which is solved numerically using a semi-discrete central scheme. These numerical results are then analyzed in the frequency domain to interpret the nonlinear effects, specifically the excitation of higher-order harmonics. To quantify and compare the nonlinearity of different materials, a new parameter is introduced, which is similar to the acoustic nonlinearity parameter beta for one-dimensional longitudinal waves. By using this new parameter, it is found that the nonlinear effects of a material depend on the point of observation in the half-space, both the angle and the distance to the excitation source. Furthermore it is illustrated that the third-order elastic constants have a linear effect on the acoustic nonlinearity of a material.

  12. Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mourad Kerboua

    2014-12-01

    Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

  13. Minimal sufficient positive-operator valued measure on a separable Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Kuramochi, Yui, E-mail: kuramochi.yui.22c@st.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, 6158540 Kyoto (Japan)

    2015-10-15

    We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.

  14. Representation Theorem for Stochastic Differential Equations in Hilbert Spaces and its Applications

    Directory of Open Access Journals (Sweden)

    Viorica Mariela Ungureanu

    2006-12-01

    Full Text Available In this survey we recall the results obtained in [Ungureanu,Electronic Journal of Qualitative Theory of Differential Equations, 2004] where we gave a representation theorem for the solutions of stochastic differential equations in Hilbert spaces. Using this representation theorem we obtained deterministic characterizations of exponential stability and uniform observability in [Ungureanu,Electronic Journal of Qualitative Theory of Differential Equations, 2004], [Ungureanu, Operator Theory: Advances and Applications, Birkhauser Verlag Basel, 2005] and we will prove a result of Datko type concerning the exponential dichotomy of stochastic equations.

  15. Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Juguo Su

    2012-01-01

    Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

  16. Hilbert-space factorization is a limited and expensive information-processing resource

    CERN Document Server

    Fields, Chris

    2014-01-01

    By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a classically-recorded observational outcome. This cost is neglected in standard treatments of decoherence that assume that observational outcomes are obtained by interacting with a collection of degrees of freedom identified a priori. Treating this cost explicitly leads to a natural measure of the probability of any particular quantum reference frame.

  17. Corrections to nucleon capture cross sections computed in truncated Hilbert spaces

    CERN Document Server

    Acharya, B; Odell, D; Papenbrock, T; Platter, L

    2016-01-01

    Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and the precise theoretical computation in this long-wavelength regime requires us to understand the corrections due to finite Hilbert spaces. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and also open the way for a more precise understanding of nucleon capture on heavier nuclei.

  18. Hilbert space of curved \\beta\\gamma systems on quadric cones

    CERN Document Server

    Aisaka, Yuri

    2008-01-01

    We clarify the structure of the Hilbert space of curved \\beta\\gamma systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.

  19. Statistical properties of fidelity in quantum tomography protocols in Hilbert spaces of different dimensions

    CERN Document Server

    Bogdanov, Yu I; Gavrichenko, A K

    2011-01-01

    A throughout study of statistical characteristics of fidelity in different protocols of quantum tomography is given. We consider protocols based on geometry of platonic solids and other polyhedrons with high degree of symmetry such as fullerene and its dual polyhedron. Characteristics of fidelity in different protocols are compared to the theoretical level of the minimum possible level of fidelity loss. Tomography of pure and mixed states in Hilbert spaces of different dimension is analyzed. Results of this work could be used for a better control of quantum gates and quantum states in quantum information technologies.

  20. Evaluation of Aqueductal Patency in Patients with Hydrocephalus: Three-Dimensional High-Sampling-Efficiency Technique (SPACE) versus Two-Dimensional Turbo Spin Echo at 3 Tesla

    National Research Council Canada - National Science Library

    Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut

    2014-01-01

    ...) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE...

  1. Electrostatic Structures in Space Plasmas: Stability of Two-dimensional Magnetic Bernstein-Greene-Kruskal Modes

    CERN Document Server

    Ng, C S; Yasin, E

    2011-01-01

    Electrostatic structures have been observed in many regions of space plasmas, including the solar wind, the magnetosphere, the auroral acceleration region, and in association with shocks, turbulence, and magnetic reconnection. Due to potentially large amplitude of electric fields within these structures, their effects on particle heating, scattering, or acceleration can be important. One possible theoretical description of some of these structures is the concept of Bernstein-Greene-Kruskal (BGK) modes, which are exact nonlinear solutions of the Vlasov-Poisson system of equations in collisionless kinetic theory. BGK modes have been studied extensively for many decades, predominately in one dimension (1D), although there have been observations showing that some of these structures have clear 3D features. While there have been approximate solutions of higher dimensional BGK modes, an exact 3D BGK mode solution in a finite magnetic field has not been found yet. Recently we have constructed exact solutions of 2D B...

  2. High-temperature superconductivity in space-charge regions of lanthanum cuprate induced by two-dimensional doping.

    Science.gov (United States)

    Baiutti, F; Logvenov, G; Gregori, G; Cristiani, G; Wang, Y; Sigle, W; van Aken, P A; Maier, J

    2015-10-20

    The exploitation of interface effects turned out to be a powerful tool for generating exciting material properties. Such properties include magnetism, electronic and ionic transport and even superconductivity. Here, instead of using conventional homogeneous doping to enhance the hole concentration in lanthanum cuprate and achieve superconductivity, we replace single LaO planes with SrO dopant planes using atomic-layer-by-layer molecular beam epitaxy (two-dimensional doping). Electron spectroscopy and microscopy, conductivity measurements and zinc tomography reveal such negatively charged interfaces to induce layer-dependent superconductivity (Tc up to 35 K) in the space-charge zone at the side of the planes facing the substrate, where the strontium (Sr) profile is abrupt. Owing to the growth conditions, the other side exhibits instead a Sr redistribution resulting in superconductivity due to conventional doping. The present study represents a successful example of two-dimensional doping of superconducting oxide systems and demonstrates its power in this field.

  3. Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study

    CERN Document Server

    Botelho, Luiz Carlos Lobato

    2010-01-01

    We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.

  4. Two-dimensional model of a Space Station Freedom thermal energy storage canister

    Science.gov (United States)

    Kerslake, Thomas W.; Ibrahim, Mounir B.

    1990-01-01

    The Solar Dynamic Power Module being developed for Space Station Freedom uses a eutectic mixture of LiF-CaF2 phase change salt contained in toroidal canisters for thermal energy storage. Results are presented from heat transfer analyses of the phase change salt containment canister. A 2-D, axisymmetric finite difference computer program which models the canister walls, salt, void, and heat engine working fluid coolant was developed. Analyses included effects of conduction in canister walls and solid salt, conduction and free convection in liquid salt, conduction and radiation across salt vapor filled void regions and forced convection in the heat engine working fluid. Void shape, location, growth or shrinkage (due to density difference between the solid and liquid salt phases) were prescribed based on engineering judgement. The salt phase change process was modeled using the enthalpy method. Discussion of results focuses on the role of free-convection in the liquid salt on canister heat transfer performance. This role is shown to be important for interpreting the relationship between ground based canister performance (in l-g) and expected on-orbit performance (in micro-g). Attention is also focused on the influence of void heat transfer on canister wall temperature distributions. The large thermal resistance of void regions is shown to accentuate canister hot spots and temperature gradients.

  5. Application of approximate pattern matching in two dimensional spaces to grid layout for biochemical network maps.

    Directory of Open Access Journals (Sweden)

    Kentaro Inoue

    Full Text Available BACKGROUND: For visualizing large-scale biochemical network maps, it is important to calculate the coordinates of molecular nodes quickly and to enhance the understanding or traceability of them. The grid layout is effective in drawing compact, orderly, balanced network maps with node label spaces, but existing grid layout algorithms often require a high computational cost because they have to consider complicated positional constraints through the entire optimization process. RESULTS: We propose a hybrid grid layout algorithm that consists of a non-grid, fast layout (preprocessor algorithm and an approximate pattern matching algorithm that distributes the resultant preprocessed nodes on square grid points. To demonstrate the feasibility of the hybrid layout algorithm, it is characterized in terms of the calculation time, numbers of edge-edge and node-edge crossings, relative edge lengths, and F-measures. The proposed algorithm achieves outstanding performances compared with other existing grid layouts. CONCLUSIONS: Use of an approximate pattern matching algorithm quickly redistributes the laid-out nodes by fast, non-grid algorithms on the square grid points, while preserving the topological relationships among the nodes. The proposed algorithm is a novel use of the pattern matching, thereby providing a breakthrough for grid layout. This application program can be freely downloaded from http://www.cadlive.jp/hybridlayout/hybridlayout.html.

  6. Identification of the dynamics of a two-dimensional grid structure using least square lattice filters. [for large space structures

    Science.gov (United States)

    Montgomery, R. C.; Sundararajan, N.

    1984-01-01

    It is doubtful whether the dynamics of large space structures (LSS) can be predicted well enough for control system design applications. Hence, dynamic modeling from on-orbit measurements followed by a modification of the control system is of interest, taking into account the utilization of adaptive control concepts. The present paper is concerned with the model determination phase of the adaptive control problem. Using spectral decoupling to determine mode shapes, mode frequency and damping data can be obtained with the aid of an equation error parameter identification method. This method employs a second-order auto-regressive moving average (ARMA) model to represent the natural mode amplitudes. The discussed procedure involves an extension of the application of the least square lattice filter in system identification to a nonintegral, two-dimensional grid structure made of overlapping bars.

  7. Phase-space properties of two-dimensional elastic phononic crystals and anharmonic effects in nano-phononic crystals

    Science.gov (United States)

    Swinteck, Nichlas Z.

    This dissertation contains research directed at investigating the behavior and properties of a class of composite materials known as phononic crystals. Two categories of phononic crystals are explicitly investigated: (I) elastic phononic crystals and (II) nano-scale phononic crystals. For elastic phononic crystals, attention is directed at two-dimensional structures. Two specific structures are evaluated (1) a two-dimensional configuration consisting of a square array of cylindrical Polyvinylchloride inclusions in air and (2) a two-dimensional configuration consisting of a square array of steel cylindrical inclusions in epoxy. For the first configuration, a theoretical model is developed to ascertain the necessary band structure and equi-frequency contour features for the realization of phase control between propagating acoustic waves. In contrasting this phononic crystal with a reference system, it is shown that phononic crystals with equifrequency contours showing non-collinear wave and group velocity vectors are ideal systems for controlling the phase between propagating acoustic waves. For the second configuration, it is demonstrated that multiple functions can be realized of a solid/solid phononic crystal. The epoxy/steel phononic crystal is shown to behave as (1) an acoustic wave collimator, (2) a defect-less wave guide, (3) a directional source for elastic waves, (4) an acoustic beam splitter, (5) a phase-control device and (6) a k-space multiplexer. To transition between macro-scale systems (elastic phononic crystals) and nano-scale systems (nano-phononic crystals), a toy model of a one-dimensional chain of masses connected with non-linear, anharmonic springs is utilized. The implementation of this model introduces critical ideas unique to nano-scale systems, particularly the concept of phonon mode lifetime. The nano-scale phononic crystal of interest is a graphene sheet with periodically spaced holes in a triangular array. It is found through equilibrium

  8. Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

    CERN Document Server

    Athalye, Vivek; Uecker, Martin

    2013-01-01

    In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated wit...

  9. Quantum-optical states in finite-dimensional Hilbert space; 1, General formalism

    CERN Document Server

    Miranowicz, A; Imoto, N; Miranowicz, Adam; Leonski, Wieslaw; Imoto, Nobuyuki

    2001-01-01

    The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leo\\'nski and Tana\\'s [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schr\\"odinger cats, and squeezed vacuum. We show some i...

  10. Even and odd coherent states of a harmonic oscillator in a finite-dimensional Hilbert space and their squeezing properties

    Energy Technology Data Exchange (ETDEWEB)

    Zhu Jiuyun (Department of Physics, Hunan Normal University, Hunan 410006 (China)); Kuang Leman (Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin 300071 (China) Department of Physics and Institute of Physics, Hunan Normal University, Hunan 410081 (China))

    1994-10-03

    The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behaviour of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing. ((orig.))

  11. Hilbert series for moduli spaces of instantons on ℂ{sup 2}/ℤ{sub n}

    Energy Technology Data Exchange (ETDEWEB)

    Dey, Anindya [Theory Group and Texas Cosmology Center, Department of Physics,University of Texas at Austin, Austin, TX 78712 (United States); Hanany, Amihay [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); Mekareeya, Noppadol [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, 80805 München (Germany); Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Rodríguez-Gómez, Diego [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain); Seong, Rak-Kyeong [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); School of Physics, Korea Institute for Advanced Study,85 Hoegi-ro, Seoul 130-722 (Korea, Republic of)

    2014-01-31

    We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A{sub n−1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.

  12. Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n

    CERN Document Server

    Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong

    2014-01-01

    We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...

  13. Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n

    CERN Document Server

    Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong

    2014-01-01

    We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...

  14. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.

    Science.gov (United States)

    Daugman, J G

    1985-07-01

    Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor's famous theory of communication [J. Inst. Electr. Eng. 93, 429 (1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial-2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace.(ABSTRACT TRUNCATED AT 250 WORDS)

  15. Twenty-first century quantum mechanics Hilbert space to quantum computers mathematical methods and conceptual foundations

    CERN Document Server

    Fano, Guido

    2017-01-01

    This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...

  16. Learning the Inverse Dynamics of Robotic Manipulators in Structured Reproducing Kernel Hilbert Space.

    Science.gov (United States)

    Cheng, Ching-An; Huang, Han-Pang; Hsu, Huan-Kun; Lai, Wei-Zh; Cheng, Chih-Chun

    2016-07-01

    We investigate the modeling of inverse dynamics without prior kinematic information for holonomic rigid-body robots. Despite success in compensating robot dynamics and friction, general inverse dynamics models are nontrivial. Rigid-body models are restrictive or inefficient; learning-based models are generalizable yet require large training data. The structured kernels address the dilemma by embedding the robot dynamics in reproducing kernel Hilbert space. The proposed kernels autonomously converge to rigid-body models but require fewer samples; with a semi-parametric framework that incorporates additional parametric basis for friction, the structured kernels can efficiently model general rigid-body robots. We tested the proposed scheme in simulations and experiments; the models that consider the structure of function space are more accurate.

  17. Gravitational instanton in Hilbert space and the mass of high energy elementary particles

    Energy Technology Data Exchange (ETDEWEB)

    El Naschie, M.S

    2004-06-01

    While the theory of relativity was formulated in real spacetime geometry, the exact formulation of quantum mechanics is in a mathematical construction called Hilbert space. For this reason transferring a solution of Einstein's field equation to a quantum gravity Hilbert space is far of being a trivial problem. On the other hand {epsilon}{sup ({infinity}}{sup )} spacetime which is assumed to be real is applicable to both, relativity theory and quantum mechanics. Consequently, one may expect that a solution of Einstein's equation could be interpreted more smoothly at the quantum resolution using the Cantorian {epsilon}{sup ({infinity}}{sup )} theory. In the present paper we will attempt to implement the above strategy to study the Eguchi-Hanson gravitational instanton solution and its interpretation by 't Hooft in the context of quantum gravity Hilbert space as an event and a possible solitonic 'extended' particle. Subsequently we do not only reproduce the result of 't Hooft but also find the mass of a fundamental 'exotic' symplictic-transfinite particle m{approx_equal}1.8 MeV as well as the mass M{sub x} and M (Planck) which are believed to determine the GUT and the total unification of all fundamental interactions respectively. This may be seen as a further confirmation to an argument which we put forward in various previous publications in favour of an alternative mass acquisition mechanism based on unification and duality considerations. Thus even in case that we never find the Higgs particle experimentally, the standard model would remain substantially intact as we can appeal to tunnelling and unification arguments to explain the mass. In fact a minority opinion at present is that finding the Higgs particle is not a final conclusive argument since one could ask further how the Higgs particle came to its mass which necessitates a second Higgs field. By contrast the present argument could be viewed as an ultimate theory

  18. Berry-Esseen's central limit theorem for non-causal linear processes in Hilbert space

    CERN Document Server

    Machkouri, Mohamed EL

    2010-01-01

    Let $H$ be a real separable Hilbert space and $(a_k)_{k\\in\\mathbb{Z}}$ a sequence of bounded linear operators from $H$ to $H$. We consider the linear process $X$ defined for any $k$ in $\\mathbb{Z}$ by $X_k=\\sum_{j\\in\\mathbb{Z}}a_j(\\varepsilon_{k-j})$ where $(\\varepsilon_k)_{k\\in\\mathbb{Z}}$ is a sequence of i.i.d. centered $H$-valued random variables. We investigate the rate of convergence in the CLT for $X$ and in particular we obtain the usual Berry-Esseen's bound provided that $\\sum_{j\\in\\mathbb{Z}}\\vert j\\vert\\|a_j\\|_{\\mathcal{L}(H)}<+\\infty$ and $\\varepsilon_0$ belongs to $L_H^{\\infty}$.

  19. Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Cho Yeol

    2011-01-01

    Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.

  20. Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

    CERN Document Server

    Vanfleteren, Diederik; Bultinck, Patrick; Ayers, Paul W; Waroquier, Michel; 10.1063/1.3521493

    2011-01-01

    A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.

  1. Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs

    Directory of Open Access Journals (Sweden)

    Ruimin Xu

    2014-01-01

    Full Text Available We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.

  2. A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

    Science.gov (United States)

    Delgado-Vences, Francisco; Flandoli, Franco

    2016-08-01

    We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.

  3. A Remark on the Unitary Group of a Tensor Product of Finite-Dimensional Hilbert Spaces

    Indian Academy of Sciences (India)

    K R Parthasarathy

    2003-02-01

    Let $H_i, 1 ≤ i ≤ n$ be complex finite-dimensional Hilbert spaces of dimension $d_i, 1 ≤ i ≤ n$ respectively with $d_i ≥ 2$ for every . By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product $H = H_1 \\otimes H_2 \\otimes\\ldots \\otimes H_n$ can be expressed as a composition of a finite number of unitary operators living on pair products $H_i \\otimes H_j, 1 ≤ i, j ≤ n$. An estimate of the number of operators appearing in such a composition is obtained.

  4. Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Mohammed Benharrat

    2015-08-01

    Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces  H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.

  5. Mathematical methods in physics distributions, Hilbert space operators, variational methods, and applications in quantum physics

    CERN Document Server

    Blanchard, Philippe

    2015-01-01

    The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas.  The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories.  All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods.   The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...

  6. Extension of Wirtinger's Calculus in Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS

    CERN Document Server

    Bouboulis, Pantelis

    2010-01-01

    Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on and real valued data sequences. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \\textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associat...

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

    Energy Technology Data Exchange (ETDEWEB)

    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 [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

    2017-06-15

    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 solution 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.

  8. Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space

    Directory of Open Access Journals (Sweden)

    Jirí Janda

    2013-01-01

    Full Text Available The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space with the usual sum of operators. The structure of the set of not only positive linear operators can be described with the notion of a weakly ordered partial commutative group (wop-group.Due to the non-constructive algebraic nature of the wop-group we introduce its stronger version called a weakly ordered partial a-commutative group (woa-group. We show that it also describes the structure of not only positive linear operators.

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

    Science.gov (United States)

    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.

  10. Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Mohammed Benharrat

    2015-08-01

    Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces  H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.

  11. Real-space and plane-wave hybrid method for electronic structure calculations for two-dimensional materials

    Science.gov (United States)

    Do, V. Nam; Le, H. Anh; Vu, V. Thieu

    2017-04-01

    We propose a computational approach to combining the plane-wave method and the real-space treatment to describe the periodic variation in the material plane and the decay of wave functions from the material surfaces. The proposed approach is natural for two-dimensional material systems and thus may circumvent some intrinsic limitations involving the artificial replication of material layers in traditional supercell methods. In particular, we show that the proposed method is easy to implement and, especially, computationally effective since low-cost computational algorithms, such as iterative and recursive techniques, can be used to treat matrices with block tridiagonal structure. Using this approach we show first-principles features that supplement the current knowledge of some fundamental issues in bilayer graphene systems, including the coupling between the two graphene layers, the preservation of the σ band of monolayer graphene in the electronic structure of the bilayer system, and the differences in low-energy band structure between the AA- and AB-stacked configurations.

  12. Construction and coupling of frames in Hilbert spaces with W-metrics

    Directory of Open Access Journals (Sweden)

    German Escobar

    2016-01-01

    Full Text Available Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.

  13. Strong convergence theorem for a generalized equilibrium problem and a κ-strict pseudocontraction in Hilbert spaces

    Institute of Scientific and Technical Information of China (English)

    Shi-sheng ZHANG; Ruo-feng RAO; Jia-lin HUANG

    2009-01-01

    The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a κ-strict pseudocontractive mapping in the Hilbert space.The presented results extend and improve the corresponding results reported in the literature.

  14. A note on stability of the integral-differential equation of the hyperbolic type in a Hilbert space

    NARCIS (Netherlands)

    Ashyraliyev, M.

    2008-01-01

    In this paper, the initial-value problem for integral-differential equation of the hyperbolic type in a Hilbert space H is considered. The unique solvability of this problem is established. The stability estimates for the solution of this problem are obtained. The difference scheme approximately sol

  15. Hilbert空间H中G-框架的扰动%Perturbations of G-Frames in Hilbert Spaces

    Institute of Scientific and Technical Information of China (English)

    姚喜妍

    2008-01-01

    In this paper,we discuss the properties of g-frames and g-frame operators for Hilbert spaces by utilizing the method of operator theory.Furthermore,we study perturbations of g-frames,and obtain some meaningful results.

  16. Group-theoretical approach to the construction of bases in 2{sup n}-dimensional Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Garcia, A.; Romero, J. L.; Klimov, A. B., E-mail: klimov@cencar.udg.mx [Universidad de Guadalajara, Departamento de Fisica (Mexico)

    2011-06-15

    We propose a systematic procedure to construct all the possible bases with definite factorization structure in 2{sup n}-dimensional Hilbert space and discuss an algorithm for the determination of basis separability. The results are applied for classification of bases for an n-qubit system.

  17. Truncated Hilbert space approach to the 2d ϕ{sup 4} theory

    Energy Technology Data Exchange (ETDEWEB)

    Bajnok, Zoltan [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,Konkoly Thege Miklós út 29-33, Budapest (Hungary); Lajer, Marton [Roland Eötvös University,Pázmány Péter sétány 1/A, Budapest (Hungary)

    2016-10-11

    We apply the massive analogue of the truncated conformal space approach to study the two dimensional ϕ{sup 4} theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We interpret the results in terms of the Bethe-Yang spectrum, from which we extract the infinite volume masses and scattering matrices for various couplings. We compare these results against semiclassical analysis and perturbation theory. We also analyze the critical point of the model and confirm that it is in the Ising universality class.

  18. Variationality with second derivatives, relativistic uniform acceleration, and the 'spin'-curvature interaction in two-dimensional space-time

    OpenAIRE

    Matsyuk, Roman

    2015-01-01

    A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.

  19. Two dimensional vernier

    Science.gov (United States)

    Juday, Richard D. (Inventor)

    1992-01-01

    A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.

  20. The discrete Fourier transform and the quantum-mechanical oscillator in a finite-dimensional Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Santhanam, Thalanayar S [Department of Physics Saint Louis University, Missouri, MO 63103 (United States); Santhanam, Balu [Department of Electrical and Computer Engineering, MSC01 1100 1, University of New Mexico Albuquerque, NM 87131-0001 (United States)], E-mail: santhats@slu.edu, E-mail: bsanthan@ece.unm.edu

    2009-05-22

    Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.

  1. Fractional Killing-Yano Tensors and Killing Vectors Using the Caputo Derivative in Some One- and Two-Dimensional Curved Space

    Directory of Open Access Journals (Sweden)

    Ehab Malkawi

    2014-01-01

    Full Text Available The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.

  2. Analytic Hilbert modules

    CERN Document Server

    Chen, Xiaoman

    2003-01-01

    The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results under one cover. Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules reports on the progress made by the authors and others, including the characteristic space theory, rigidity, the equivalence problem, the Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.

  3. Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

    CERN Document Server

    Strauss, Y; Eisenberg, E

    2000-01-01

    We show that models for the quantum Lax-Phillips theory of scattering and unstable systems can be constructed for which the evolution is pointwise on a time axis that can be put into correspondence with laboratory time; in the Lax-Phillips free translation representation the evolution operator acts as a smooth kernel, thus satisfying the condition for a nontrivial relation between the singularities of the S-matrix and the spectrum of the generator of the semigroup describing resonance decay. We show, furthermore, that the Lax-Phillips S-matrix is unitarily related to the S-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\\sigma$ of the Lax-Phillips theory. Analytic continuation in $\\sigma$ to find the null space has some of the properties of a method developed some time ago for application to dilation analytic potentials, but, in Lax-Phillips theory, results in a resonant state which lies in the original Hilbert space of states. We work out an illustrativ...

  4. On the continuity of the map square root of nonnegative isomorphisms in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Jeovanny de Jesus Muentes Acevedo

    2015-06-01

    Full Text Available Let H be a real (or complex Hilbert space. Every nonnegative operator L ∈ L(H admits a unique nonnegative square root R ∈ L(H, i.e., a nonnegative operator R ∈ L(H such that R2 = L. Let GL+ S (H be the set of nonnegative isomorphisms in L(H. First we will show that GL+ S (H is a convex (real Banach manifold. Denoting by L1/2 the nonnegative square root of L. In [3], Richard Bouldin proves that L1/2 depends continuously on L (this proof is non-trivial. This result has several applications. For example, it is used to find the polar decomposition of a bounded operator. This polar decomposition allows us to determine the positive and negative spectral subespaces of any self-adjoint operator, and moreover, allows us to define the Maslov index. The autor of the paper under review provides an alternative proof (and a little more simplified that L1/2 depends continuously on L, and moreover, he shows that the map is a homeomorphism. Resumen. Sea H un espacio de Hilbert real (o complejo. Todo operador no negativo L ∈ L(H admite una única raíz cuadrada no negativa R ∈ L(H, esto es, un operador no negativo R ∈ L(H tal que R2 = L. Sea GL+ S (H el conjunto de los isomorfismos no negativos en L(H. Primero probaremos que GL+ S (H es una variedad de Banach (real. Denotando como L1/2 la raíz cuadrada no negativa de L, en [3] Richard Bouldin prueba que L1/2 depende continuamente de L (esta prueba es no trivial. Este resultado tiene varias aplicaciones. Por ejemplo, es usado para encontrar la descomposición polar de un operador limitado. Esta descomposición polar nos lleva a determinar los subespacios espectrales positivos y negativos de cualquier operador autoadjunto, y además, lleva a definir el índice de Máslov. El autor de este artículo da una prueba alternativa (y un poco más simplificada de que L1/2 depende continuamente de L, y además, prueba que la aplicación es un homeomorfismo

  5. Simulating the Generalized Gibbs Ensemble (GGE): A Hilbert space Monte Carlo approach

    Science.gov (United States)

    Alba, Vincenzo

    By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg (XXX) chain. The key idea is to sample the Hilbert space of the model with the appropriate GGE probability measure. The method can be extended to other integrable systems, such as the Lieb-Liniger model. We benchmark the approach focusing on GGE expectation values of several local observables. As finite-size effects decay exponentially with system size, moderately large chains are sufficient to extract thermodynamic quantities. The Monte Carlo results are in agreement with both the Thermodynamic Bethe Ansatz (TBA) and the Quantum Transfer Matrix approach (QTM). Remarkably, it is possible to extract in a simple way the steady-state Bethe-Gaudin-Takahashi (BGT) roots distributions, which encode complete information about the GGE expectation values in the thermodynamic limit. Finally, it is straightforward to simulate extensions of the GGE, in which, besides the local integral of motion (local charges), one includes arbitrary functions of the BGT roots. As an example, we include in the GGE the first non-trivial quasi-local integral of motion.

  6. On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint.

    Science.gov (United States)

    Zhang, Chong; Liu, Yufeng; Wu, Yichao

    2016-04-01

    For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint.

  7. WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES

    Directory of Open Access Journals (Sweden)

    Yu Miao

    2008-08-01

    Full Text Available In a real {sc Hilbert} space $H$, starting from an arbitrary initialpoint $x_0in H$, an iterative process is defined as follows:$x_{n+1}=a_nx_n+(1-a_nT^{lambda_{n+1}}_fy_n$, $y_n= b_nx_n+(1-b_nT^{eta_{n}}_gx_n$, $nge 0$, where$T^{lambda_{n+1}}_f x= Tx-lambda_{n+1} mu_f f(Tx$,$T^{eta_{n}}_g x= Tx-eta_{n} mu_g g(Tx$, ($forall xinH$, $T: Ho H$ a nonexpansive mappingwith $F(T eemptyset$ and $f$ (resp. $g$ $: Ho H$ an$eta_f$ (resp. $eta_g$-strongly monotone and $k_f$ (resp. $k_g$-Lipschitzianmapping, ${a_n}subset(0,1$, ${b_n}subset(0,1$ and ${lambda_n}subset[0,1$,${eta_n}subset[0,1$. Under some suitable conditions, severalconvergence results of the sequence ${x_n}$ are shown.

  8. Representation of quantum mechanical resonances in the Lax-Phillips Hilbert space

    Energy Technology Data Exchange (ETDEWEB)

    Strauss, Y. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Horwitz, L. P. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Eisenberg, E. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

    2000-01-01

    We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips S-matrix is unitarily related to the S-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable σ of the Lax-Phillips theory. Analytic continuation in σ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.

  9. Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spaces

    CERN Document Server

    Niemiec, Piotr

    2011-01-01

    An \\textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) for $N$-tuples of closed densely defined linear operators acting in a common (arbitrary) Hilbert space are presented. Algebraic and order (with respect to containment) properties of the class $CDD_N$ of all unitary equivalence classes of such $N$-tuples are established and certain ideals in $CDD_N$ are distinguished. It is proved that infinite operations in $CDD_N$ may be reconstructed from the direct sum operation of a pair. \\textit{Prime decomposition} in $CDD_N$ is proposed and its (in a sense) uniqueness is established. The issue of classification of ideals in $CDD_N$ (up to isomorphism) is discussed. A model for $CDD_N$ is described and its concrete realization is presented. A new partial order of $N$-tuples of operators is introduced and its fundamental...

  10. Dimensions of subspaces of a Hilbert space and index of the semi-Fredholm operator

    Institute of Scientific and Technical Information of China (English)

    马吉溥

    1996-01-01

    Let 2" denote the set of all closed subspaces of the Hilbert space H. The generalized dimension, dim gH0 for any , is introduced. Then an order is defined in [2H], the set of generalized dimensions of 2H. It makes [2H] totally ordered such that 0m. Based on these facts, the generalized index, indg is defined for any A SF(H) (the set of all semi-Fredholm operators) and Tnd gA = is proved for any pure semi-Fredholm operator A SF+(H)(SF.(H)). The generalized index and dimension defined here are topologjcal and geometric, similar to the index of a Fredholm operator and the finite dimension. Some calculus of analysis can be performed on them (usually, and 1, 2,..., are identified with A known result deduced from this fact is not very proper, as will be shown later). For example, considering isometric operators in I (H) it is proved that V1,V2 are arcwise connected in B1x (H) (the set of all

  11. Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space

    Science.gov (United States)

    Ioan Boţ, Radu; Hofmann, Bernd

    2016-12-01

    In the literature on singular perturbation (Lavrentiev regularization) for the stable approximate solution of operator equations with monotone operators in the Hilbert space the phenomena of conditional stability and local well-posedness or ill-posedness are rarely investigated. Our goal is to present some studies which try to bridge this gap. So we present new results on the impact of conditional stability on error estimates and convergence rates for the Lavrentiev regularization and distinguish for linear problems well-posedness and ill-posedness in a specific manner motivated by a saturation result. Taking into account that the behavior of the bias (regularization error in the noise-free case) is crucial, general convergence rates, including logarithmic rates, are derived for linear operator equations by means of the method of approximate source conditions. This allows us to extend well-known convergence rate results for the Lavrentiev regularization that were based on general source conditions to the case of non-selfadjoint linear monotone forward operators for which general source conditions fail. Examples presenting the self-adjoint multiplication operator as well as the non-selfadjoint fractional integral operator and Cesàro operator illustrate the theoretical results. Extensions to the nonlinear case under specific conditions on the nonlinearity structure complete the paper.

  12. Band-gap tuning and optical response of two-dimensional SixC1 -x : A first-principles real-space study of disordered two-dimensional materials

    Science.gov (United States)

    Sadhukhan, Banasree; Singh, Prashant; Nayak, Arabinda; Datta, Sujoy; Johnson, Duane D.; Mookerjee, Abhijit

    2017-08-01

    We present a real-space formulation for calculating the electronic structure and optical conductivity of random alloys based on Kubo-Greenwood formalism interfaced with augmented space recursion technique [Mookerjee, J. Phys. C 6, 1340 (1973), 10.1088/0022-3719/6/8/003] formulated with the tight-binding linear muffin-tin orbital basis with the van Leeuwen-Baerends corrected exchange potential [Singh, Harbola, Hemanadhan, Mookerjee, and Johnson, Phys. Rev. B 93, 085204 (2016), 10.1103/PhysRevB.93.085204]. This approach has been used to quantitatively analyze the effect of chemical disorder on the configuration averaged electronic properties and optical response of two-dimensional honeycomb siliphene SixC1 -x beyond the usual Dirac-cone approximation. We predicted the quantitative effect of disorder on both the electronic structure and optical response over a wide energy range, and the results are discussed in the light of the available experimental and other theoretical data. Our proposed formalism may open up a facile way for planned band-gap engineering in optoelectronic applications.

  13. Stability for a New Class of GNOVI with (γG,λ-Weak-GRD Mappings in Positive Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Hong Gang Li

    2016-01-01

    Full Text Available By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions with (γG,λ-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained.

  14. A Fibonacci collocation method for solving a class of Fredholm–Volterra integral equations in two-dimensional spaces

    Directory of Open Access Journals (Sweden)

    Farshid Mirzaee

    2014-06-01

    Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.

  15. Real Operator Algebras on a Complex Hilbert Space%复Hilbert空间上的实算子代数

    Institute of Scientific and Technical Information of China (English)

    李炳仁

    2009-01-01

    We study real operator algebras on a complex Hilbert space H. From H, we can get a real Hilbert space H_r. Further, we have a complex Hilbert space H_(rc)= H_r+iH_r. Through this process, we prove the following. If A and M are uniformly closed and weakly closed real * operator algebras on H respectively, then their complex span A + iA and M + iM are (complex) C*-algebra and (complex) von Neumann algebra on H, respectively. Here, we don't need the condition: A∩iA = {0}, M∩iM = {0}. So our result is a generalization of Stormer's result.%本文研究在一个复Hilbert空间H上的实算子代数.从H可以得到一个实Hilbert空间Hr珥,进而又有一个复Hilbert空间H_(rc)=H_r+iH_r.通过这个过程,证明了如下结果.如果A,M分别是H上一致闭的,弱闭的实*算子代数,则它们的复扩张A+iA,M4-iM分别是日上的(复)C~*代数,(复)von Neumann代数.这里,不需要条件A∩iA={0},MniM={0}.因此,我们的结果是Stormer结果的推广.

  16. New Čebyšev Type Inequalities and Applications for Functions of Self-Adjoint Operators on Complex Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Mohammad W. Alomari

    2014-01-01

    Full Text Available Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of self-adjoint operators on complex Hilbert spaces are provided as well.

  17. The Nonrelativistic Ground State Energy Spectra of Potential Counting Coulomb and Quad-ratic Terms in Non-commutative Two Dimensional Real Spaces and Phases

    OpenAIRE

    Abdelmadjid Maireche

    2016-01-01

    A novel theoretical study for the exact solvability of nonrelativistic quantum spectrum systems for potential containing coulomb and quadratic terms is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), it has been observed that the exact corrections for the ground states spectrum of studied potential was depended on two infinitesimals parameters and which plays an opposite rolls, and we ha...

  18. Unitary and Non-Unitary Matrices as a Source of Different Bases of Operations Acting on Hilbert Spaces

    CERN Document Server

    Filippov, S N

    2010-01-01

    The columns of $d^2 \\times N$ matrices are shown to create different kinds of sets of $N$ operators acting on $d$-dimensional Hilbert space. This construction corresponds to formalism of star-product of the operator symbols. The known bases are shown to be partial cases of generic formulas obtained by using $d^2 \\times d^2$ matrices as the source for constructing the arbitrary bases. The known examples of the SIC, MUB and phase-space descriptions of qubit states are considered from the viewpoint of a developed unified approach. Qubit examples are given in detail.

  19. Quantum algorithms and mathematical formulations of biomolecular solutions of the vertex cover problem in the finite-dimensional hilbert space.

    Science.gov (United States)

    Chang, Weng-Long; Ren, Ting-Ting; Feng, Mang

    2015-01-01

    In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.

  20. Two-dimensional function photonic crystals

    CERN Document Server

    Wu, Xiang-Yao; Liu, Xiao-Jing; Liang, Yu

    2016-01-01

    In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates $\\vec{r}$, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed into the appropriate band gaps structures by the two-dimensional function photonic crystals.

  1. Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space

    Institute of Scientific and Technical Information of China (English)

    WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie

    2008-01-01

    In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.

  2. Two-dimensional T2 distribution mapping in rock core plugs with optimal k-space sampling.

    Science.gov (United States)

    Xiao, Dan; Balcom, Bruce J

    2012-07-01

    Spin-echo single point imaging has been employed for 1D T(2) distribution mapping, but a simple extension to 2D is challenging since the time increase is n fold, where n is the number of pixels in the second dimension. Nevertheless 2D T(2) mapping in fluid saturated rock core plugs is highly desirable because the bedding plane structure in rocks often results in different pore properties within the sample. The acquisition time can be improved by undersampling k-space. The cylindrical shape of rock core plugs yields well defined intensity distributions in k-space that may be efficiently determined by new k-space sampling patterns that are developed in this work. These patterns acquire 22.2% and 11.7% of the k-space data points. Companion density images may be employed, in a keyhole imaging sense, to improve image quality. T(2) weighted images are fit to extract T(2) distributions, pixel by pixel, employing an inverse Laplace transform. Images reconstructed with compressed sensing, with similar acceleration factors, are also presented. The results show that restricted k-space sampling, in this application, provides high quality results.

  3. The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation

    CERN Document Server

    Bishop, Raymond F

    2013-01-01

    The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the ground-state wave functions $|\\Psi\\rangle= e^S |\\Phi\\rangle$ which live in the "physical" Hilbert space ${\\cal H}^{(P)}$ using an elementary ansatz for $|\\Phi\\rangle$ plus a formal expansion of $S$ in an operator basis of multi-configurational creation operators. In our paper a reinterpretation of the method is proposed. Using parallels between the CCM and the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum mechanics, the CCM transition from the known microscopic Hamiltonian (denoted by usual symbol $H$), which is self-adjoint in ${\\cal H}^{(P)}$, to its effective lower-case isospectral avatar $\\hat{h}=e^{-S} H e^S$, is assigned a THS interpretation. In the opposite direction, a THS-prescribed, non-CCM, innovative reinstallation of Hermiticity is shown to be possible for the CCM effective Hamiltonian $\\hat{h}$, ...

  4. Entanglement in a two-dimensional string theory

    CERN Document Server

    Donnelly, William

    2016-01-01

    What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider entanglement entropy in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large $N$. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space, giving a precise state-counting interpretation to the entropy, including its leading $O(N^2)$ piece. In the process we reinterpret the sphere partition function as a thermal ensemble of of open strings whose endpoints are anchored to an object at the entangling surface that we call an E-brane.

  5. A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation

    Indian Academy of Sciences (India)

    Ibrahim A Abbas

    2011-06-01

    The theory of thermoelasticity with energy dissipation is employed to study plane waves in a fibre-reinforced anisotropic thermoelastic half-space. We apply a thermal shock on the surface of the half-space which is taken to be traction free. The problem is solved numerically using a finite element method. Moreover, the numerical solutions of the non-dimensional governing partial differential equations of the problem are shown graphically. Comparisons are made with the results predicted by Green–Naghdi theory of the two types (GNII without energy dissipation) and (GNIII with energy dissipation). We found that the reinforcement has great effect on the distribution of field quantities. Results carried out in this paper can be used to design various fibre-reinforced anisotropic thermoelastic elements under thermal load to meet special engineering requirements.

  6. The rigged Hilbert space approach to the Lippmann-Schwinger equation: II. The analytic continuation of the Lippmann-Schwinger bras and kets

    Energy Technology Data Exchange (ETDEWEB)

    Madrid, Rafael de la [Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States)

    2006-04-14

    The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting in a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.

  7. Two-dimensional NMR relaxometry study of pore space characteristics of carbonate rocks from a Permian aquifer

    Science.gov (United States)

    Schoenfelder, Wiete; Gläser, Hans-Reinhard; Mitreiter, Ivonne; Stallmach, Frank

    2008-06-01

    Limestones and karstified limestones (dolostones) from a Permian aquifer in Central Germany were studied by 1H 2D NMR relaxometry and PFG NMR diffusometry, aiming at a non-destructive characterization of the pore space. Information concerning pore size distribution and water diffusion were in accord for different samples of each type of rock, but differed fundamentally between limestones and dolostones. The results of the 2D relaxometry measurements revealed a ratio of surface relaxation times Ts1/ Ts2 of about 2 for the limestones and about 4.5 for the dolostones, mirroring the different content of iron and manganese in the solid pore walls. In consideration of thin section interpretation, the corresponding fraction in the T1- T2 relaxation time distributions was attributed to interparticle porosity. Porosity of large vugs is clearly displayed by relaxation times longer than 1 s in the dolostones only. A third fraction of the total water-saturated pore space in the dolostones, which is clearly displayed in the 2D relaxation time distributions at the smallest relaxation times and a Ts1/ Ts2 ratio of about 12, is attributed to intrafossil porosity. The porosity classification, basing on non-destructive NMR experiments, is verified by mercury intrusion porosimetry and thin section interpretation.

  8. On the Extrema of Dirichlet's First Eigenvalue of a Family of Punctured Regular Polygons in Two Dimensional Space Forms

    Indian Academy of Sciences (India)

    A R Aithal; Rajesh Raut

    2012-05-01

    Let $\\wp 1,\\wp 0$ be two regular polygons of sides in a space form $M^2()$ of constant curvature =0,1 or -1 such that $\\wp 0\\subset\\wp 1$ and having the same center of mass. Suppose $\\wp 0$ is circumscribed by a circle contained in $\\wp 1$. We fix $\\wp 1$ and vary $\\wp 0$ by rotating it in about its center of mass. Put $ =(\\wp 1\\backslash\\wp 0)^0$, the interior of $\\wp 1\\backslash\\wp 0$ in $M^2()$. It is shown that the first Dirichlet’s eigenvalue 1() attains extremum when the axes of symmetry of $\\wp 0$ coincide with those of $\\wp 1$.

  9. A new method for the determination of peak distribution across a two-dimensional separation space for the identification of optimal column combinations.

    Science.gov (United States)

    Leonhardt, Juri; Teutenberg, Thorsten; Buschmann, Greta; Gassner, Oliver; Schmidt, Torsten C

    2016-11-01

    For the identification of the optimal column combinations, a comparative orthogonality study of single columns and columns coupled in series for the first dimension of a microscale two-dimensional liquid chromatographic approach was performed. In total, eight columns or column combinations were chosen. For the assessment of the optimal column combination, the orthogonality value as well as the peak distributions across the first and second dimension was used. In total, three different methods of orthogonality calculation, namely the Convex Hull, Bin Counting, and Asterisk methods, were compared. Unfortunately, the first two methods do not provide any information of peak distribution. The third method provides this important information, but is not optimal when only a limited number of components are used for method development. Therefore, a new concept for peak distribution assessment across the separation space of two-dimensional chromatographic systems and clustering detection was developed. It could be shown that the Bin Counting method in combination with additionally calculated histograms for the respective dimensions is well suited for the evaluation of orthogonality and peak clustering. The newly developed method could be used generally in the assessment of 2D separations. Graphical Abstract ᅟ.

  10. Two-Dimensional Vernier Scale

    Science.gov (United States)

    Juday, Richard D.

    1992-01-01

    Modified vernier scale gives accurate two-dimensional coordinates from maps, drawings, or cathode-ray-tube displays. Movable circular overlay rests on fixed rectangular-grid overlay. Pitch of circles nine-tenths that of grid and, for greatest accuracy, radii of circles large compared with pitch of grid. Scale enables user to interpolate between finest divisions of regularly spaced rule simply by observing which mark on auxiliary vernier rule aligns with mark on primary rule.

  11. Invariant Robust 3-D Face Recognition based on the Hilbert Transform in Spectral Space

    Directory of Open Access Journals (Sweden)

    Eric Paquet

    2006-04-01

    Full Text Available One of the main objectives of face recognition is to determine whether an acquired face belongs to a reference database and to subsequently identify the corresponding individual. Face recognition has application in, for instance, forensic science and security. A face recognition algorithm, to be useful in real applications, must discriminate in between individuals, process data in real-time and be robust against occlusion, facial expression and noise.A new method for robust recognition of three-dimensional faces is presented. The method is based on harmonic coding, Hilbert transform and spectral analysis of 3-D depth distributions. Experimental results with three-dimensional faces, which were scanned with a laser scanner, are presented. The proposed method recognises a face with various facial expressions in the presence of occlusion, has a good discrimination, is able to compare a face against a large database of faces in real-time and is robust against shot noise and additive noise.

  12. On orthogonal systems in Hilbert C*-modules

    OpenAIRE

    Landi, Giovanni; PAVLOV, Alexander

    2009-01-01

    Analogues for Hilbert C*-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C*-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.

  13. Mayet-Godowski Hilbert Lattice Equations

    OpenAIRE

    Megill, Norman D.; Pavicic, Mladen

    2006-01-01

    Several new results in the field of Hilbert lattice equations based on states defined on the lattice as well as novel techniques used to arrive at these results are presented. An open problem of Mayet concerning Hilbert lattice equations based on Hilbert-space-valued states is answered.

  14. Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds

    CERN Document Server

    Ivashkovich, S

    2011-01-01

    We prove the Royden's Lemma for complex Hilbert manifolds, i.e., that a holomorphic imbedding of the closure of a finite dimensional, strictly pseudoconvex domain into a complex Hilbert manifold extends to a biholomorphic mapping onto a product of this domain with the unit ball in Hilbert space. This reduces several problems concerning complex Hilbert manifolds to open subsets of a Hilbert space. As an illustration we prove some results on generalized loop spaces of complex manifolds.

  15. 赋范线性空间中的Hilbert型积分不等式%Hilbert-type Integral Inequalities in Normed Linear Spaces

    Institute of Scientific and Technical Information of China (English)

    匡继昌

    2013-01-01

    基于利用一个积分恒等式的新技巧,建立了赋范线性空间中新的Hilbert型积分不等式.这些新的结果包含了n维欧氏空间中n重积分的Hilbert型积分不等式作为其特殊情形.%In this paper we employ a new technique based on an integral identity to study some new Hilbert-type integral inequalities in normed linear spaces. These new results include the corresponding multiple Hilbert-type integral inequalities in Rn as special cases.

  16. Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

    Institute of Scientific and Technical Information of China (English)

    Muhammad Ashfaq Ahmad; Lin Jie; Qian Yan; Ma Zhi-Min; Ma Ai-Qun; Liu Shu-Tian

    2007-01-01

    This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.

  17. Evaluation of aqueductal patency in patients with hydrocephalus: three-dimensional high-sampling-efficiency technique (SPACE) versus two-dimensional turbo spin echo at 3 Tesla.

    Science.gov (United States)

    Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut

    2014-01-01

    To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.

  18. Evaluation of aqueductal patency in patients with hydrocephalus: Three-dimensional high-sampling efficiency technique(SPACE) versus two-dimensional turbo spin echo at 3 Tesla

    Energy Technology Data Exchange (ETDEWEB)

    Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut [School of Medicine, Gazi University, Ankara (Turkey)

    2014-12-15

    To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.

  19. Two-dimensional calculus

    CERN Document Server

    Osserman, Robert

    2011-01-01

    The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

  20. Model independent search for new particles in two-dimensional mass space using events with missing energy, two jets and two leptons with the CMS detector

    CERN Document Server

    AUTHOR|(CDS)2080070; Hebbeker, Thomas

    2017-07-07

    The discovery of a new particle consistent with the standard model Higgs boson at the Large Hadron Collider in 2012 completed the standard model of particle physics (SM). Despite its remarkable success many questions remain unexplained. Numerous theoretical models, predicting the existence of new heavy particles, provide answers to these unresolved questions and are tested at high energy experiments such as the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC). In this thesis a model independent search method for new particles in two-dimensional mass space in events with missing transverse energy is presented using 19.7 $\\mbox{fb}^{-1}$ of proton-proton collision data recorded by the CMS detector at a centre of mass energy $\\sqrt{s}$ = 8 TeV at the LHC. The analysis searches for signatures of pair-produced new heavy particles $\\mbox{T}^\\prime$ which decay further into unknown heavy particles $\\mbox{W}^\\prime$ and SM quarks $q$ ($\\mbox{T}^\\prime\\overline{\\mbox{T}^\\prime} \\rightarrow {...

  1. Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space

    CERN Document Server

    Xin, Jun-Li

    2010-01-01

    We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level-space of angular momentum being greater or less than $\\hbar$ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily $2\\pi$-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The quantum mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144) becomes a special case of th...

  2. Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

    Science.gov (United States)

    Xin, Jun-Li; Liang, Jiu-Qing

    2012-04-01

    We study quantum—classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than ħ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

  3. Two-dimensional optical spectroscopy

    CERN Document Server

    Cho, Minhaeng

    2009-01-01

    Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.

  4. Coherent States for generalized oscillator with finite-dimensional Hilbert space

    OpenAIRE

    Borzov, Vadim V.; Damaskinsky, Eugene V.

    2006-01-01

    The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider the generalized oscillator connected with Krawtchouk polynomials.

  5. 模糊紧空间在其一个自然的Hilbert方体紧化中的拓扑位置%The Topological Place of the Space of Fuzzy Compacta in Its Naturnal Hilbert Cube Compactification

    Institute of Scientific and Technical Information of China (English)

    张丽丽

    2012-01-01

    In this paper, our aim is to discuss the topological place of the space of fuzzy compacta in its Naturnal Hilbert cube compactification. By using the topological characterization of the pseudoboundary in the Hilbert cube, we show that the space of fuzzy compacta is a pseudointerior of its Hilbert cube compact if ication.%以讨论模糊紧空间在其一个自然的Hilbert方体紧化中的拓扑位置为目的,利用Hilbert方体中伪边界的拓扑刻画,得出模糊紧空间是其Hilbert方体紧化的伪内部.

  6. Quantum Hilbert Hotel

    Science.gov (United States)

    Potoček, Václav; Miatto, Filippo M.; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S.; Liapis, Andreas C.; Oi, Daniel K. L.; Boyd, Robert W.; Jeffers, John

    2015-10-01

    In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

  7. Quantum Hilbert Hotel.

    Science.gov (United States)

    Potoček, Václav; Miatto, Filippo M; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; Liapis, Andreas C; Oi, Daniel K L; Boyd, Robert W; Jeffers, John

    2015-10-16

    In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

  8. Feynman's Operational Calculus and the Stochastic Functional Calculus in Hilbert Space

    OpenAIRE

    Jefferies, Brian

    2010-01-01

    Let $A_1, A_2$ be bounded linear operators acting on a Banach space $E$. A pair $(\\mu_1, \\mu_2)$ of continuous probability measures on $[0,1]$ determines a functional calculus $f \\rightarrowtail f_{\\mu1,|mu2}(A_1, A_2)$ for analytic functions $f$ by weighting all possible orderings of operator products of $A_1$ and $A_2$ via the probability measures $\\mu_1$ and $\\mu_2$. For example, $f \\rightarrowtail f_{\\mu,\\mu}(A_1, A_2)$ is the Weyl functional calculus with equally weighted operator produc...

  9. Examples of bosonic de Finetti states over finite dimensional Hilbert spaces

    CERN Document Server

    Gottlieb, A D

    2005-01-01

    According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose-Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consider Gibbs ensembles for systems of bosons in a finite dimensional setting and discover limits as the number of particles tends to infinity, provided the temperature is scaled in proportion to particle number.

  10. Quasi-static deformation due to two-dimensional seismic sources embedded in an elastic half-space in welded contact with a poroelastic half-space

    Indian Academy of Sciences (India)

    Sunita Rani; Sarva Jit Singh

    2007-04-01

    The Biot linearized theory of fluid saturated porous materials is used to study the plane strain deformation of a two-phase medium consisting of a homogeneous, isotropic, poroelastic half-space in welded contact with a homogeneous, isotropic, perfectly elastic half-space caused by a twodimensional source in the elastic half-space. The integral expressions for the displacements and stresses in the two half-spaces in welded contact are obtained from the corresponding expressions for an unbounded elastic medium by applying suitable boundary conditions at the interface. The case of a long dip-slip fault is discussed in detail. The integrals for this source are solved analytically for two limiting cases: (i) undrained conditions in the high frequency limit, and (ii) steady state drained conditions as the frequency approaches zero. It has been verified that the solution for the drained case ( → 0) coincides with the known elastic solution. The drained and undrained displacements and stresses are compared graphically. Diffusion of the pore pressure with time is also studied.

  11. Two-dimensional function photonic crystals

    Science.gov (United States)

    Liu, Xiao-Jing; Liang, Yu; Ma, Ji; Zhang, Si-Qi; Li, Hong; Wu, Xiang-Yao; Wu, Yi-Heng

    2017-01-01

    In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.

  12. Truncated Hilbert Space Approach for the 1+1D phi^4 Theory

    CERN Document Server

    CERN. Geneva

    2016-01-01

    (an informal seminar, not a regular string seminar) We used the massive analogue of the truncated conformal space approach to study the broken phase of the 1+1 dimensional scalar phi^4 model in finite volume, similarly to the work by S. Rychkov and L. Vitale. In our work, the finite size spectrum was determined numerically using an effective eigensolver routine, which was followed by a simple extrapolation in the cutoff energy. We analyzed both the periodic and antiperiodic sectors. The results were compared with semiclassical and Bethe-Yang results as well as perturbation theory. We obtained the coupling dependence of the infinite volume breather and kink masses for moderate couplings. The results fit well with semiclassics and perturbative estimations, and confirm the conjecture of Mussardo that at most two neutral excitations can exist in the spectrum. We believe that improving our method with the renormalization procedure of Rychkov et al. enables to measure further interesting quantities such as decay ra...

  13. A Novel Approach for Microgrid Protection Based upon Combined ANFIS and Hilbert Space-Based Power Setting

    Directory of Open Access Journals (Sweden)

    Ali Hadi Abdulwahid

    2016-12-01

    Full Text Available Nowadays, the use of distributed generation (DG has increased because of benefits such as increased reliability, reduced losses, improvement in the line capacity, and less environmental pollution. The protection of microgrids, which consist of generation sources, is one of the most crucial concerns of basic distribution operators. One of the key issues in this field is the protection of microgrids against permanent and temporary failures by improving the safety and reliability of the network. The traditional method has a number of disadvantages. The reliability and stability of a power system in a microgrid depend to a great extent on the efficiency of the protection scheme. The application of Artificial Intelligence approaches was introduced recently in the protection of distribution networks. The fault detection method depends on differential relay based on Hilbert Space-Based Power (HSBP theory to achieve fastest primary protection. It is backed up by a total harmonic distortion (THD detection method that takes over in case of a failure in the primary method. The backup protection would be completely independent of the main protection. This is rarely attained in practice. This paper proposes a new algorithm to improve protection performance by adaptive network-based fuzzy inference system (ANFIS. The protection can be obtained in a novel way based on this theory. An advantage of this algorithm is that the protection system operates in fewer than two cycles after the occurrence of the fault. Another advantage is that the error detection is not dependent on the selection of threshold values, and all types of internal fault can identify and show that the algorithm operates correctly for all types of faults while preventing unwanted tripping, even if the data were distorted by current transformer (CT saturation or by data mismatches. The simulation results show that the proposed circuit can identify the faulty phase in the microgrid quickly and

  14. A new iterative method for solving a system of generalized equilibrium problems, generalized mixed equilibrium problems and common fixed point problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Benjawan Rodjanadid

    2013-12-01

    Full Text Available In this paper, we introduce an iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem (GMEP, the solutions of a general system of equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Then, we prove that the sequence converges strongly to a common element of the above three sets. Furthermore, we apply our result to prove four new strong convergence theorems in fixed point problems, mixed equilibrium problems, generalized equilibrium problems , equilibrium problems and variational inequality.

  15. Exponential Attractor for the Derivative Two dimensional Ginaburg-Landau Equation in Banach Spaces%二维广义Ginzburg-Landau方程在Banach空间的指数吸引子

    Institute of Scientific and Technical Information of China (English)

    黄健; 戴正德

    2004-01-01

    在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计.%In this paper, we consider the exponential attractor for the derivative two - dimensional Ginzburg - Landau equation in Banach space Xαp and also obtain the estimation of the fractal dimension.

  16. Two-dimensional Kinematics of SLACS Lenses: I. Phase-space Analysis of the Early-Type Galaxy SDSS J2321-097 at z=0.1

    CERN Document Server

    Czoske, Oliver; Koopmans, Leon V E; Treu, Tommaso; Bolton, Adam S

    2007-01-01

    We present the first results of a combined VLT VIMOS-IFU and HST-ACS study of the early-type lens galaxy SDSS J2321-097 at z=0.0819, extending kinematic studies to a look-back time of 1 Gyr. This system, discovered in the Sloan Lens ACS Survey (SLACS), has been observed as part of a VLT Large Programme with the goal of obtaining two-dimensional stellar kinematics of 17 early-type galaxies to z~0.35 and Keck spectroscopy of an additional dozen lens systems. Bayesian modelling of both the surface brightness distribution of the lensed source and the two-dimensional measurements of velocity and velocity dispersion has allowed us to dissect this galaxy in three dimensions and break the classical mass--anisotropy, mass-sheet and inclination--oblateness degeneracies. Our main results are that the galaxy (i) has a total density profile well described by a single power-law \\rho propto r^{-\\gamma'} with \\gamma' = 2.06^{+0.03}_{-0.06}; (ii) is a very slow rotator (specific stellar angular momentum parameter \\lambda_R = ...

  17. Review of photonic Hilbert transformers

    Institute of Scientific and Technical Information of China (English)

    Chaotan SIMA

    2013-01-01

    This paper reviews the demonstrations of photonic Hilbert transformers (PHTs), describing their progress and recent developments. The physical operating principles of PHTs including fractional Hilbert transformers are discussed, together with device applications in all-optical signal processing. Versatile approaches to realize PHTs are discussed, e.g., discrete free space optics, fiber-based schemes and integrated planar geometry. The numerical designs and experimental performances of these PHTs are analyzed in terms of spectral quality, operating bandwidth, system integration, and mechanical and thermal stability. Recent developments of the monolithically integrated photonic Hilbert transform (HT) devices include directional couplers and planar Bragg gratings which allow all-optical single-sideband (SSB) suppression and sideband switching.

  18. Hilbert Series for Theories with Aharony Duals

    CERN Document Server

    Hanany, Amihay; Kim, Hyungchul; Park, Jaemo; Seong, Rak-Kyeong

    2015-01-01

    The algebraic structure of moduli spaces of 3d N=2 supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(N_c) theories with N_f flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In order to compute the Hilbert series, recently developed techniques for Coulomb branch Hilbert series in 3d N=4 are extended to 3d N=2. The Hilbert series computation leads to a general expression of the algebraic variety which represents the moduli space of the U(N_c) theory with N_f flavors and its Aharony dual theory. A detailed analysis of the moduli space is given, including an analysis of the various components of the moduli space.

  19. The moduli spaces of $3d$ ${\\cal N} \\ge 2$ Chern-Simons gauge theories and their Hilbert series

    CERN Document Server

    Cremonesi, Stefano; Zaffaroni, Alberto

    2016-01-01

    We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\\cal N} \\ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperK\\"ahler twofold singularities with ${\\cal N} = 2$ and ${\\cal N} = 3$ supersymmetry.

  20. Two-dimensional liquid chromatography

    DEFF Research Database (Denmark)

    Græsbøll, Rune

    of this thesis is on online comprehensive two-dimensional liquid chromatography (online LC×LC) with reverse phase in both dimensions (online RP×RP). Since online RP×RP has not been attempted before within this research group, a significant part of this thesis consists of knowledge and experience gained...

  1. Quantum Physics and Signal Processing in Rigged Hilbert Spaces by means of Special Functions, Lie Algebras and Fourier and Fourier-like Transforms

    CERN Document Server

    Celeghini, Enrico

    2014-01-01

    Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A Rigged Hilbert space is found and a new discrete basis in R obtained. The operators {O[R]} defined on R are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in this way, their algebraic discussion. Introducing in the half-line a Fourier-like Transform, the procedure is extended to R^+ and can be easily generalized to R^n and to spherical reference systems.

  2. Two dimensional unstable scar statistics.

    Energy Technology Data Exchange (ETDEWEB)

    Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)

    2006-12-01

    This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.

  3. Hilbert, completeness and geometry

    Directory of Open Access Journals (Sweden)

    Giorgio Venturi

    2011-11-01

    Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.

  4. Spectral Anisotropy of Els\\"asser Variables in Two Dimensional Wave-vector Space as Observed in the Fast Solar Wind Turbulence

    CERN Document Server

    Yan, Limei; Zhang, Lei; Tu, Chuanyi; Marsch, Eckart; Chen, Christopher H K; Wang, Xin; Wang, Linghua; Wicks, Robert T

    2016-01-01

    Intensive studies have been conducted to understand the anisotropy of solar wind turbulence. However, the anisotropy of Els\\"asser variables ($\\textbf{Z}^\\pm$) in 2D wave-vector space has yet to be investigated. Here we first verify the transformation based on the projection-slice theorem between the power spectral density PSD$_{2D}(k_\\parallel,k_\\perp )$ and the spatial correlation function CF$_{2D} (r_\\parallel,r_\\perp )$. Based on the application of the transformation to the magnetic field and the particle measurements from the WIND spacecraft, we investigate the spectral anisotropy of Els\\"asser variables ($\\textbf{Z}^\\pm$), and the distribution of residual energy E$_{R}$, Alfv\\'en ratio R$_{A}$ and Els\\"asser ratio R$_{E}$ in the $(k_\\parallel,k_\\perp)$ space. The spectra PSD$_{2D}(k_\\parallel,k_\\perp )$ of $\\textbf{B}$, $\\textbf{V}$, and $\\textbf{Z}_{major}$ (the larger of $\\textbf{Z}^\\pm$) show a similar pattern that PSD$_{2D}(k_\\parallel,k_\\perp )$ is mainly distributed along a ridge inclined toward t...

  5. Two-dimensional deformation of a uniform half-space due to non-uniform movement accompanying a long vertical tensile fracture

    Indian Academy of Sciences (India)

    Sunita Rani; Ram Chander Verma

    2013-08-01

    The solution of the static deformation of a homogeneous, isotropic, perfectly elastic half-space caused by uniform movement along a long vertical tensile fracture is well known. In this paper, we study the problem of static deformation of a homogeneous, isotropic, perfectly elastic half-space caused by a nonuniform movement along a long vertical tensile fracture of infinite length and finite depth. Four movement profiles are considered: linear, parabolic, elliptic and cubic. The deformation corresponding to the four non-uniform movement profiles is compared numerically with the deformation due to a uniform case, assuming the source potency to be the same. The equality in source potency is achieved in two ways: One, by varying the depth of fracture and keeping the surface discontinuity constant and the other way, by keeping the depth of fracture constant and varying the surface discontinuity. It is found that the effect of non-uniformity in movement in the near field is noteworthy. The far field is not affected significantly by the non-uniformity in movement. In the first case, horizontal displacement is significantly affected rather than vertical displacement. In the second case, non-uniformity in movement changes the magnitude of the displacement at the surface. Also, the displacements around a long vertical tensile fracture for different movement profiles are plotted in three dimensions.

  6. Bound states of two-dimensional relativistic harmonic oscillators

    Institute of Scientific and Technical Information of China (English)

    Qiang Wen-Chao

    2004-01-01

    We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.

  7. Application of Three-dimensional Hilbert Curve in Image Scrambling%三维Hilbert曲线在图像置乱中的应用

    Institute of Scientific and Technical Information of China (English)

    万里红; 孙燮华; 林旭亮

    2011-01-01

    研究三维Hilbert曲线基元在空间中的24种形态,提出一种基于基元分形走向的n阶三维Hilbert曲线生成算法,将图像像素点存入到一个空间立方体数组中,按三维Hilbert曲线遍历顺序对空间立方体中的像素点进行顺序扫描存储,从而实现图像置乱处理.实验结果表明,相比二维Hilbert曲线,三维Hilbert曲线置乱具有更强的图像置乱度和更高的图像加密安全性.%This paper researches twenty-four space forms of three-dimensional Hilbert curve primitives, and proposes a n-order three-dimensional Hilbert curve generation algorithm based on the orientation of the primitives.It puts the pixels into a space cube array, sequentially scans them and stores them based on the traversal sequence of three-dimensional Hilbert to realize image scrambling.Experimental results show that three-dimensional Hilbert curve scrambling has a stronger image scrambling degree and higher encryption security compared with the two-dimensional Hilbert curve.

  8. Reduction of Z classification of a two-dimensional weak topological insulator: Real-space dynamical mean-field theory study

    Science.gov (United States)

    Yoshida, Tsuneya; Kawakami, Norio

    2017-01-01

    One of the remarkable interaction effects on topological insulators is the reduction of topological classification in free-fermion systems. We address this issue in a bilayer honeycomb lattice model by taking into account temperature effects on the reduction. Our analysis, based on the real-space dynamical mean-field theory, elucidates the following results. (i) Even when the reduction occurs, the winding number defined by the Green's function can take a nontrivial value at zero temperature. (ii) The winding number taking the nontrivial value becomes consistent with the absence of gapless edge modes due to Mott behaviors emerging only at the edges. (iii) Temperature effects can restore the gapless edge modes, provided that the energy scale of interactions is smaller than the bulk gap. In addition, we observe the topological edge Mott behavior only in some finite-temperature region.

  9. New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

    Science.gov (United States)

    Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

    1994-01-01

    A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

  10. Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

    Institute of Scientific and Technical Information of China (English)

    Xin Jun-Li; Liang Jiu-Qing

    2012-01-01

    We study quantum-classical correspondence in terms of the coherent wave functions of a charged particle in twodimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits.For both closed and open classical orbits,the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions,which is not necessarily 2π-periodic.The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value,which results in a common topological phase for all wave functions in the given model.The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization,where the classical orbits are 2π-periodic.

  11. Two-dimensional liquid chromatography

    DEFF Research Database (Denmark)

    Græsbøll, Rune

    Two-dimensional liquid chromatography has received increasing interest due to the rise in demand for analysis of complex chemical mixtures. Separation of complex mixtures is hard to achieve as a simple consequence of the sheer number of analytes, as these samples might contain hundreds or even...... dimensions. As a consequence of the conclusions made within this thesis, the research group has, for the time being, decided against further development of online LC×LC systems, since it was not deemed ideal for the intended application, the analysis of the polar fraction of oil. Trap-and...

  12. Two-dimensional photonic crystal surfactant detection.

    Science.gov (United States)

    Zhang, Jian-Tao; Smith, Natasha; Asher, Sanford A

    2012-08-07

    We developed a novel two-dimensional (2-D) crystalline colloidal array photonic crystal sensing material for the visual detection of amphiphilic molecules in water. A close-packed polystyrene 2-D array monolayer was embedded in a poly(N-isopropylacrylamide) (PNIPAAm)-based hydrogel film. These 2-D photonic crystals placed on a mirror show intense diffraction that enables them to be used for visual determination of analytes. Binding of surfactant molecules attaches ions to the sensor that swells the PNIPAAm-based hydrogel. The resulting increase in particle spacing red shifts the 2-D diffracted light. Incorporation of more hydrophobic monomers increases the sensitivity to surfactants.

  13. Sums of two-dimensional spectral triples

    DEFF Research Database (Denmark)

    Christensen, Erik; Ivan, Cristina

    2007-01-01

    construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly......, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval....

  14. Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations

    Directory of Open Access Journals (Sweden)

    Chunrong Zhu

    2016-11-01

    Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.

  15. Two-dimensional capillary origami

    Energy Technology Data Exchange (ETDEWEB)

    Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu

    2016-01-08

    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

  16. Hilbert's programs and beyond

    CERN Document Server

    2013-01-01

    David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. Ten essays are devoted to the analysis of classical as well as modern proof theory; three papers on the mathematical roots of Hilbert's work precede the analytical core, and three final essays exploit an open philosophical horizon for reflection on the nature of mathematics in the 21st century.

  17. Haces de estructuras topológicas sobre el orden parcial de subespacios de dimensión finita de un espacio de Hilbert / Sheaves of topological structures over the partial order of finite dimensional subspaces of a hilbert space

    OpenAIRE

    2010-01-01

    Motivados por el estudio de espacios de Hilbert asociados a sistemas físicos y la construcción de modelos como el espacio cociente del ultraproducto de estructuras, se ha establecido la teoría de los haces de estructuras topológicas como una extensión natural de la teoría de los haces de estructuras de primer orden, desarrollada por Caicedo y otros. Se analiza el problema de la completes de Cauchy en los casos que la topología sobre cada fibra es inducida por una métrica. Esta discusión lleva...

  18. Two-dimensional quantum repeaters

    Science.gov (United States)

    Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.

    2016-11-01

    The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.

  19. Two-dimensional capillary origami

    Science.gov (United States)

    Brubaker, N. D.; Lega, J.

    2016-01-01

    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid.

  20. Two-dimensional cubic convolution.

    Science.gov (United States)

    Reichenbach, Stephen E; Geng, Frank

    2003-01-01

    The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.

  1. Many-body basis-set reduction applied to the two-dimensional t-Jz model

    Science.gov (United States)

    Riera, J.; Dagotto, E.

    1993-06-01

    A simple variation of the Lanczos method is discussed. The technique is based on a systematic reduction of the size of the Hilbert space of the model under consideration, and it has many similarities with the basis-set-reduction approach recently introduced by Wenzel and Wilson in the context of quantum chemistry. As an example, the two-dimensional t-Jz model of strongly correlated electrons is studied. Accurate results for the ground-state energy can be obtained on clusters of up to 50 sites, which are unreachable by conventional Lanczos approaches. In particular, the energy of one and two holes is analyzed as a function of Jz/t. In the bulk limit, the numerical results suggest that a finite coupling Jz/t]c~0.18 is necessary to induce ``binding'' of holes in the model.

  2. 一种基于Snell定理反演二维斜界面的几何方法%A geometric algorithm based on Snell theorem for the inclined interface inversion in two-dimensional space

    Institute of Scientific and Technical Information of China (English)

    张义德; 关威

    2011-01-01

    在二维情况下,如果地质结构的分界面为一条有固定斜率的斜线,则反演该界面时所需要确定的参数可以归结为两个:一个是界面上的反射点,另一个是界面的斜率.依据Snell定理,利用源点与反射波最短路径点之间的几何关系,导出一种快速反演斜界面的方法.作为算例,首先利用时域有限差分法对一个二维倾斜界面模型进行了数值模拟,而后利用该方法进行反演,界面位置误差在1%以内.%In two-dimensional space, if an interface of geologic structure has one fixed slope, then only two parameters needs to determined for the inversion of the interface. One is a reflect point in it, and another is the slope. Using the geometrical relationship between the source point and the fastest travel point of the reflect wave, a quick inversion algorithm was gained based on Snell theorem. At last, some examples of numerical simulation were given and it is very good. The inversion data was got from a two-dimensional model with a slope interface using FDTD.

  3. A CHARACTERIZATION OF SIGNED GENERALIZED FRAMES IN A HILBERT SPACE%Hilbert空间H中带符号广义框架的一个刻画

    Institute of Scientific and Technical Information of China (English)

    姚喜妍

    2006-01-01

    本文研究了可分的Hilbert空间H中带符号广义框架,利用算子理论方法,给出了H中一族向量{hm}m∈M是一个带符号广义框架当且仅当带符号广义框架的框架算子的正部S+和负部S-是有界线性算子,讨论了H中带符号广义框架的框架算子S的可逆性,并且得到了H中每个向量f关于带符号广义框架{h~m}m∈M和其对偶带符号广义框架{m}m∈M的表示式.%In this paper, we study signed generalized frames in a separable Hilbert space H. Using operator-theoretic methods, we give that a family of vectors {hm}m∈M for H is a signed generalized frame if and only if positive and negative parts S+, S- of the signed generalized frame operators S are bounded linear operators. We also discuss that the signed generalized frame operators S is invertible for every f∈H, and obtain the signed generalized frame representation, with respect to a signed generalized frame {hm}m∈M and its dual signed generalized frame {(h~)m}m∈M.

  4. Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space.

    Science.gov (United States)

    Sánchez, C M; Levstein, P R; Buljubasich, L; Pastawski, H M; Chattah, A K

    2016-06-13

    In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an 'infinite' network. By contrast, the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.

  5. Two-Dimensional Weak Pseudomanifolds on Eight Vertices

    Indian Academy of Sciences (India)

    Basudeb Datta; Nandini Nilakantan

    2002-05-01

    We explicitly determine all the two-dimensional weak pseudomanifolds on 8 vertices. We prove that there are (up to isomorphism) exactly 95 such weak pseudomanifolds, 44 of which are combinatorial 2-manifolds. These 95 weak pseudomanifolds triangulate 16 topological spaces. As a consequence, we prove that there are exactly three 8-vertex two-dimensional orientable pseudomanifolds which allow degree three maps to the 4-vertex 2-sphere.

  6. Approximation of a Common Element of the Fixed Point Sets of Multivalued Strictly Pseudocontractive-Type Mappings and the Set of Solutions of an Equilibrium Problem in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    F. O. Isiogugu

    2016-01-01

    Full Text Available The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature.

  7. Classifying Two-dimensional Hyporeductive Triple Algebras

    CERN Document Server

    Issa, A Nourou

    2010-01-01

    Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple systems) and two-dimensional real Bol algebras is given.

  8. Orthogonal apartments in Hilbert Grassmannians

    OpenAIRE

    Pankov, Mark

    2015-01-01

    Let $H$ be an infinite-dimensional complex Hilbert space and let ${\\mathcal L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural $k$ we denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces. An orthogonal apartment of ${\\mathcal G}_{k}(H)$ is the set consisting of all $k$-dimensional subspaces spanned by subsets of a certain orthogonal base of $H$. Orthogonal apartments can be characterized as maximal sets of mutually compatible eleme...

  9. Microscopic description of irreversibility in quantum Lorentz gas by complex spectral analysis of the Liouvillian outside the Hilbert space

    Science.gov (United States)

    Petrosky, T.; Hashimoto, K.; Kanki, K.; Tanaka, S.

    2017-10-01

    Irreversible process of a weakly coupled one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouvillian. Without any phenomenological operations, such as a coarse-graining of space-time or a truncation of the higher order correlation, we obtained irreversible processes on a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free-length. The list of development of the complex spectral analysis of the Hamiltonian (instead of the Liouvillian) in quantum optical systems and in quantum nano-devices is also presented.

  10. Spatiotemporal dissipative solitons in two-dimensional photonic lattices.

    Science.gov (United States)

    Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S

    2008-11-01

    We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.

  11. Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm

    CERN Document Server

    Cardot, Hervé; Zitt, Pierre-André

    2011-01-01

    With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get thousands of samples of observations taking values in high dimension spaces such as functional spaces. In such large samples of high dimensional data, outlying curves may not be uncommon and even a few individuals may corrupt simple statistical indicators such as the mean trajectory. We focus here on the estimation of the geometric median which is a direct generalization of the real median and has nice robustness properties. The geometric median being defined as the minimizer of a simple convex functional that is differentiable everywhere when the distribution has no atoms, it is possible to estimate it with online gradient algorithms. Such algorithms are very fast and can deal with large samples. Furthermore they also can be simply updated when the data arrive sequentially. We state the almost sure consistency and the L2 rates of convergence of the stochastic gradient estimator as well as the ...

  12. Two-dimensional manifold with point-like defects

    CERN Document Server

    Gani, Vakhid A; Rubin, Sergei G

    2014-01-01

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

  13. Intermittency measurement in two-dimensional bacterial turbulence

    Science.gov (United States)

    Qiu, Xiang; Ding, Long; Huang, Yongxiang; Chen, Ming; Lu, Zhiming; Liu, Yulu; Zhou, Quan

    2016-06-01

    In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84 % provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β -limitation. A dual-power-law behavior separated by the viscosity scale ℓν was observed for the q th -order Hilbert moment Lq(k ) . This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R , e.g., the bacterial body length. The measured scaling exponents ζ (q ) of both the small-scale (k >kν ) and large-scale (k two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation.

  14. Hadamard States and Two-dimensional Gravity

    CERN Document Server

    Salehi, H

    2001-01-01

    We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.

  15. Topological defects in two-dimensional crystals

    OpenAIRE

    Chen, Yong; Qi, Wei-Kai

    2008-01-01

    By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal, one for dislocations and the other for disclinations. The topological quantization and evolution of topological defects in two-dimensional crystals are discussed. Finally, We compare our theory with Brownian-dynamics simulations in 2D Yukawa systems.

  16. IMMUNOHISTOCHEMICAL IMAGE SEGMENTATION USING IMPROVED TWO-DIMENSIONAL OTSU AND COMBINING HSV SPACE%结合 HSV 空间的改进二维 Otsu 免疫组化图像分割

    Institute of Scientific and Technical Information of China (English)

    兰红; 胡涵

    2016-01-01

    肝脏免疫组化图像中阳性区域的定量分析对肝癌的早期诊断有非常重要的意义。针对真彩色免疫组化图像特征,结合HSV 空间对二维 Otsu 算法进行改进。首先针对二维 Otsu 算法每次计算类间测度矩阵的迹需要遍历整幅图像导致运算量大耗时多的不足,提出一种快速递推算法,利用快速 Otsu 算法对图像进行预分割;然后针对分割结果中目标区域包含的少量阴性区域,结合图像的 HSV 空间特征进行优化。将预分割结果与 H 分量作交集运算,将交集运算结果与预分割结果作差集运算,得到初分割结果;将初分割结果与 H 分量和 S 分量的交集运算结果做并集运算,得到最终分割结果。通过与 Otsu 的对比实验表明,改进算法更好地实现了阳性区域的目标提取,提高了分割的精度。%The quantitative analysis of the positive area of liver immunohistochemical image is significant to the early diagnosis of liver cancer.Aiming at the features of true colour immunohistochemical image,we improved the two-dimensional Otsu algorithm in combination with HSV space.First,in view of the disadvantage that the two-dimensional Otsu has to traverse entire image when ever to calculate the trace of inter-class measure matrix and in turn leads to heavy computation and large time consumption,we proposed a fast recursion algorithm, which uses the fast Otsu to do the pre-segmentation on the image.Then,aiming at the small amount of negative area contained in target area of the segmented result,we optimised it combining the HSV space feature of the image.We carried out the intersection operation on the presegmentation result and the H component,and the subtraction operation on the intersection operation result and the pre-segmentation result to get initial segmentation result,and then carried out the union operation on the initial segmentation result and the result of H and S components

  17. Hilbert space and quantum mechanics

    CERN Document Server

    Gallone, Franco

    2015-01-01

    The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...

  18. Realization Theory in Hilbert Space

    Science.gov (United States)

    1985-07-01

    Furthermore, a sufficient condition is that G(t) e R P x m is locally of bounded variation and satisfies an estimate of the form (6.10) VAR G r Me wt [0...not be of bounded variation . In the same way there exist time invariant, causal, linear input-output operators T which cannot be represented in the form...6.12) Tu(t) - f d(s)u(t-s) , t e R 0 for some matrix function U(t) of bounded variation . -29- " " " """. r . .................. .. . . . iliI

  19. Quantum mechanics in Hilbert space

    CERN Document Server

    Prugovecki, Eduard

    2006-01-01

    A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the

  20. Strongly interacting two-dimensional Dirac fermions

    NARCIS (Netherlands)

    Lim, L.K.; Lazarides, A.; Hemmerich, Andreas; de Morais Smith, C.

    2009-01-01

    We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature

  1. Topology optimization of two-dimensional waveguides

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2003-01-01

    In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....

  2. Existence of Weak Solutions of Two-dimensional Euler Equations with Initial Vorticity in Lorentz Space L(2,1)(R2)%当初始旋度属于Lornetz空间L(2,1)(R2)时二维Euler方程弱解的存在性

    Institute of Scientific and Technical Information of China (English)

    酒全森

    2000-01-01

    Some estimates on 2-D Euler equations are given when initial vorticity ω belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dimensional Euler equations when ω0(2,1)∈L.

  3. Gorenstein Hilbert Coefficients

    CERN Document Server

    Khoury, Sabine El

    2012-01-01

    We prove upper and lower bounds for all the coefficients in the Hilbert Polynomial of a graded Gorenstein algebra $S=R/I$ with a quasi-pure resolution over $R$. The bounds are in terms of the minimal and the maximal shifts in the resolution of $R$ . These bounds are analogous to the bounds for the multiplicity found in \\cite{S} and are stronger than the bounds for the Cohen Macaulay algebras found in \\cite{HZ}.

  4. Fractional vortex Hilbert's Hotel

    CERN Document Server

    Gbur, Greg

    2015-01-01

    We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of "open rooms," i.e. topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary.

  5. On Hilbert dynamical systems

    CERN Document Server

    Glasner, Eli

    2010-01-01

    Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the circle, the dual group of Z, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.

  6. From Tarski to Hilbert

    OpenAIRE

    Braun, Gabriel; Narboux, Julien

    2012-01-01

    International audience; In this paper, we report on the formal proof that Hilbert's axiom system can be derived from Tarski's system. For this purpose we mechanized the proofs of the first twelve chapters of Schwabauser, Szmielew and Tarski's book: Metamathematische Methoden in der Geometrie. The proofs are checked formally within classical logic using the Coq proof assistant. The goal of this development is to provide clear foundations for other formalizations of geometry and implementations...

  7. Two-dimensional assignment with merged measurements using Langrangrian relaxation

    Science.gov (United States)

    Briers, Mark; Maskell, Simon; Philpott, Mark

    2004-01-01

    Closely spaced targets can result in merged measurements, which complicate data association. Such merged measurements violate any assumption that each measurement relates to a single target. As a result, it is not possible to use the auction algorithm in its simplest form (or other two-dimensional assignment algorithms) to solve the two-dimensional target-to-measurement assignment problem. We propose an approach that uses the auction algorithm together with Lagrangian relaxation to incorporate the additional constraints resulting from the presence of merged measurements. We conclude with some simulated results displaying the concepts introduced, and discuss the application of this research within a particle filter context.

  8. Tracking dynamics of two-dimensional continuous attractor neural networks

    Science.gov (United States)

    Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si

    2009-12-01

    We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.

  9. Control Operator for the Two-Dimensional Energized Wave Equation

    Directory of Open Access Journals (Sweden)

    Sunday Augustus REJU

    2006-07-01

    Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

  10. Two-dimensional topological photonic systems

    Science.gov (United States)

    Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

    2017-09-01

    The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

  11. Radiation effects on two-dimensional materials

    Energy Technology Data Exchange (ETDEWEB)

    Walker, R.C. II; Robinson, J.A. [Department of Materials Science, Penn State, University Park, PA (United States); Center for Two-Dimensional Layered Materials, Penn State, University Park, PA (United States); Shi, T. [Department of Mechanical and Nuclear Engineering, Penn State, University Park, PA (United States); Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States); Silva, E.C. [GlobalFoundries, Malta, NY (United States); Jovanovic, I. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States)

    2016-12-15

    The effects of electromagnetic and particle irradiation on two-dimensional materials (2DMs) are discussed in this review. Radiation creates defects that impact the structure and electronic performance of materials. Determining the impact of these defects is important for developing 2DM-based devices for use in high-radiation environments, such as space or nuclear reactors. As such, most experimental studies have been focused on determining total ionizing dose damage to 2DMs and devices. Total dose experiments using X-rays, gamma rays, electrons, protons, and heavy ions are summarized in this review. We briefly discuss the possibility of investigating single event effects in 2DMs based on initial ion beam irradiation experiments and the development of 2DM-based integrated circuits. Additionally, beneficial uses of irradiation such as ion implantation to dope materials or electron-beam and helium-beam etching to shape materials have begun to be used on 2DMs and are reviewed as well. For non-ionizing radiation, such as low-energy photons, we review the literature on 2DM-based photo-detection from terahertz to UV. The majority of photo-detecting devices operate in the visible and UV range, and for this reason they are the focus of this review. However, we review the progress in developing 2DMs for detecting infrared and terahertz radiation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  12. Two-dimensional hydrogen negative ion in a magnetic field

    Institute of Scientific and Technical Information of China (English)

    Xie Wen-Fang

    2004-01-01

    Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional hydrogen negative ion H- in a magnetic field. The results show that the ground and low-excited states of H- in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.

  13. Two Dimensional Plasmonic Cavities on Moire Surfaces

    Science.gov (United States)

    Balci, Sinan; Kocabas, Askin; Karabiyik, Mustafa; Kocabas, Coskun; Aydinli, Atilla

    2010-03-01

    We investigate surface plasmon polariton (SPP) cavitiy modes on two dimensional Moire surfaces in the visible spectrum. Two dimensional hexagonal Moire surface can be recorded on a photoresist layer using Interference lithography (IL). Two sequential exposures at slightly different angles in IL generate one dimensional Moire surfaces. Further sequential exposure for the same sample at slightly different angles after turning the sample 60 degrees around its own axis generates two dimensional hexagonal Moire cavity. Spectroscopic reflection measurements have shown plasmonic band gaps and cavity states at all the azimuthal angles (omnidirectional cavity and band gap formation) investigated. The plasmonic band gap edge and the cavity states energies show six fold symmetry on the two dimensional Moire surface as measured in reflection measurements.

  14. Two-Dimensional Planetary Surface Lander

    Science.gov (United States)

    Hemmati, H.; Sengupta, A.; Castillo, J.; McElrath, T.; Roberts, T.; Willis, P.

    2014-06-01

    A systems engineering study was conducted to leverage a new two-dimensional (2D) lander concept with a low per unit cost to enable scientific study at multiple locations with a single entry system as the delivery vehicle.

  15. Takesaki-Takai Duality Theorem in Hilbert C*-Modules

    Institute of Scientific and Technical Information of China (English)

    Mao Zheng GUO; Xiao Xia ZHANG

    2004-01-01

    In this paper, we generalize the Takesaki-Takai duality theorem in Hilbert C*-modules;that is to say, if (H, V, U) is a Kac-system, where H is a Hilbert space, V is a multiplicative unitary operator on H (×) H and U is a unitary operator on H, and if E is an (j)-compatible Hilbert (A)-module,then E × (j∧) × (j) (≌) E (×) K(H), where K(H) is the set of all compact operators on H, and (j) and (j) are Hopf C*-algebras corresponding to the Kac-system (H, V, U).

  16. Hilbert C*-模中本原理想子模的一些性质%Some properties of primitive ideal submodules in Hilbert C*-modules

    Institute of Scientific and Technical Information of China (English)

    杨功林; 纪培胜

    2014-01-01

    给出了Hilbert C*-模中本原理想子模的定义,研究了Hilbert C*-模的本原理想子模空间以及谱空间的一些性质,所得结果推广和改进了已有的结果。%The definition of the primitive ideal submodules in Hilbert C*-modules is given.Some properties of primi-tive ideal submodule space and the spectrum space in Hilbert C*-modules are studied.It is shown that these results ex-tend and improve the existing results.

  17. Intermittency measurement in two dimensional bacterial turbulence

    CERN Document Server

    Qiu, Xiang; Huang, Yongxiang; Chen, Ming; Lu, Zhiming; Liu, Yulu; Zhou, Quan

    2016-01-01

    In this paper, an experimental velocity database of a bacterial collective motion , e.g., \\textit{B. subtilis}, in turbulent phase with volume filling fraction $84\\%$ provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the $\\beta-$limitation. A dual-power-law behavior separated by the viscosity scale $\\ell_{\

  18. Decomposition theorems for Hilbert modular newforms

    CERN Document Server

    Linowitz, Benjamin

    2011-01-01

    Let $\\mathscr{S}_k^+(\\cn,\\Phi)$ denote the space generated by Hilbert modular newforms (over a fixed totally real field $K$) of weight $k$, level $\\cn$ and Hecke character $\\Phi$. We show how to decompose $\\mathscr{S}_k^+(\\cn,\\Phi)$ into direct sums of twists of other spaces of newforms. This sheds light on the behavior of a newform under a character twist: the exact level of the twist of a newform, when such a twist is itself a newform, and when a newform may be realized as the twist of a primitive newform. These results were proven for elliptic modular forms by Hijikata, Pizer and Shemanske by employing a formula for the trace of the Hecke operator $T_k(n)$. We obtain our results not by employing a more general formula for the trace of Hecke operators on spaces of Hilbert modular forms, but instead by using basic properties of newforms which were proven for elliptic modular forms by Li, and Atkin and Li, and later extended to Hilbert modular forms by Shemanske and Walling.

  19. Interpolation by two-dimensional cubic convolution

    Science.gov (United States)

    Shi, Jiazheng; Reichenbach, Stephen E.

    2003-08-01

    This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.

  20. TWO-DIMENSIONAL TOPOLOGY OF COSMOLOGICAL REIONIZATION

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yougang; Xu, Yidong; Chen, Xuelei [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 China (China); Park, Changbom [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Kim, Juhan, E-mail: wangyg@bao.ac.cn, E-mail: cbp@kias.re.kr [Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)

    2015-11-20

    We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two-dimensional genus curve for the early, middle, and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometre Array.

  1. Two dimensional topology of cosmological reionization

    CERN Document Server

    Wang, Yougang; Xu, Yidong; Chen, Xuelei; Kim, Juhan

    2015-01-01

    We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two dimensional genus curve for the early, middle and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometer Array.

  2. Two-dimensional x-ray diffraction

    CERN Document Server

    He, Bob B

    2009-01-01

    Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea

  3. Matching Two-dimensional Gel Electrophoresis' Spots

    DEFF Research Database (Denmark)

    Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza

    2012-01-01

    This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar......This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches...

  4. Mobility anisotropy of two-dimensional semiconductors

    Science.gov (United States)

    Lang, Haifeng; Zhang, Shuqing; Liu, Zhirong

    2016-12-01

    The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, BC2N , MXene, TiS3, and GeCH3) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.

  5. Towards two-dimensional search engines

    OpenAIRE

    Ermann, Leonardo; Chepelianskii, Alexei D.; Shepelyansky, Dima L.

    2011-01-01

    We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Statistical properties of inf...

  6. Reflexion and Diffraction of Internal Waves analyzed with the Hilbert Transform

    CERN Document Server

    Mercier, Matthieu; Dauxois, Thierry

    2008-01-01

    We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: this is very helpful in answering several fundamental questions in the context of internal waves. We focus more precisely in this paper on phenomena associated with dissipation, diffraction and reflection of internal waves.

  7. A Riemann-Hilbert approach to Painleve IV

    NARCIS (Netherlands)

    Put, M. van der; Top, J.

    2013-01-01

    The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painleve equation. One obtains a Riemann-Hilbert correspondence between moduli spaces of rank two connections on P-1 and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto-Painleve va

  8. A Riemann-Hilbert approach to Painleve IV

    NARCIS (Netherlands)

    Put, M. van der; Top, J.

    2013-01-01

    The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painleve equation. One obtains a Riemann-Hilbert correspondence between moduli spaces of rank two connections on P-1 and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto-Painleve va

  9. Complex dynamical invariants for two-dimensional complex potentials

    Indian Academy of Sciences (India)

    J S Virdi; F Chand; C N Kumar; S C Mishra

    2012-08-01

    Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}. y = x_{2} + ip_{4}, p_{x} = p_{1} + ix_{3}, p_{y} = p_{2} + ix_{4}$. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. THe obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.

  10. Numerical Study of Two-Dimensional Viscous Flow over Dams

    Institute of Scientific and Technical Information of China (English)

    王利兵; 刘宇陆; 涂敏杰

    2003-01-01

    In this paper, the characteristics of two-dimensional viscous flow over two dams were numerically investigated. The results show that the behavior of the vortices is closely related to the space between two dams, water depth, Fr number and Reynolds number. In addition, the flow properties behind each dam are different, and the changes over two dams are more complex than over one dam. Finally, the relevant turbulent characteristics were analyzed.

  11. Tricritical behavior in a two-dimensional field theory

    Science.gov (United States)

    Hamber, Herbert

    1980-05-01

    The critical behavior of a two-dimensional scalar Euclidean field theory with a potential term that allows for three minima is analyzed using an approximate position-space renormalization-group transformation on the equivalent quantum spin Hamiltonian. The global phase diagram shows a tricritical point separating a critical line from a line of first-order transitions. Other critical properties are examined, and good agreement is found with results on classical spin models belonging to the same universality class.

  12. Coll Positioning systems: a two-dimensional approach

    CERN Document Server

    Ferrando, J J

    2006-01-01

    The basic elements of Coll positioning systems (n clocks broadcasting electromagnetic signals in a n-dimensional space-time) are presented in the two-dimensional case. This simplified approach allows us to explain and to analyze the properties and interest of these relativistic positioning systems. The positioning system defined in flat metric by two geodesic clocks is analyzed. The interest of the Coll systems in gravimetry is pointed out.

  13. Towards complete integrability of two dimensional Poincar\\'e gauge gravity

    CERN Document Server

    Mielke, E W; Obukhov, Yu N; Tresguerres, R; Hehl, F W

    1993-01-01

    It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational {\\it boundary} term. The resulting model is equivalent to a Yang-Mills theory of local {\\it translations} and frozen Lorentz gauge degrees. We will show that this restricted Poincar\\'e gauge model in 2 dimensions is completely integrable. {\\it Exact} wave, charged black hole, and `dilaton' solutions are then readily found. In vacuum, the integrability of the {\\it general} 2D Poincar\\'e gauge theory is formally proved along the same line of reasoning.

  14. Sufficient Controllability Condition for Affine Systems with Two-Dimensional Control and Two-Dimensional Zero Dynamics

    Directory of Open Access Journals (Sweden)

    D. A. Fetisov

    2015-01-01

    Full Text Available The controllability conditions are well known if we speak about linear stationary systems: a linear stationary system is controllable if and only if the dimension of the state vector is equal to the rank of the controllability matrix. The concept of the controllability matrix is extended to affine systems, but relations between affine systems controllability and properties of this matrix are more complicated. Various controllability conditions are set for affine systems, but they deal as usual either with systems of some special form or with controllability in some small neighborhood of the concerned point. An affine system is known to be controllable if the system is equivalent to a system of a canonical form, which is defined and regular in the whole space of states. In this case, the system is said to be feedback linearizable in the space of states. However there are examples, which illustrate that a system can be controllable even if it is not feedback linearizable in any open subset in the space of states. In this article we deal with such systems.Affine systems with two-dimensional control are considered. The system in question is assumed to be equivalent to a system of a quasicanonical form with two-dimensional zero dynamics which is defined and regular in the whole space of states. Therefore the controllability of the original system is equivalent to the controllability of the received system of a quasicanonical form. In this article the sufficient condition for an available solution of the terminal problem is proven for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. The condition is valid in the case of an arbitrary time interval and arbitrary initial and finite states of the system. Therefore the controllability condition is set for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. An example is given which illustrates how the proved

  15. Piezoelectricity in Two-Dimensional Materials

    KAUST Repository

    Wu, Tao

    2015-02-25

    Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.

  16. Kronecker Product of Two-dimensional Arrays

    Institute of Scientific and Technical Information of China (English)

    Lei Hu

    2006-01-01

    Kronecker sequences constructed from short sequences are good sequences for spread spectrum communication systems. In this paper we study a similar problem for two-dimensional arrays, and we determine the linear complexity of the Kronecker product of two arrays. Our result shows that similar good property on linear complexity holds for Kronecker product of arrays.

  17. Two-Dimensional Toda-Heisenberg Lattice

    Directory of Open Access Journals (Sweden)

    Vadim E. Vekslerchik

    2013-06-01

    Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.

  18. A novel two dimensional particle velocity sensor

    NARCIS (Netherlands)

    Pjetri, Olti; Wiegerink, Remco J.; Lammerink, Theo S.; Krijnen, Gijs J.

    2013-01-01

    In this paper we present a two wire, two-dimensional particle velocity sensor. The miniature sensor of size 1.0x2.5x0.525 mm, consisting of only two crossed wires, shows excellent directional sensitivity in both directions, thus requiring no directivity calibration, and is relatively easy to fabrica

  19. Two-dimensional microstrip detector for neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Oed, A. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1997-04-01

    Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.

  20. Two-dimensional magma-repository interactions

    NARCIS (Netherlands)

    Bokhove, O.

    2001-01-01

    Two-dimensional simulations of magma-repository interactions reveal that the three phases --a shock tube, shock reflection and amplification, and shock attenuation and decay phase-- in a one-dimensional flow tube model have a precursor. This newly identified phase ``zero'' consists of the impact of

  1. Two-dimensional subwavelength plasmonic lattice solitons

    CERN Document Server

    Ye, F; Hu, B; Panoiu, N C

    2010-01-01

    We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai

  2. A two-dimensional Dirac fermion microscope

    DEFF Research Database (Denmark)

    Bøggild, Peter; Caridad, Jose; Stampfer, Christoph

    2017-01-01

    in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2...

  3. Gamow, not Hilbert: The Architect of Hilbert's Grand Hotel

    CERN Document Server

    Kragh, Helge

    2014-01-01

    What is known as "Hilbert's hotel" is a story of an imaginary hotel with infinitely many rooms that illustrates the bizarre consequences of assuming an actual infinity of objects or events. Since the 1970s it has been used in a variety of arguments, some of them relating to cosmology and others to philosophy and theology. It turns out that the name is a misnomer, as Hilbert was not responsible for the story. The originator was George Gamow, who invented the hotel in 1947, jokingly attributing it to Hilbert. Although well known, the counter-intuitive hotel only attracted wide interest in the 1970s, first in philosophical and theological contexts. The paper outlines the origin and early history of what might be called the Gamow-Hilbert hotel paradox.

  4. Entanglement Entropy in Two-Dimensional String Theory.

    Science.gov (United States)

    Hartnoll, Sean A; Mazenc, Edward A

    2015-09-18

    To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.

  5. Topological Quantum Optics in Two-Dimensional Atomic Arrays

    Science.gov (United States)

    Perczel, J.; Borregaard, J.; Chang, D. E.; Pichler, H.; Yelin, S. F.; Zoller, P.; Lukin, M. D.

    2017-07-01

    We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with nontrivial Chern numbers and topologically protected, long-lived edge states. Due to the inherent nonlinearity of constituent emitters, such systems provide a platform for exploring quantum optical analogs of interacting topological systems.

  6. Electronics based on two-dimensional materials.

    Science.gov (United States)

    Fiori, Gianluca; Bonaccorso, Francesco; Iannaccone, Giuseppe; Palacios, Tomás; Neumaier, Daniel; Seabaugh, Alan; Banerjee, Sanjay K; Colombo, Luigi

    2014-10-01

    The compelling demand for higher performance and lower power consumption in electronic systems is the main driving force of the electronics industry's quest for devices and/or architectures based on new materials. Here, we provide a review of electronic devices based on two-dimensional materials, outlining their potential as a technological option beyond scaled complementary metal-oxide-semiconductor switches. We focus on the performance limits and advantages of these materials and associated technologies, when exploited for both digital and analog applications, focusing on the main figures of merit needed to meet industry requirements. We also discuss the use of two-dimensional materials as an enabling factor for flexible electronics and provide our perspectives on future developments.

  7. Two-dimensional ranking of Wikipedia articles

    Science.gov (United States)

    Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L.

    2010-10-01

    The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.

  8. Two-Dimensional NMR Lineshape Analysis

    Science.gov (United States)

    Waudby, Christopher A.; Ramos, Andres; Cabrita, Lisa D.; Christodoulou, John

    2016-04-01

    NMR titration experiments are a rich source of structural, mechanistic, thermodynamic and kinetic information on biomolecular interactions, which can be extracted through the quantitative analysis of resonance lineshapes. However, applications of such analyses are frequently limited by peak overlap inherent to complex biomolecular systems. Moreover, systematic errors may arise due to the analysis of two-dimensional data using theoretical frameworks developed for one-dimensional experiments. Here we introduce a more accurate and convenient method for the analysis of such data, based on the direct quantum mechanical simulation and fitting of entire two-dimensional experiments, which we implement in a new software tool, TITAN (TITration ANalysis). We expect the approach, which we demonstrate for a variety of protein-protein and protein-ligand interactions, to be particularly useful in providing information on multi-step or multi-component interactions.

  9. Towards two-dimensional search engines

    CERN Document Server

    Ermann, Leonardo; Shepelyansky, Dima L

    2011-01-01

    We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Information flow properties on PageRank-CheiRank plane are analyzed for networks of British, French and Italian Universities, Wikipedia, Linux Kernel, gene regulation and other networks. Methods of spam links control are also analyzed.

  10. Toward two-dimensional search engines

    Science.gov (United States)

    Ermann, L.; Chepelianskii, A. D.; Shepelyansky, D. L.

    2012-07-01

    We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank-CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed.

  11. A two-dimensional Dirac fermion microscope

    Science.gov (United States)

    Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads

    2017-06-01

    The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.

  12. A two-dimensional Dirac fermion microscope.

    Science.gov (United States)

    Bøggild, Peter; Caridad, José M; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads

    2017-06-09

    The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.

  13. Unmanned Aerial System and Spaceflight Microwave Radiometers? Radio-Frequency Interference Direct Detection and Science Data Recovery Based on the Hilbert-Huang Transform for Two Dimensions Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The three goals of this IRAD are:1.1 Research and develop the Hilbert-Huang Transform for 2D second and last component – the Hilbert Spectral Analysis for 2D...

  14. Two-Dimensional Scheduling: A Review

    Directory of Open Access Journals (Sweden)

    Zhuolei Xiao

    2013-07-01

    Full Text Available In this study, we present a literature review, classification schemes and analysis of methodology for scheduling problems on Batch Processing machine (BP with both processing time and job size constraints which is also regarded as Two-Dimensional (TD scheduling. Special attention is given to scheduling problems with non-identical job sizes and processing times, with details of the basic algorithms and other significant results.

  15. Two dimensional fermions in four dimensional YM

    CERN Document Server

    Narayanan, R

    2009-01-01

    Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\\frac{1}{\\Lambda_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.

  16. Two-dimensional Kagome photonic bandgap waveguide

    DEFF Research Database (Denmark)

    Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou;

    2000-01-01

    The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....

  17. String breaking in two-dimensional QCD

    CERN Document Server

    Hornbostel, K J

    1999-01-01

    I present results of a numerical calculation of the effects of light quark-antiquark pairs on the linear heavy-quark potential in light-cone quantized two-dimensional QCD. I extract the potential from the Q-Qbar component of the ground-state wavefunction, and observe string breaking at the heavy-light meson pair threshold. I briefly comment on the states responsible for the breaking.

  18. Two-dimensional supramolecular electron spin arrays.

    Science.gov (United States)

    Wäckerlin, Christian; Nowakowski, Jan; Liu, Shi-Xia; Jaggi, Michael; Siewert, Dorota; Girovsky, Jan; Shchyrba, Aneliia; Hählen, Tatjana; Kleibert, Armin; Oppeneer, Peter M; Nolting, Frithjof; Decurtins, Silvio; Jung, Thomas A; Ballav, Nirmalya

    2013-05-07

    A bottom-up approach is introduced to fabricate two-dimensional self-assembled layers of molecular spin-systems containing Mn and Fe ions arranged in a chessboard lattice. We demonstrate that the Mn and Fe spin states can be reversibly operated by their selective response to coordination/decoordination of volatile ligands like ammonia (NH3). Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  19. Two dimensional echocardiographic detection of intraatrial masses.

    Science.gov (United States)

    DePace, N L; Soulen, R L; Kotler, M N; Mintz, G S

    1981-11-01

    With two dimensional echocardiography, a left atrial mass was detected in 19 patients. Of these, 10 patients with rheumatic mitral stenosis had a left atrial thrombus. The distinctive two dimensional echocardiographic features of left atrial thrombus included a mass of irregular nonmobile laminated echos within an enlarged atrial cavity, usually with a broad base of attachment to the posterior left atrial wall. Seven patients had a left atrial myxoma. Usually, the myxoma appeared as a mottled ovoid, sharply demarcated mobile mass attached to the interatrial septum. One patient had a right atrial angiosarcoma that appeared as a nonmobile mass extending from the inferior vena caval-right atrial junction into the right atrial cavity. One patient had a left atrial leiomyosarcoma producing a highly mobile mass attached to the lateral wall of the left atrium. M mode echocardiography detected six of the seven myxomas, one thrombus and neither of the other tumors. Thus, two dimensional echocardiography appears to be the technique of choice in the detection, localization and differentiation of intraatrial masses.

  20. The high order Schwarz-Pick lemma on complex Hilbert balls

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper we prove a high order Schwarz-Pick lemma for holomorphic mappings between unit balls in complex Hilbert spaces.In addition,a Schwarz-Pick estimate for high order Fréchet derivatives of a holomorphic function f of a Hilbert ball into the right half-plane is obtained.

  1. Weakly disordered two-dimensional Frenkel excitons

    Science.gov (United States)

    Boukahil, A.; Zettili, Nouredine

    2004-03-01

    We report the results of studies of the optical properties of weakly disordered two- dimensional Frenkel excitons in the Coherent Potential Approximation (CPA). An approximate complex Green's function for a square lattice with nearest neighbor interactions is used in the self-consistent equation to determine the coherent potential. It is shown that the Density of States is very much affected by the logarithmic singularities in the Green's function. Our CPA results are in excellent agreement with previous investigations by Schreiber and Toyozawa using the Monte Carlo simulation.

  2. Theory of two-dimensional transformations

    OpenAIRE

    Kanayama, Yutaka J.; Krahn, Gary W.

    1998-01-01

    The article of record may be found at http://dx.doi.org/10.1109/70.720359 Robotics and Automation, IEEE Transactions on This paper proposes a new "heterogeneous" two-dimensional (2D) transformation group ___ to solve motion analysis/planning problems in robotics. In this theory, we use a 3×1 matrix to represent a transformation as opposed to a 3×3 matrix in the homogeneous formulation. First, this theory is as capable as the homogeneous theory, Because of the minimal size, its implement...

  3. Two-dimensional ranking of Wikipedia articles

    CERN Document Server

    Zhirov, A O; Shepelyansky, D L

    2010-01-01

    The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. We analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.

  4. Mobility anisotropy of two-dimensional semiconductors

    CERN Document Server

    Lang, Haifeng; Liu, Zhirong

    2016-01-01

    The carrier mobility of anisotropic two-dimensional (2D) semiconductors under longitudinal acoustic (LA) phonon scattering was theoretically studied with the deformation potential theory. Based on Boltzmann equation with relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was deduced, which shows that the influence of effective mass to the mobility anisotropy is larger than that of deformation potential constant and elastic modulus. Parameters were collected for various anisotropic 2D materials (black phosphorus, Hittorf's phosphorus, BC$_2$N, MXene, TiS$_3$, GeCH$_3$) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio was overestimated in the past.

  5. Binding energy of two-dimensional biexcitons

    DEFF Research Database (Denmark)

    Singh, Jai; Birkedal, Dan; Vadim, Lyssenko;

    1996-01-01

    Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories....

  6. Dynamics of film. [two dimensional continua theory

    Science.gov (United States)

    Zak, M.

    1979-01-01

    The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples.

  7. Three-dimensional versus two-dimensional vision in laparoscopy

    DEFF Research Database (Denmark)

    Sørensen, Stine Maya Dreier; Savran, Mona M; Konge, Lars;

    2016-01-01

    BACKGROUND: Laparoscopic surgery is widely used, and results in accelerated patient recovery time and hospital stay were compared with laparotomy. However, laparoscopic surgery is more challenging compared with open surgery, in part because surgeons must operate in a three-dimensional (3D) space...... through a two-dimensional (2D) projection on a monitor, which results in loss of depth perception. To counter this problem, 3D imaging for laparoscopy was developed. A systematic review of the literature was performed to assess the effect of 3D laparoscopy. METHODS: A systematic search of the literature...

  8. Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence.

    Science.gov (United States)

    Servidio, S; Matthaeus, W H; Shay, M A; Cassak, P A; Dmitruk, P

    2009-03-20

    Systematic analysis of numerical simulations of two-dimensional magnetohydrodynamic turbulence reveals the presence of a large number of X-type neutral points where magnetic reconnection occurs. We examine the statistical properties of this ensemble of reconnection events that are spontaneously generated by turbulence. The associated reconnection rates are distributed over a wide range of values and scales with the geometry of the diffusion region. Locally, these events can be described through a variant of the Sweet-Parker model, in which the parameters are externally controlled by turbulence. This new perspective on reconnection is relevant in space and astrophysical contexts, where plasma is generally in a fully turbulent regime.

  9. Size-dispersity effects in two-dimensional melting.

    Science.gov (United States)

    Watanabe, Hiroshi; Yukawa, Satoshi; Ito, Nobuyasu

    2005-01-01

    In order to investigate the effect of size dispersity on two-dimensional melting transitions, hard-disk systems with equimolar bidispersity are studied by means of particle dynamics simulations. From the nonequilibrium relaxation behaviors of bond-orientational order parameters, we find that (i) there is a critical dispersity at which the melting transition of the hexagonal solid vanishes and (ii) the quadratic structure is metastable in a certain region of the dispersity-density parameter space. These results suggest that the dispersity not only destroys order but produces new structures under certain specific conditions.

  10. Local kinetic effects in two-dimensional plasma turbulence.

    Science.gov (United States)

    Servidio, S; Valentini, F; Califano, F; Veltri, P

    2012-01-27

    Using direct numerical simulations of a hybrid Vlasov-Maxwell model, kinetic processes are investigated in a two-dimensional turbulent plasma. In the turbulent regime, kinetic effects manifest through a deformation of the ion distribution function. These patterns of non-Maxwellian features are concentrated in space nearby regions of strong magnetic activity: the distribution function is modulated by the magnetic topology, and can elongate along or across the local magnetic field. These results open a new path on the study of kinetic processes such as heating, particle acceleration, and temperature anisotropy, commonly observed in astrophysical and laboratory plasmas.

  11. A two-dimensional approach to relativistic positioning systems

    CERN Document Server

    Coll, B; Morales, J A; Coll, Bartolom\\'{e}; Ferrando, Joan Josep; Morales, Juan Antonio

    2006-01-01

    A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allow to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.

  12. Two-dimensional gauge theoretic supergravities

    Science.gov (United States)

    Cangemi, D.; Leblanc, M.

    1994-05-01

    We investigate two-dimensional supergravity theories, which can be built from a topological and gauge invariant action defined on an ordinary surface. One is the N = 1 supersymmetric extension of the Jackiw-Teitelboim model presented by Chamseddine in a superspace formalism. We complement the proof of Montano, Aoaki and Sonnenschein that this extension is topological and gauge invariant, based on the graded de Sitter algebra. Not only do the equations of motion correspond to the supergravity ones and do gauge transformations encompass local supersymmetries, but we also identify the ∫-theory with the superfield formalism action written by Chamseddine. Next, we show that the N = 1 supersymmetric extension of string-inspired two-dimensional dilaton gravity put forward by Park and Strominger cannot be written as a ∫-theory. As an alternative, we propose two topological and gauge theories that are based on a graded extension of the extended Poincaré algebra and satisfy a vanishing-curvature condition. Both models are supersymmetric extensions of the string-inspired dilaton gravity.

  13. Two-Dimensional Theory of Scientific Representation

    Directory of Open Access Journals (Sweden)

    A Yaghmaie

    2013-03-01

    Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.

  14. Two-dimensional shape memory graphene oxide

    Science.gov (United States)

    Chang, Zhenyue; Deng, Junkai; Chandrakumara, Ganaka G.; Yan, Wenyi; Liu, Jefferson Zhe

    2016-06-01

    Driven by the increasing demand for micro-/nano-technologies, stimuli-responsive shape memory materials at nanoscale have recently attracted great research interests. However, by reducing the size of conventional shape memory materials down to approximately nanometre range, the shape memory effect diminishes. Here, using density functional theory calculations, we report the discovery of a shape memory effect in a two-dimensional atomically thin graphene oxide crystal with ordered epoxy groups, namely C8O. A maximum recoverable strain of 14.5% is achieved as a result of reversible phase transition between two intrinsically stable phases. Our calculations conclude co-existence of the two stable phases in a coherent crystal lattice, giving rise to the possibility of constructing multiple temporary shapes in a single material, thus, enabling highly desirable programmability. With an atomic thickness, excellent shape memory mechanical properties and electric field stimulus, the discovery of a two-dimensional shape memory graphene oxide opens a path for the development of exceptional micro-/nano-electromechanical devices.

  15. Hilbert complexes of nonlinear elasticity

    Science.gov (United States)

    Angoshtari, Arzhang; Yavari, Arash

    2016-12-01

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

  16. Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices

    Institute of Scientific and Technical Information of China (English)

    XU Quan; TIAN Qiang

    2007-01-01

    Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.

  17. Optimal excitation of two dimensional Holmboe instabilities

    CERN Document Server

    Constantinou, Navid C

    2010-01-01

    Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However these instabilities occur in tongues for a limited range of parameters. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that obtains for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges for parameter values ...

  18. Phonon hydrodynamics in two-dimensional materials.

    Science.gov (United States)

    Cepellotti, Andrea; Fugallo, Giorgia; Paulatto, Lorenzo; Lazzeri, Michele; Mauri, Francesco; Marzari, Nicola

    2015-03-06

    The conduction of heat in two dimensions displays a wealth of fascinating phenomena of key relevance to the scientific understanding and technological applications of graphene and related materials. Here, we use density-functional perturbation theory and an exact, variational solution of the Boltzmann transport equation to study fully from first-principles phonon transport and heat conductivity in graphene, boron nitride, molybdenum disulphide and the functionalized derivatives graphane and fluorographene. In all these materials, and at variance with typical three-dimensional solids, normal processes keep dominating over Umklapp scattering well-above cryogenic conditions, extending to room temperature and more. As a result, novel regimes emerge, with Poiseuille and Ziman hydrodynamics, hitherto typically confined to ultra-low temperatures, characterizing transport at ordinary conditions. Most remarkably, several of these two-dimensional materials admit wave-like heat diffusion, with second sound present at room temperature and above in graphene, boron nitride and graphane.

  19. Probabilistic Universality in two-dimensional Dynamics

    CERN Document Server

    Lyubich, Mikhail

    2011-01-01

    In this paper we continue to explore infinitely renormalizable H\\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with the one-dimensional Cantor attractor is at most 1/2-H\\"older. Another formulation of this phenomenon is that the scaling structure of the H\\'enon Cantor attractor differs from its one-dimensional counterpart. However, in this paper we prove that the weight assigned by the canonical invariant measure to these bad spots tends to zero on microscopic scales. This phenomenon is called {\\it Probabilistic Universality}. It implies, in particular, that the Hausdorff dimension of the canonical measure is universal. In this way, universality and rigidity phenomena of one-dimensional dynamics assume a probabilistic nature in the two-dimensional world.

  20. Two-dimensional position sensitive neutron detector

    Indian Academy of Sciences (India)

    A M Shaikh; S S Desai; A K Patra

    2004-08-01

    A two-dimensional position sensitive neutron detector has been developed. The detector is a 3He + Kr filled multiwire proportional counter with charge division position readout and has a sensitive area of 345 mm × 345 mm, pixel size 5 mm × 5 mm, active depth 25 mm and is designed for efficiency of 70% for 4 Å neutrons. The detector is tested with 0.5 bar 3He + 1.5 bar krypton gas mixture in active chamber and 2 bar 4He in compensating chamber. The pulse height spectrum recorded at an anode potential of 2000 V shows energy resolution of ∼ 25% for the 764 keV peak. A spatial resolution of 8 mm × 6 mm is achieved. The detector is suitable for SANS studies in the range of 0.02–0.25 Å-1.

  1. Two-dimensional heterostructures for energy storage

    Science.gov (United States)

    Pomerantseva, Ekaterina; Gogotsi, Yury

    2017-07-01

    Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. We also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.

  2. Rationally synthesized two-dimensional polymers.

    Science.gov (United States)

    Colson, John W; Dichtel, William R

    2013-06-01

    Synthetic polymers exhibit diverse and useful properties and influence most aspects of modern life. Many polymerization methods provide linear or branched macromolecules, frequently with outstanding functional-group tolerance and molecular weight control. In contrast, extending polymerization strategies to two-dimensional periodic structures is in its infancy, and successful examples have emerged only recently through molecular framework, surface science and crystal engineering approaches. In this Review, we describe successful 2D polymerization strategies, as well as seminal research that inspired their development. These methods include the synthesis of 2D covalent organic frameworks as layered crystals and thin films, surface-mediated polymerization of polyfunctional monomers, and solid-state topochemical polymerizations. Early application targets of 2D polymers include gas separation and storage, optoelectronic devices and membranes, each of which might benefit from predictable long-range molecular organization inherent to this macromolecular architecture.

  3. Janus Spectra in Two-Dimensional Flows

    Science.gov (United States)

    Liu, Chien-Chia; Cerbus, Rory T.; Chakraborty, Pinaki

    2016-09-01

    In large-scale atmospheric flows, soap-film flows, and other two-dimensional flows, the exponent of the turbulent energy spectra, α , may theoretically take either of two distinct values, 3 or 5 /3 , but measurements downstream of obstacles have invariably revealed α =3 . Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which α transitions from 3 to 5 /3 for the streamwise fluctuations but remains equal to 3 for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows.

  4. Local doping of two-dimensional materials

    Science.gov (United States)

    Wong, Dillon; Velasco, Jr, Jairo; Ju, Long; Kahn, Salman; Lee, Juwon; Germany, Chad E.; Zettl, Alexander K.; Wang, Feng; Crommie, Michael F.

    2016-09-20

    This disclosure provides systems, methods, and apparatus related to locally doping two-dimensional (2D) materials. In one aspect, an assembly including a substrate, a first insulator disposed on the substrate, a second insulator disposed on the first insulator, and a 2D material disposed on the second insulator is formed. A first voltage is applied between the 2D material and the substrate. With the first voltage applied between the 2D material and the substrate, a second voltage is applied between the 2D material and a probe positioned proximate the 2D material. The second voltage between the 2D material and the probe is removed. The first voltage between the 2D material and the substrate is removed. A portion of the 2D material proximate the probe when the second voltage was applied has a different electron density compared to a remainder of the 2D material.

  5. Two-dimensional fourier transform spectrometer

    Energy Technology Data Exchange (ETDEWEB)

    DeFlores, Lauren; Tokmakoff, Andrei

    2016-10-25

    The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

  6. Two-dimensional fourier transform spectrometer

    Science.gov (United States)

    DeFlores, Lauren; Tokmakoff, Andrei

    2013-09-03

    The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

  7. FACE RECOGNITION USING TWO DIMENSIONAL LAPLACIAN EIGENMAP

    Institute of Scientific and Technical Information of China (English)

    Chen Jiangfeng; Yuan Baozong; Pei Bingnan

    2008-01-01

    Recently,some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaces method considered the manifold structures of the face images,it has limits to solve face recognition problem. This paper proposes a new feature extraction method,Two Dimensional Laplacian EigenMap (2DLEM),which especially considers the manifold structures of the face images,and extracts the proper features from face image matrix directly by using a linear transformation. As opposed to Laplacianfaces,2DLEM extracts features directly from 2D images without a vectorization preprocessing. To test 2DLEM and evaluate its performance,a series of ex-periments are performed on the ORL database and the Yale database. Moreover,several experiments are performed to compare the performance of three 2D methods. The experiments show that 2DLEM achieves the best performance.

  8. On the 5d instanton index as a Hilbert series

    Energy Technology Data Exchange (ETDEWEB)

    Rodríguez-Gómez, Diego, E-mail: d.rodriguez.gomez@uniovi.es [Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007 Oviedo (Spain); Zafrir, Gabi, E-mail: gabizaf@techunix.technion.ac.il [Department of Physics, Technion, Israel Institute of Technology, Haifa 32000 (Israel)

    2014-01-15

    The superconformal index for N=2 5d theories contains a non-perturbative part arising from 5d instantonic operators which coincides with the Nekrasov instanton partition function. In this article, for pure gauge theories, we elaborate on the relation between such instanton index and the Hilbert series of the instanton moduli space. We propose a non-trivial identification of fugacities allowing the computation of the instanton index through the Hilbert series. We show the agreement of our proposal with existing results in the literature, as well as use it to compute the exact index for a pure U(1) gauge theory.

  9. Equivalency of two-dimensional algebras

    Energy Technology Data Exchange (ETDEWEB)

    Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S. [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica

    2011-07-01

    Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)

  10. Lectures on Hilbert modular varieties and modular forms

    CERN Document Server

    Goren, Eyal Z

    2001-01-01

    This book is devoted to certain aspects of the theory of p-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of p-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelian varieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of p-adic Hilbert modular forms and the geometry of moduli spaces of abelian varieties are related. This relation is used to study q-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-exper...

  11. Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

    CERN Document Server

    Fougeirol, Jérémie

    2016-01-01

    We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

  12. A TCAM-based Two-dimensional Prefix Packet Classification Algorithm

    Institute of Scientific and Technical Information of China (English)

    王志恒; 刘刚; 白英彩

    2004-01-01

    Packet classification (PC) has become the main method to support the quality of service and security of network application. And two-dimensional prefix packet classification (PPC) is the popular one. This paper analyzes the problem of ruler conflict, and then presents a TCAMbased two-dimensional PPC algorithm. This algorithm makes use of the parallelism of TCAM to lookup the longest prefix in one instruction cycle. Then it uses a memory image and associated data structures to eliminate the conflicts between rulers, and performs a fast two-dimensional PPC.Compared with other algorithms, this algorithm has the least time complexity and less space complexity.

  13. A support theorem for Hilbert schemes of planar curves

    CERN Document Server

    Migliorini, Luca

    2011-01-01

    Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve encodes the cohomology of all Hilbert schemes of points on the curve. Globally, it follows that a family of such curves with smooth relative compactified Jacobian ("moduli space of D-branes") in an irreducible curve class on a Calabi-Yau threefold will contribute equally to the BPS invariants in the formulation of Pandharipande and Thomas, and in the formulation of Hosono, Saito, and Takahashi.

  14. The Fermionic Signature Operator and Quantum States in Rindler Space-Time

    CERN Document Server

    Finster, Felix; Röken, Christian

    2016-01-01

    The fermionic signature operator is constructed in Rindler space-time. It is shown to be an unbounded self-adjoint operator on the Hilbert space of solutions of the massive Dirac equation. In two-dimensional Rindler space-time, we prove that the resulting fermionic projector state coincides with the Fulling-Rindler vacuum. Moreover, the fermionic signature operator gives a covariant construction of general thermal states, in particular of the Unruh state. The fermionic signature operator is shown to be well-defined in asymptotically Rindler space-times. In four-dimensional Rindler space-time, our construction gives rise to new quantum states.

  15. Topological freeness for Hilbert bimodules

    DEFF Research Database (Denmark)

    Kwasniewski, Bartosz

    2014-01-01

    It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description and a s...

  16. Atom-Based Geometrical Fingerprinting of Conformal Two-Dimensional Materials

    Science.gov (United States)

    Mehboudi, Mehrshad

    The shape of two-dimensional materials plays a significant role on their chemical and physical properties. Two-dimensional materials are basic meshes that are formed by mesh points (vertices) given by atomic positions, and connecting lines (edges) between points given by chemical bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated. The local geometry of a surface embodied in 3D space is determined using four invariant numbers from the metric and curvature tensors which indicates how much the surface is stretched and curved under a deformation as compared to a reference pre-deformed conformation. Many different disciplines advance theories on conformal two-dimensional materials by relying on continuum mechanics and fitting continuum surfaces to the shape of conformal two-dimensional materials. However two-dimensional materials are inherently discrete. The continuum models are only applicable when the size of two-dimensional materials is significantly large and the deformation is less than a few percent. In this research, the knowledge of discrete differential geometry was used to tell the local shape of conformal two-dimensional materials. Three kind of two-dimensional materials are discussed: 1) one atom thickness structures such as graphene and hexagonal boron nitride; 2) high and low buckled 2D meshes like stanene, leadene, aluminum phosphate; and, 3) multi layer 2D materials such as Bi2Se3 and WSe2. The lattice structures of these materials were created by designing a mechanical model - the mechanical model was devised in the form of a Gaussian bump and density-functional theory was used to inform the local height; and, the local geometries are also discussed.

  17. The encoding complexity of two dimensional range minimum data structures

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Brodnik, Andrej; Davoodi, Pooya

    2013-01-01

    In the two-dimensional range minimum query problem an input matrix A of dimension m ×n, m ≤ n, has to be preprocessed into a data structure such that given a query rectangle within the matrix, the position of a minimum element within the query range can be reported. We consider the space complexity...... of the encoding variant of the problem where queries have access to the constructed data structure but can not access the input matrix A, i.e. all information must be encoded in the data structure. Previously it was known how to solve the problem with space O(mn min {m,logn}) bits (and with constant query time...

  18. On numerical evaluation of two-dimensional phase integrals

    DEFF Research Database (Denmark)

    Lessow, H.; Rusch, W.; Schjær-Jacobsen, Hans

    1975-01-01

    The relative advantages of several common numerical integration algorithms used in computing two-dimensional phase integrals are evaluated.......The relative advantages of several common numerical integration algorithms used in computing two-dimensional phase integrals are evaluated....

  19. On the physics of the symbol--matter problem in biological systems and the origin of life: affine Hilbert spaces model of the robustness of the internal quantum dynamics of biological systems.

    Science.gov (United States)

    Balázs, András

    2003-06-01

    In the present paper, some physical considerations of the biological symbol-matter problem is exposed. First of all, the physical concept of quantum dynamical internal measuremental robustness is discussed. In this context, the significance of introducing affine molecular Hilbert spaces, the original (primordeal) internal quantum measurement, and the global constraining nature of time-inversion symmetry restoring, as a special restoration force, is discussed at some length. It is pointed out, as a summary, that global robustness of the internal dynamics of quantum measurements is due to two basic factors: on one hand, the global constraining nature of the chosen specific (symmetry-) restoring force, and on the other, the individual robustness of the discrete local internal measuremental interactions. The second condition is supposed to follow from a system-internalised ("objective") Bohr-type Copenhagen interpretation of quantum mechanics, corresponding, in an external context, to the Generalized Complementarity Principle of Bohr and Elsasser. It is not claimed, however, that this latter problem has been, as yet, satisfactorily settled physically. In fact, if it were, it would amount to a specifically biological quantum theory of internal measurement, which had to be rooted in the original primordeal global internal measurement, amounting to the origin of the genetic code.

  20. 关于有限维空间谐振子偶相干态的非经典特性%Numerical Studies on the Nonclassical Properties of Even Coherent States in a Finite-Dimensional Hilbert Space

    Institute of Scientific and Technical Information of China (English)

    邓宏贵; 朱从旭

    2001-01-01

    该文运用数值计算方法研究了有限维希尔伯特空间谐振子偶相干态的非经典特性.研究表明.在有限维情景,偶相干态不仅出现振幅正交分量压缩,而且出现振幅平方压缩和反聚束效应.随着维数s减少,出现两种压缩的区域均缩小且压缩强度减弱;而出现反聚束效应的区域却变大且反聚束程度加强.%The nonclassical properties of even coherent states in a finite-dimensional Hilbert spaces (FDHS) case are studied by numerical method . It is found that, not only quadrature squeezing but also amplitude-squeezing and antibunching effects exist in the states. With the number of dimension reducing, both quadrate squeezing and amplitudesqueezing effects are weakened,but the antibunching effect is Enhanced.

  1. Perturbations of Standard Generalized Frames in Hilbert W*-Module%HILBERT W*-模上标准广义框架的摄动

    Institute of Scientific and Technical Information of China (English)

    付焕坤; 孟彬; 董芳芳

    2011-01-01

    In this paper, the stability of Hilbert W*-modular standard generalized frames under perturbations are studied intensively by using operator-theoretic-methods, and some useful conditions of perturbation and results which are similar to the frames in Hilbert space are given.%该文主要用算子理论的方法详细讨论了Hilbert W*-模中标准广义框架的摄动性,且给出了类似于Hilbert空间中的很有用的摄动条件和相应结论.

  2. Antibunching effect of a new kind of odd and even nonlinear coherent states in a finite-dimensional hilbert space%有限维Hilbert空间一种新的奇偶非线性相干态的反聚束效应

    Institute of Scientific and Technical Information of China (English)

    卢道明

    2008-01-01

    Using the numerical method,the antibunching effects of a new kind of odd and even nonlinear CO- herent states in a finite-dimensional Hilbert space are studied.The results show that the new kind of odd non- 1inear coherent state exhibits antibunching effect and the new kind of even nonlinear coherent state does not exhibits antibunching effect in a finite-dimensional Hilbert space.%利用数值计算方法,研究了有限维Hilbert空间一种新的奇偶非线性相干态的反聚束效应.研究结果表明:各有限维Hilbert空间新的偶非线性相干态均不出现反聚束效应.但各有限维Hilbert空间新的奇非线性相干态均可出现反聚束效应.

  3. The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Borzov, V. V., E-mail: borzov.vadim@yandex.ru [Department of Mathematics, St. Petersburg State University of Telecommunications, 191186, Moika 61, St. Petersburg (Russian Federation); Damaskinsky, E. V., E-mail: evd@pdmi.ras.ru [Department of Natural Sciences, Institute of Defense Technical Engineering (VITI), 191123, Zacharievskaya 22, St. Petersburg (Russian Federation)

    2014-10-15

    In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

  4. Chaotic spread spectrum watermark of optimal space-filling curves

    Energy Technology Data Exchange (ETDEWEB)

    Feng Guorui [Shanghai Jiao-Tong University, Room 1908 Haoran High-tech Building, 1954 Hua-shan Road, Shanghai 200030 (China); Jiang Lingge [Shanghai Jiao-Tong University, Room 1908 Haoran High-tech Building, 1954 Hua-shan Road, Shanghai 200030 (China); He Chen [Shanghai Jiao-Tong University, Room 1908 Haoran High-tech Building, 1954 Hua-shan Road, Shanghai 200030 (China); Xue Yi [Shanghai Jiao-Tong University, Room 1908 Haoran High-tech Building, 1954 Hua-shan Road, Shanghai 200030 (China)

    2006-02-01

    Spread spectrum watermarking scheme is becoming an important research subject. In this paper, we present a method based on Peano-Hilbert space-filling curves for enhancing the robustness. Peano-Hilbert curve is a continuous mapping from one-dimensional space onto two-dimensional space. It is useful in many applications including quantum mechanics even, and preserves optimal locality. At the same time, we utilize a specified chaotic dynamic system-ICMIC map, which shows lowpass properties when the controlling parameter is devised. In this case, the watermarking detection resorts to the Neyman-Pearson criterion based on some statistical assumptions. Experimental results show that the proposed scheme can work well under JPEG compression and resist line-removal test.

  5. Perspective: Two-dimensional resonance Raman spectroscopy

    Science.gov (United States)

    Molesky, Brian P.; Guo, Zhenkun; Cheshire, Thomas P.; Moran, Andrew M.

    2016-11-01

    Two-dimensional resonance Raman (2DRR) spectroscopy has been developed for studies of photochemical reaction mechanisms and structural heterogeneity in complex systems. The 2DRR method can leverage electronic resonance enhancement to selectively probe chromophores embedded in complex environments (e.g., a cofactor in a protein). In addition, correlations between the two dimensions of the 2DRR spectrum reveal information that is not available in traditional Raman techniques. For example, distributions of reactant and product geometries can be correlated in systems that undergo chemical reactions on the femtosecond time scale. Structural heterogeneity in an ensemble may also be reflected in the 2D spectroscopic line shapes of both reactive and non-reactive systems. In this perspective article, these capabilities of 2DRR spectroscopy are discussed in the context of recent applications to the photodissociation reactions of triiodide and myoglobin. We also address key differences between the signal generation mechanisms for 2DRR and off-resonant 2D Raman spectroscopies. Most notably, it has been shown that these two techniques are subject to a tradeoff between sensitivity to anharmonicity and susceptibility to artifacts. Overall, recent experimental developments and applications of the 2DRR method suggest great potential for the future of the technique.

  6. Janus spectra in two-dimensional flows

    CERN Document Server

    Liu, Chien-Chia; Chakraborty, Pinaki

    2016-01-01

    In theory, large-scale atmospheric flows, soap-film flows and other two-dimensional flows may host two distinct types of turbulent energy spectra---in one, $\\alpha$, the spectral exponent of velocity fluctuations, equals $3$ and the fluctuations are dissipated at the small scales, and in the other, $\\alpha=5/3$ and the fluctuations are dissipated at the large scales---but measurements downstream of obstacles have invariably revealed $\\alpha = 3$. Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which $\\alpha$ has transitioned from $3$ to $5/3$ for the streamwise fluctuations but remains equal to $3$ for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows...

  7. Comparative Two-Dimensional Fluorescence Gel Electrophoresis.

    Science.gov (United States)

    Ackermann, Doreen; König, Simone

    2018-01-01

    Two-dimensional comparative fluorescence gel electrophoresis (CoFGE) uses an internal standard to increase the reproducibility of coordinate assignment for protein spots visualized on 2D polyacrylamide gels. This is particularly important for samples, which need to be compared without the availability of replicates and thus cannot be studied using differential gel electrophoresis (DIGE). CoFGE corrects for gel-to-gel variability by co-running with the sample proteome a standardized marker grid of 80-100 nodes, which is formed by a set of purified proteins. Differentiation of reference and analyte is possible by the use of two fluorescent dyes. Variations in the y-dimension (molecular weight) are corrected by the marker grid. For the optional control of the x-dimension (pI), azo dyes can be used. Experiments are possible in both vertical and horizontal (h) electrophoresis devices, but hCoFGE is much easier to perform. For data analysis, commercial software capable of warping can be adapted.

  8. Two-dimensional hexagonal semiconductors beyond graphene

    Science.gov (United States)

    Nguyen, Bich Ha; Hieu Nguyen, Van

    2016-12-01

    The rapid and successful development of the research on graphene and graphene-based nanostructures has been substantially enlarged to include many other two-dimensional hexagonal semiconductors (THS): phosphorene, silicene, germanene, hexagonal boron nitride (h-BN) and transition metal dichalcogenides (TMDCs) such as MoS2, MoSe2, WS2, WSe2 as well as the van der Waals heterostructures of various THSs (including graphene). The present article is a review of recent works on THSs beyond graphene and van der Waals heterostructures composed of different pairs of all THSs. One among the priorities of new THSs compared to graphene is the presence of a non-vanishing energy bandgap which opened up the ability to fabricate a large number of electronic, optoelectronic and photonic devices on the basis of these new materials and their van der Waals heterostructures. Moreover, a significant progress in the research on TMDCs was the discovery of valley degree of freedom. The results of research on valley degree of freedom and the development of a new technology based on valley degree of freedom-valleytronics are also presented. Thus the scientific contents of the basic research and practical applications os THSs are very rich and extremely promising.

  9. Two-Dimensional Phononic Crystals: Disorder Matters.

    Science.gov (United States)

    Wagner, Markus R; Graczykowski, Bartlomiej; Reparaz, Juan Sebastian; El Sachat, Alexandros; Sledzinska, Marianna; Alzina, Francesc; Sotomayor Torres, Clivia M

    2016-09-14

    The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the gigahertz (GHz) and terahertz (THz) regime, respectively. Finite element method simulations of the phonon dispersion relation and three-dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short-range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room-temperature thermal conductivity. On the basis of these findings, we suggest a criteria for predicting phonon coherence as a function of roughness and disorder.

  10. Photodetectors based on two dimensional materials

    Science.gov (United States)

    Zheng, Lou; Zhongzhu, Liang; Guozhen, Shen

    2016-09-01

    Two-dimensional (2D) materials with unique properties have received a great deal of attention in recent years. This family of materials has rapidly established themselves as intriguing building blocks for versatile nanoelectronic devices that offer promising potential for use in next generation optoelectronics, such as photodetectors. Furthermore, their optoelectronic performance can be adjusted by varying the number of layers. They have demonstrated excellent light absorption, enabling ultrafast and ultrasensitive detection of light in photodetectors, especially in their single-layer structure. Moreover, due to their atomic thickness, outstanding mechanical flexibility, and large breaking strength, these materials have been of great interest for use in flexible devices and strain engineering. Toward that end, several kinds of photodetectors based on 2D materials have been reported. Here, we present a review of the state-of-the-art in photodetectors based on graphene and other 2D materials, such as the graphene, transition metal dichalcogenides, and so on. Project supported by the National Natural Science Foundation of China (Nos. 61377033, 61574132, 61504136) and the State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences.

  11. Asymptotics for Two-dimensional Atoms

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip

    2012-01-01

    We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....

  12. Predicting Two-Dimensional Silicon Carbide Monolayers.

    Science.gov (United States)

    Shi, Zhiming; Zhang, Zhuhua; Kutana, Alex; Yakobson, Boris I

    2015-10-27

    Intrinsic semimetallicity of graphene and silicene largely limits their applications in functional devices. Mixing carbon and silicon atoms to form two-dimensional (2D) silicon carbide (SixC1-x) sheets is promising to overcome this issue. Using first-principles calculations combined with the cluster expansion method, we perform a comprehensive study on the thermodynamic stability and electronic properties of 2D SixC1-x monolayers with 0 ≤ x ≤ 1. Upon varying the silicon concentration, the 2D SixC1-x presents two distinct structural phases, a homogeneous phase with well dispersed Si (or C) atoms and an in-plane hybrid phase rich in SiC domains. While the in-plane hybrid structure shows uniform semiconducting properties with widely tunable band gap from 0 to 2.87 eV due to quantum confinement effect imposed by the SiC domains, the homogeneous structures can be semiconducting or remain semimetallic depending on a superlattice vector which dictates whether the sublattice symmetry is topologically broken. Moreover, we reveal a universal rule for describing the electronic properties of the homogeneous SixC1-x structures. These findings suggest that the 2D SixC1-x monolayers may present a new "family" of 2D materials, with a rich variety of properties for applications in electronics and optoelectronics.

  13. Two-Dimensional Impact Reconstruction Method for Rail Defect Inspection

    Directory of Open Access Journals (Sweden)

    Jie Zhao

    2014-01-01

    Full Text Available The safety of train operating is seriously menaced by the rail defects, so it is of great significance to inspect rail defects dynamically while the train is operating. This paper presents a two-dimensional impact reconstruction method to realize the on-line inspection of rail defects. The proposed method utilizes preprocessing technology to convert time domain vertical vibration signals acquired by wireless sensor network to space signals. The modern time-frequency analysis method is improved to reconstruct the obtained multisensor information. Then, the image fusion processing technology based on spectrum threshold processing and node color labeling is proposed to reduce the noise, and blank the periodic impact signal caused by rail joints and locomotive running gear. This method can convert the aperiodic impact signals caused by rail defects to partial periodic impact signals, and locate the rail defects. An application indicates that the two-dimensional impact reconstruction method could display the impact caused by rail defects obviously, and is an effective on-line rail defects inspection method.

  14. Strong Convergence Theorem for a Generalized Equilibrium Problem and Fixed Points of a Finite Family of Nonexpansive Mappings in A Hilbert Space%希尔伯特空间中关于广义均衡问题和有限组非扩张映像的不动点的强收敛定理

    Institute of Scientific and Technical Information of China (English)

    闫明刚; 刘海防; 陈汝栋

    2009-01-01

    在希尔伯特空间,我们引入一个新的迭代序列来逼近广义均衡问题和有限组扩张映像的不动点的公共元素.相应推广了 Satoru Takahashi,Wararu Takahashif Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69(2008)0250-1033

  15. Compatibility and Schur Complements of Operators on Hilbert C*-Module

    Institute of Scientific and Technical Information of China (English)

    Xiaochun FANG; Jing YU

    2011-01-01

    Let E be a Hilbert C*-module, and (J) be an orthogonally complemented closed submodule of E. The authors generalize the definitions of (J)-complementability and (J)compatibility for general (adjointable) operators from Hilbert space to Hilbert C*-module,and discuss the relationship between each other. Several equivalent statements about (J)complementability and (J)-compatibility, and several representations of Schur complements of (J)-complementable operators (especially, of (J)-compatible operators and of positive (J)compatible operators) on a Hilbert C*-module are obtained. In addition, the quotient property for Schur complements of matrices is generalized to the quotient property for Schur complements of (J)-complementable operators and (J)*-complementable operators on a Hilbert C*-module.

  16. Interaction of two-dimensional magnetoexcitons

    Science.gov (United States)

    Dumanov, E. V.; Podlesny, I. V.; Moskalenko, S. A.; Liberman, M. A.

    2017-04-01

    We study interaction of the two-dimensional magnetoexcitons with in-plane wave vector k→∥ = 0 , taking into account the influence of the excited Landau levels (ELLs) and of the external electric field perpendicular to the surface of the quantum well and parallel to the external magnetic field. It is shown that the account of the ELLs gives rise to the repulsion between the spinless magnetoexcitons with k→∥ = 0 in the Fock approximation, with the interaction constant g decreasing inverse proportional to the magnetic field strength B (g (0) ∼ 1 / B) . In the presence of the perpendicular electric field the Rashba spin-orbit coupling (RSOC), Zeeman splitting (ZS) and nonparabolicity of the heavy-hole dispersion law affect the Landau quantization of the electrons and holes. They move along the new cyclotron orbits, change their Coulomb interactions and cause the interaction between 2D magnetoexcitons with k→∥ = 0 . The changes of the Coulomb interactions caused by the electrons and by the holes moving with new cyclotron orbits are characterized by some coefficients, which in the absence of the electric field turn to be unity. The differences between these coefficients of the electron-hole pairs forming the magnetoexcitons determine their affinities to the interactions. The interactions between the homogeneous, semihomogeneous and heterogeneous magnetoexcitons forming the symmetric states with the same signs of their affinities are attractive whereas in the case of different sign affinities are repulsive. In the heterogeneous asymmetric states the interactions have opposite signs in comparison with the symmetric states. In all these cases the interaction constant g have the dependence g (0) 1 /√{ B} .

  17. A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

    Energy Technology Data Exchange (ETDEWEB)

    Chatterjee, Kausik, E-mail: kausik.chatterjee@aggiemail.usu.edu [Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341 (United States); Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322 (United States); Roadcap, John R., E-mail: john.roadcap@us.af.mil [Air Force Research Laboratory, Kirtland AFB, NM 87117 (United States); Singh, Surendra, E-mail: surendra-singh@utulsa.edu [Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104 (United States)

    2014-11-01

    The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

  18. 2DCOS and I. Three decades of two-dimensional correlation spectroscopy

    Science.gov (United States)

    Noda, Isao

    2016-11-01

    Historical and personal accounts of the development of two-dimensional correlation spectroscopy (2DCOS) in the last 30 years are presented. 2DCOS originally started as a data sorting technique developed specifically for dynamic IR linear dichroism (DIRLD) spectra of polymers observed under a small amplitude sinusoidal strain. The concept was later generalized to provide a surprisingly versatile analytical tool to study many different types of samples under the influence of not only dynamic but also various static perturbations. Introduction of the efficient computational method based on discrete Hilbert transform and availability of software, as well as the comprehensive textbook in the field, have made the widespread and continuously growing use of 2DCOS technique possible. Evolution of the technique to incorporate new and variant forms of 2DCOS is also noted.

  19. Two-dimensional materials and their prospects in transistor electronics.

    Science.gov (United States)

    Schwierz, F; Pezoldt, J; Granzner, R

    2015-05-14

    During the past decade, two-dimensional materials have attracted incredible interest from the electronic device community. The first two-dimensional material studied in detail was graphene and, since 2007, it has intensively been explored as a material for electronic devices, in particular, transistors. While graphene transistors are still on the agenda, researchers have extended their work to two-dimensional materials beyond graphene and the number of two-dimensional materials under examination has literally exploded recently. Meanwhile several hundreds of different two-dimensional materials are known, a substantial part of them is considered useful for transistors, and experimental transistors with channels of different two-dimensional materials have been demonstrated. In spite of the rapid progress in the field, the prospects of two-dimensional transistors still remain vague and optimistic opinions face rather reserved assessments. The intention of the present paper is to shed more light on the merits and drawbacks of two-dimensional materials for transistor electronics and to add a few more facets to the ongoing discussion on the prospects of two-dimensional transistors. To this end, we compose a wish list of properties for a good transistor channel material and examine to what extent the two-dimensional materials fulfill the criteria of the list. The state-of-the-art two-dimensional transistors are reviewed and a balanced view of both the pros and cons of these devices is provided.

  20. Two-dimensional static deformation of an anisotropic medium

    Indian Academy of Sciences (India)

    Kuldip Singh; Dinesh Kumar Madan; Anita Goel; Nat Ram Garg

    2005-08-01

    The problem of two-dimensional static deformation of a monoclinic elastic medium has been studied using the eigenvalue method, following a Fourier transform. We have obtained expressions for displacements and stresses for the medium in the transformed domain. As an application of the above theory, the particular case of a normal line-load acting inside an orthotropic elastic half-space has been considered in detail and closed form expressions for the displacements and stresses are obtained. Further, the results for the displacements for a transversely isotropic as well as for an isotropic medium have also been derived in the closed form. The use of matrix notation is straightforward and avoids unwieldy mathematical expressions. To examine the effect of anisotropy, variations of dimensionless displacements for an orthotropic, transversely isotropic and isotropic elastic medium have been compared numerically and it is found that anisotropy affects the deformation significantly.

  1. Two-Dimensional Planetary Surface Landers Project

    Data.gov (United States)

    National Aeronautics and Space Administration — We propose to develop a new landing approach that significantly reduces development time and obviates the most complicated, most expensive and highest-risk phase of...

  2. Ultrafast two dimensional infrared chemical exchange spectroscopy

    Science.gov (United States)

    Fayer, Michael

    2011-03-01

    The method of ultrafast two dimensional infrared (2D IR) vibrational echo spectroscopy is described. Three ultrashort IR pulses tuned to the frequencies of the vibrational transitions of interest are directed into the sample. The interaction of these pulses with the molecular vibrational oscillators produces a polarization that gives rise to a fourth pulse, the vibrational echo. The vibrational echo pulse is combined with another pulse, the local oscillator, for heterodyne detection of the signal. For fixed time between the second and third pulses, the waiting time, the first pulse is scanned. Two Fourier transforms of the data yield a 2D IR spectrum. The waiting time is increased, and another spectrum is obtained. The change in the 2D IR spectra with increased waiting time provides information on the time evolution of the structure of the molecular system under observation. In a 2D IR chemical exchange experiment, two species A and B, are undergoing chemical exchange. A's are turning into B's, and B's are turning into A's, but the overall concentrations of the species are not changing. The kinetics of the chemical exchange on the ground electronic state under thermal equilibrium conditions can be obtained 2D IR spectroscopy. A vibration that has a different frequency for the two species is monitored. At very short time, there will be two peaks on the diagonal of the 2D IR spectrum, one for A and one for B. As the waiting time is increased, chemical exchange causes off-diagonal peaks to grow in. The time dependence of the growth of these off-diagonal peaks gives the chemical exchange rate. The method is applied to organic solute-solvent complex formation, orientational isomerization about a carbon-carbon single bond, migration of a hydrogen bond from one position on a molecule to another, protein structural substate interconversion, and water hydrogen bond switching between ions and water molecules. This work was supported by the Air Force Office of Scientific

  3. Molecular assembly on two-dimensional materials

    Science.gov (United States)

    Kumar, Avijit; Banerjee, Kaustuv; Liljeroth, Peter

    2017-02-01

    Molecular self-assembly is a well-known technique to create highly functional nanostructures on surfaces. Self-assembly on two-dimensional (2D) materials is a developing field driven by the interest in functionalization of 2D materials in order to tune their electronic properties. This has resulted in the discovery of several rich and interesting phenomena. Here, we review this progress with an emphasis on the electronic properties of the adsorbates and the substrate in well-defined systems, as unveiled by scanning tunneling microscopy. The review covers three aspects of the self-assembly. The first one focuses on non-covalent self-assembly dealing with site-selectivity due to inherent moiré pattern present on 2D materials grown on substrates. We also see that modification of intermolecular interactions and molecule–substrate interactions influences the assembly drastically and that 2D materials can also be used as a platform to carry out covalent and metal-coordinated assembly. The second part deals with the electronic properties of molecules adsorbed on 2D materials. By virtue of being inert and possessing low density of states near the Fermi level, 2D materials decouple molecules electronically from the underlying metal substrate and allow high-resolution spectroscopy and imaging of molecular orbitals. The moiré pattern on the 2D materials causes site-selective gating and charging of molecules in some cases. The last section covers the effects of self-assembled, acceptor and donor type, organic molecules on the electronic properties of graphene as revealed by spectroscopy and electrical transport measurements. Non-covalent functionalization of 2D materials has already been applied for their application as catalysts and sensors. With the current surge of activity on building van der Waals heterostructures from atomically thin crystals, molecular self-assembly has the potential to add an extra level of flexibility and functionality for applications ranging

  4. Digital watermarking : An approach based on Hilbert transform

    CERN Document Server

    Agarwal, Rashmi; Santhanam, M S; Srinivas, K; Venugopalan, K

    2010-01-01

    Most of the well known algorithms for watermarking of digital images involve transformation of the image data to Fourier or singular vector space. In this paper, we introduce watermarking in Hilbert transform domain for digital media. Generally, if the image is a matrix of order $m$ by $n$, then the transformed space is also an image of the same order. However, with Hilbert transforms, the transformed space is of order $2m$ by $2n$. This allows for more latitude in storing the watermark in the host image. Based on this idea, we propose an algorithm for embedding and extracting watermark in a host image and analytically obtain a parameter related to this procedure. Using extensive simulations, we show that the algorithm performs well even if the host image is corrupted by various attacks.

  5. Some introductory formalizations on the affine Hilbert spaces model of the origin of life. I. On quantum mechanical measurement and the origin of the genetic code: a general physical framework theory.

    Science.gov (United States)

    Balázs, András

    2006-08-01

    A physical (affine Hilbert spaces) frame is developed for the discussion of the interdependence of the problem of the origin (symbolic assignment) of the genetic code and a possible endophysical (a kind of "internal") quantum measurement in an explicite way, following the general considerations of Balázs (Balázs, A., 2003. BioSystems 70, 43-54; Balázs, A., 2004a. BioSystems 73, 1-11). Using the Everett (a dynamic) interpretation of quantum mechanics, both the individual code assignment and the concatenated linear symbolism is discussed. It is concluded that there arises a skewed quantal probability field, with a natural dynamic non-linearity in codon assignment within the physical model adopted (essentially corresponding to a much discussed biochemical frame of self-catalyzed binding (charging) of t RNA like proto RNAs (ribozymes) with amino acids). This dynamic specific molecular complex assumption of individual code assignment, and the divergence of the code in relation to symbol concatenation, are discussed: our frame supports the former and interpret the latter as single-type codon (triplet), also unambiguous and extended assignment, selection in molecular evolution, corresponding to converging towards the fixedpoint of the internal dynamics of measurement, either in a protein- or RNA-world. In this respect, the general physical consequence is the introduction of a fourth rank semidiagonal energy tensor (see also Part II) ruling the internal dynamics as a non-linear in principle second-order one. It is inferred, as a summary, that if the problem under discussion could be expressed by the concepts of the Copenhagen interpretation of quantum mechanics in some yet not quite specified way, the matter would be particularly interesting with respect to both the origin of life and quantum mechanics, as a dynamically supported natural measurement-theoretical split between matter ("hardware") and (internal) symbolism ("software") aspects of living matter.

  6. Model and observed seismicity represented in a two dimensional space

    Directory of Open Access Journals (Sweden)

    M. Caputo

    1976-06-01

    Full Text Available In recent years theoretical seismology lias introduced
    some formulae relating the magnitude and the seismic moment of earthquakes
    to the size of the fault and the stress drop which generated the
    earthquake.
    In the present paper we introduce a model for the statistics of the
    earthquakes based on these formulae. The model gives formulae which
    show internal consistency and are also confirmed by observations.
    For intermediate magnitudes the formulae reproduce also the trend
    of linearity of the statistics of magnitude and moment observed in all the
    seismic regions of the world. This linear trend changes into a curve with
    increasing slope for large magnitudes and moment.
    When a catalogue of the magnitudes and/or the seismic moment of
    the earthquakes of a seismic region is available, the model allows to estimate
    the maximum magnitude possible in the region.

  7. The convolution theorem for two-dimensional continuous wavelet transform

    Institute of Scientific and Technical Information of China (English)

    ZHANG CHI

    2013-01-01

    In this paper , application of two -dimensional continuous wavelet transform to image processes is studied. We first show that the convolution and correlation of two continuous wavelets satisfy the required admissibility and regularity conditions ,and then we derive the convolution and correlation theorem for two-dimensional continuous wavelet transform. Finally, we present numerical example showing the usefulness of applying the convolution theorem for two -dimensional continuous wavelet transform to perform image restoration in the presence of additive noise.

  8. 有限维希尔伯特空间偶奇q-相干态的高阶反聚束效应%Higher-order Antibunching Effect of Even and Odd Q-coherent States in a Finite-dimensional Hilbert Space

    Institute of Scientific and Technical Information of China (English)

    张勇; 王维玺

    2000-01-01

    构造了有限维希尔伯特空间偶奇q-相干态,并通过数值计算研究了它们的高阶反聚束效应,分析了空间维数和形变参数q对反聚束效应的影响.%Even and odd q-coherent states in a finite-dimensional Hilbert space are constructed. Their antibunching effects are studied through the numerical method, and the function of the dimension of space and deformation parameter q to the antibunching effect is analyzed.

  9. Equivalence of Quotient Hilbert Modules

    Indian Academy of Sciences (India)

    Ronald G Douglas; Gadadhar Misra

    2003-08-01

    Let $\\mathcal{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\\mathcal{A}()$, where $ \\subseteq \\mathbb{C}^m$ is a bounded domain. Let $\\mathcal{M}_0 \\subseteq \\mathcal{M}$ be the submodule of functions vanishing to order on a hypersurface $\\mathcal{Z} \\subseteq $. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules $\\mathcal{Q} = \\mathcal{M} \\ominus \\mathcal{M}_0$. The invariants are given explicitly in the particular case of = 2.

  10. ON A HYPER HILBERT TRANSFORM

    Institute of Scientific and Technical Information of China (English)

    CHEN JIECHENG; DING YONG; FAN DASHAN

    2003-01-01

    The authors define the directional hyper Hilbert transform and give its mixed norm estimate.The similar conclusions for the directional fractional integral of one dimension are also obtainedin this paper. As an application of the above results, the authors give the Lp-boundedness for aclass of the hyper singular integrals and the fractional integrals with variable kernel. Moreover,as another application of the above results, the authors prove the dimension free estimate forthe hyper Riesz transform. This is an extension of the related result obtained by Stein.

  11. An image encryption algorithm utilizing julia sets and hilbert curves.

    Science.gov (United States)

    Sun, Yuanyuan; Chen, Lina; Xu, Rudan; Kong, Ruiqing

    2014-01-01

    Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets' parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets' properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack.

  12. Orthogonal apartments in Hilbert Grassmannians. Finite-dimensional case

    OpenAIRE

    Pankov, Mark

    2015-01-01

    Let $H$ be a complex Hilbert space of finite dimension $n\\ge 3$. Denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces of $H$. Every orthogonal apartment of ${\\mathcal G}_{k}(H)$ is defined by a certain orthogonal base of $H$ and consists of all $k$-dimensional subspaces spanned by subsets of this base. For $n\

  13. Contractive Hilbert modules and their dilations over natural function algebras

    CERN Document Server

    Douglas, Ronald G; Sarkar, Jaydeb

    2009-01-01

    In this note, we show that quasi-free Hilbert modules R defined over natural function algebras satisfying a certain positivity condition, defined via the hereditary functional calculus, admit a dilation (actually a co-extension) to the Hardy module over the polydisk. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. Some consequences of this basic fact is then explored in the case of several natural function algebras.

  14. Non-Linear Non Stationary Analysis of Two-Dimensional Time-Series Applied to GRACE Data Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The proposed innovative two-dimensional (2D) adaptive analysis will be tested NASA's Gravity Recovery and Climate Experiment (GRACE) mission database in phase I in...

  15. Non-Linear Non Stationary Analysis of Two-Dimensional Time-Series Applied to GRACE Data Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The proposed innovative two-dimensional (2D) empirical mode decomposition (EMD) analysis was applied to NASA's Gravity Recovery and Climate Experiment (GRACE)...

  16. Two-Dimensional Einstein Manifolds in Geometrothermodynamics

    Directory of Open Access Journals (Sweden)

    Antonio C. Gutiérrez-Piñeres

    2013-01-01

    Full Text Available We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates. We conjecture that solutions on the characteristic circumference are of physical relevance, separating them from those of pure mathematical interest. We present the case of a one-parameter family of fundamental relations that—when lying in the circumference—describe a polytropic fluid.

  17. The Chandrasekhar's Equation for Two-Dimensional Hypothetical White Dwarfs

    CERN Document Server

    De, Sanchari

    2014-01-01

    In this article we have extended the original work of Chandrasekhar on the structure of white dwarfs to the two-dimensional case. Although such two-dimensional stellar objects are hypothetical in nature, we strongly believe that the work presented in this article may be prescribed as Master of Science level class problem for the students in physics.

  18. Beginning Introductory Physics with Two-Dimensional Motion

    Science.gov (United States)

    Huggins, Elisha

    2009-01-01

    During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…

  19. Spatiotemporal surface solitons in two-dimensional photonic lattices.

    Science.gov (United States)

    Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S

    2007-11-01

    We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.

  20. Explorative data analysis of two-dimensional electrophoresis gels

    DEFF Research Database (Denmark)

    Schultz, J.; Gottlieb, D.M.; Petersen, Marianne Kjerstine;

    2004-01-01

    Methods for classification of two-dimensional (2-DE) electrophoresis gels based on multivariate data analysis are demonstrated. Two-dimensional gels of ten wheat varieties are analyzed and it is demonstrated how to classify the wheat varieties in two qualities and a method for initial screening...

  1. Mechanics of Apparent Horizon in Two Dimensional Dilaton Gravity

    CERN Document Server

    Cai, Rong-Gen

    2016-01-01

    In this article, we give a definition of apparent horizon in a two dimensional general dilaton gravity theory. With this definition, we construct the mechanics of the apparent horizon by introducing a quasi-local energy of the theory. Our discussion generalizes the apparent horizons mechanics in general spherically symmetric spactimes in four or higher dimensions to the two dimensional dilaton gravity case.

  2. Topological aspect of disclinations in two-dimensional crystals

    Institute of Scientific and Technical Information of China (English)

    Qi Wei-Kai; Zhu Tao; Chen Yong; Ren Ji-Rong

    2009-01-01

    By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.

  3. Quantum Hilbert matrices and orthogonal polynomials

    DEFF Research Database (Denmark)

    Andersen, Jørgen Ellegaard; Berg, Christian

    2009-01-01

    Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|matrices...... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....

  4. Quantum mechanics: why complex Hilbert space?

    Science.gov (United States)

    Cassinelli, G; Lahti, P

    2017-11-13

    We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

  5. Hilbert space methods for partial differential equations

    Directory of Open Access Journals (Sweden)

    Ralph E. Showalter

    1994-09-01

    Full Text Available This book is an outgrowth of a course which we have given almost periodically over the last eight years. It is addressed to beginning graduate students of mathematics, engineering, and the physical sciences. Thus, we have attempted to present it while presupposing a minimal background: the reader is assumed to have some prior acquaintance with the concepts of ``linear'' and ``continuous'' and also to believe $L^2$ is complete. An undergraduate mathematics training through Lebesgue integration is an ideal background but we dare not assume it without turning away many of our best students. The formal prerequisite consists of a good advanced calculus course and a motivation to study partial differential equations.

  6. Construction of exact complex dynamical invariant of a two-dimensional classical system

    Indian Academy of Sciences (India)

    Fakir Chand; S C Mishra

    2006-12-01

    We present the construction of exact complex dynamical invariant of a two-dimensional classical dynamical system on an extended complex space utilizing Lie algebraic approach. These invariants are expected to play a vital role in understanding the complex trajectories of both classical and quantum systems.

  7. A two-dimensional embedded-boundary method for convection problems with moving boundaries

    NARCIS (Netherlands)

    Hassen, Y.J.; Koren, B.

    2010-01-01

    In this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes in the imme

  8. RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH MULTIPLICATIVE NOISE

    Institute of Scientific and Technical Information of China (English)

    Zhao Caidi; Li Yongsheng; Zhou Shengfan

    2011-01-01

    This article proves that the random dynamical system generated by a two- dimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.

  9. 一种基于非完整二维相空间分量置换的混沌检测方法∗%A chaotic signal detection metho d based on the comp onent p ermutation of the incomplete two-dimensional phase-space

    Institute of Scientific and Technical Information of China (English)

    朱胜利; 甘露

    2016-01-01

    由于混沌时间序列和随机过程具有很多类似的性质,因而在实际中很难将两者区分开来。混沌信号检测与识别是混沌时间序列分析中一个重要的课题。混沌信号是由确定性的混沌映射或混沌系统产生的,相比于高斯白噪声序列,其在非完整的二维相空间中表现出更加丰富的结构特性。本文通过研究混沌时间序列和高斯白噪声序列在非完整二维相空间中的分布特性,利用混沌信号的非线性动力学特性,提出了一种基于非完整二维相空间分量置换的混沌信号检测方法。该方法首先由接收序列得到非完整的二维相空间,基于第一维分量大小关系实现对第二维分量的置换与分组,进一步求得F检验统计量。然后利用混沌系统的局部特性,获取非完整二维相空间的动力学结构信息,实现对混沌序列的有效检测。在高斯白噪声条件下对多种混沌信号进行了信号检测的数值仿真。仿真结果表明:相比置换熵检测,本文所提算法所需数据量小、计算简单以及具有更低的时间复杂度,同时对噪声具有更好的鲁棒性。%Detection and identification of chaotic signal is very important in the chaotic time series analysis. It is not easy to distinguish chaotic time series from stochastic processes since they share some similar natures. The detection methods to capture and utilize the structure of state-space dynamics can be very effective. In practice, it is very hard to obtain full information about the structure, and accurate phase-space reconstruction from scalar time series data is also a real challenge. However, the chaotic signals also show fundamental dynamical structure in the incomplete two-dimensional phase-space for the reason that they are generated by the deterministic chaotic systems or maps. Based on the fact that the distribution of chaotic signals is quite different from that of the noise

  10. Hilbert transform and its application to modulation of capillary gravity waves

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    In this paper, the following important problem is answered: Under what condition can the Hilbert transform be put in the simple form. Then, using the Hilbert technique, it is demonstrated that,with some relative weak restrictions, the particle motion at the sea surface and energy transmission may be obtained from a wave record. The analysis shows that for the two-dimensional and narrow-band mo tion (or a physical phenomena, such as capillary waves breaking, which satisfy the narrow-band approx imation) the local kinetic energy fluctuates in time as the envelope squared multiplied by a constant factor and can be obtained directly from a wave record. It is pointed that the local fluctuations of the potential energy as well as the local fluctuations of the total energy can be separated into a slowly varying part and a more rapid oscillating part. Both parts can be evaluated by means of the Hilbert transform. Finally, a physical interpretation of the envelope of the two-dimensional capillary waves as well as the method for wave group analysis is presented.

  11. Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice

    Institute of Scientific and Technical Information of China (English)

    XU Quan; QIANG Tian

    2009-01-01

    We study the existence and stability of two-dimensional discrete breathers in a two-dimensional discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling.Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive)and the center of the two-dimensional gap breather (on a light or a heavy atom).

  12. Asymmetrical interference effects between two-dimensional geometric shapes and their corresponding shape words.

    Science.gov (United States)

    Sturz, Bradley R; Edwards, Joshua E; Boyer, Ty W

    2014-01-01

    Nativists have postulated fundamental geometric knowledge that predates linguistic and symbolic thought. Central to these claims is the proposal for an isolated cognitive system dedicated to processing geometric information. Testing such hypotheses presents challenges due to difficulties in eliminating the combination of geometric and non-geometric information through language. We present evidence using a modified matching interference paradigm that an incongruent shape word interferes with identifying a two-dimensional geometric shape, but an incongruent two-dimensional geometric shape does not interfere with identifying a shape word. This asymmetry in interference effects between two-dimensional geometric shapes and their corresponding shape words suggests that shape words activate spatial representations of shapes but shapes do not activate linguistic representations of shape words. These results appear consistent with hypotheses concerning a cognitive system dedicated to processing geometric information isolated from linguistic processing and provide evidence consistent with hypotheses concerning knowledge of geometric properties of space that predates linguistic and symbolic thought.

  13. Two Dimensional Heat Transfer around Penetrations in Multilayer Insulation

    Science.gov (United States)

    Johnson, Wesley L.; Kelly, Andrew O.; Jumper, Kevin M.

    2012-01-01

    The objective of this task was to quantify thermal losses involving integrating MLI into real life situations. Testing specifically focused on the effects of penetrations (including structural attachments, electrical conduit/feedthroughs, and fluid lines) through MLI. While there have been attempts at quantifying these losses both analytically and experimentally, none have included a thorough investigation of the methods and materials that could be used in such applications. To attempt to quantify the excess heat load coming into the system due to the integration losses, a calorimeter was designed to study two dimensional heat transfer through penetrated MLI. The test matrix was designed to take as many variables into account as was possible with the limited test duration and system size. The parameters varied were the attachment mechanism, the buffer material (for buffer attachment mechanisms only), the thickness of the buffer, and the penetration material. The work done under this task is an attempt to measure the parasitic heat loads and affected insulation areas produced by system integration, to model the parasitic loads, and from the model produce engineering equations to allow for the determination of parasitic heat loads in future applications. The methods of integration investigated were no integration, using a buffer to thermally isolate the strut from the MLI, and temperature matching the MLI on the strut. Several materials were investigated as a buffer material including aerogel blankets, aerogel bead packages, cryolite, and even an evacuated vacuum space (in essence a no buffer condition).

  14. Generalized non-separable two-dimensional Dammann encoding method

    Science.gov (United States)

    Yu, Junjie; Zhou, Changhe; Zhu, Linwei; Lu, Yancong; Wu, Jun; Jia, Wei

    2017-01-01

    We generalize for the first time, to the best of our knowledge, the Dammann encoding method into non-separable two-dimensional (2D) structures for designing various pure-phase Dammann encoding gratings (DEGs). For examples, three types of non-separable 2D DEGs, including non-separable binary Dammann vortex gratings, non-separable binary distorted Dammann gratings, and non-separable continuous-phase cubic gratings, are designed theoretically and demonstrated experimentally. Correspondingly, it is shown that 2D square arrays of optical vortices with topological charges proportional to the diffraction orders, focus spots shifting along both transversal and axial directions with equal spacings, and Airy-like beams with controllable orientation for each beam, are generated in symmetry or asymmetry by these three DEGs, respectively. Also, it is shown that a more complex-shaped array of modulated beams could be achieved by this non-separable 2D Dammann encoding method, which will be a big challenge for those conventional separable 2D Dammann encoding gratings. Furthermore, the diffractive efficiency of the gratings can be improved around ∼10% when the non-separable structure is applied, compared with their conventional separable counterparts. Such improvement in the efficiency should be of high significance for some specific applications.

  15. Two-dimensional networks of lanthanide cubane-shaped dumbbells.

    Science.gov (United States)

    Savard, Didier; Lin, Po-Heng; Burchell, Tara J; Korobkov, Ilia; Wernsdorfer, Wolfgang; Clérac, Rodolphe; Murugesu, Muralee

    2009-12-21

    The syntheses, structures, and magnetic properties are reported for three new lanthanide complexes, [Ln(III)(4)(mu(3)-OH)(2)(mu(3)-O)(2)(cpt)(6)(MeOH)(6)(H(2)O)](2) (Ln = Dy (1.15MeOH), Ho (2.14MeOH), and Tb (3.18MeOH)), based on 4-(4-carboxyphenyl)-1,2,4-triazole ligand (Hcpt). The three complexes were confirmed to be isomorphous by infrared spectroscopy and single-crystal X-ray diffraction. The crystal structure of 1 reveals that the eight-coordinate metal centers are organized in two cubane-shaped moieties composed of four Dy(III) ions each. All metal centers in the cubane core are bridged by two mu(3)-oxide and two mu(3)-hydroxide asymmetrical units. Moreover, each cubane is linked to its neighbor by two externally coordinating ligands, forming the dumbbell {Dy(III)(4)}(2) moiety. Electrostatic interactions between the ligands of the triazole-bridged dimers form an extended supramolecular two-dimensional arrangement analogous to a metal-organic framework with quadrilateral spaces occupied by ligands from axial sheets and by four solvent molecules. The magnetic properties of the three compounds have been investigated using dc and ac susceptibility measurements. For 1, the static and dynamic data corroborate the fact that the {Dy(III)(4)} cubane-shaped core exhibits slow relaxation of its magnetization below 5 K associated with a single-molecule magnet behavior.

  16. Conformal QED in two-dimensional topological insulators

    CERN Document Server

    Menezes, N; Smith, C Morais

    2016-01-01

    It has been shown recently that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). In this work, we provide a first-principle derivation of this non-Fermi-liquid phase based on the gauge-theory approach. Firstly, we derive a gauge theory for the edge states by simply assuming that the interactions between the Dirac fermions at the edge are mediated by a quantum dynamical electromagnetic field. Here, the massless Dirac fermions are confined to live on the one-dimensional boundary, while the (virtual) photons of the U(1) gauge field are free to propagate in all the three spatial dimensions that represent the physical space where the topological insulator is embedded. We then determine the effective 1+1-dimensional conformal field theory (CFT) given by the conformal quantum electrodynamics (CQED). By integrating out the gauge field in the corresponding partition function, ...

  17. The planiverse computer contact with a two-dimensional world

    CERN Document Server

    Dewdney, Alexander Keewatin

    2000-01-01

    When The Planiverse ?rst appeared 16 years ago, it caught more than a few readers off guard. The line between willing suspension of dis- lief and innocent acceptance, if it exists at all, is a thin one. There were those who wanted to believe, despite the tongue-in-cheek subtext, that we had made contact with a two-dimensional world called Arde, a di- shaped planet embedded in the skin of a vast, balloon-shaped space called the planiverse. It is tempting to imagine that those who believed, as well as those who suspended disbelief, did so because of a persuasive consistency in the cosmology and physics of this in?nitesimally thin universe, and x preface to the millennium edition in its bizarre but oddly workable organisms. This was not just your r- of-the-mill universe fashioned out of the whole cloth of wish-driven imagination. The planiverse is a weirder place than that precisely - cause so much of it was “worked out” by a virtual team of scientists and technologists. Reality, even the pseudoreality of su...

  18. Quantifying leaf venation patterns: two-dimensional maps.

    Science.gov (United States)

    Rolland-Lagan, Anne-Gaëlle; Amin, Mira; Pakulska, Malgosia

    2009-01-01

    The leaf vasculature plays crucial roles in transport and mechanical support. Understanding how vein patterns develop and what underlies pattern variation between species has many implications from both physiological and evolutionary perspectives. We developed a method for extracting spatial vein pattern data from leaf images, such as vein densities and also the sizes and shapes of the vein reticulations. We used this method to quantify leaf venation patterns of the first rosette leaf of Arabidopsis thaliana throughout a series of developmental stages. In particular, we characterized the size and shape of vein network areoles (loops), which enlarge and are split by new veins as a leaf develops. Pattern parameters varied in time and space. In particular, we observed a distal to proximal gradient in loop shape (length/width ratio) which varied over time, and a margin-to-center gradient in loop sizes. Quantitative analyses of vein patterns at the tissue level provide a two-way link between theoretical models of patterning and molecular experimental work to further explore patterning mechanisms during development. Such analyses could also be used to investigate the effect of environmental factors on vein patterns, or to compare venation patterns from different species for evolutionary studies. The method also provides a framework for gathering and overlaying two-dimensional maps of point, line and surface morphological data.

  19. Tunable states of interlayer cations in two-dimensional materials

    Energy Technology Data Exchange (ETDEWEB)

    Sato, K.; Numata, K. [Department of Environmental Sciences, Tokyo Gakugei University, Koganei, Tokyo 184-8501 (Japan); Dai, W. [Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), College of Chemistry, Nankai University, Tianjin 300071 (China); Hunger, M. [Institute of Chemical Technology, University of Stuttgart, 70550 Stuttgart (Germany)

    2014-03-31

    The local state of cations inside the Ångstrom-scale interlayer spaces is one of the controlling factors for designing sophisticated two-dimensional (2D) materials consisting of 2D nanosheets. In the present work, the molecular mechanism on how the interlayer cation states are induced by the local structures of the 2D nanosheets is highlighted. For this purpose, the local states of Na cations in inorganic 2D materials, in which the compositional fluctuations of a few percent are introduced in the tetrahedral and octahedral units of the 2D nanosheets, were systematically studied by means of {sup 23}Na magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) and {sup 23}Na multiple-quantum MAS (MQMAS) NMR spectroscopy. In contrast with an uniform distribution of Na cations expected so far, various well-defined cation states sensitive to the local structures of the 2D nanosheets were identified. The tunability of the interlayer cation states along with the local structure of the 2D nanosheets, as the smallest structural unit of the 2D material, is discussed.

  20. Two-dimensional investigation of forced bubble oscillation under microgravity

    Institute of Scientific and Technical Information of China (English)

    HONG Ruoyu; Masahiro KAWAJI

    2003-01-01

    Recent referential studies of fluid interfaces subjected to small vibration under microgravity conditions are reviewed. An experimental investigation was carried out aboard the American Space Shuttle Discovery. Two-dimensional (2-D) modeling and simulation were conducted to further understand the experimental results. The oscillation of a bubble in fluid under surface tension is governed by the incompressible Navier-Stokes equations. The SIMPLEC algorithm was used to solve the partial differential equations on an Eulerian mesh in a 2-D coordinate. Free surfaces were represented with the volume of fluid (VOF) obtained by solving a kinematic equation. Surface tension was modeled via a continuous surface force (CSF) algorithm that ensures robustness and accuracy. A new surface reconstruction scheme, alternative phase integration (API) scheme, was adopted to solve the kinematic equation, and was compared with referential schemes. Numerical computations were conducted to simulate the transient behavior of an oscillating gas bubble in mineral oil under different conditions. The bubble positions and shapes under different external vibrations were obtained numerically. The computed bubble oscillation amplitudes were compared with experimental data.