Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
Dynamics of infinite-dimensional groups the Ramsey-Dvoretzky-Milman phenomenon
Pestov, Vladimir
2006-01-01
The "infinite-dimensional groups" in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of transformations of measure spaces, etc. The book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups, combinatorial Ramsey-type theorems, and the phenomenon of concentration of measure. The dynamics of infinite-dimensional groups is very much unlike that of locally compact groups. For instance, every locally compact group acts freely on a suitable compact space (Veech). By contrast, a 1983 result by Gromov and Milman states that whenever the unitary group of a separable Hilbert space continuously acts on a compact space, it has a common fixed point. In the book, this new fast-growing theory is built strictly from well-understood examples up. The book has no close counterpart and is based on recent research articles. At t...
The Lagrangian and Hamiltonian Analysis of Integrable Infinite-Dimensional Dynamical Systems
International Nuclear Information System (INIS)
Bogolubov, Nikolai N. Jr.; Prykarpatsky, Yarema A.; Blackmorte, Denis; Prykarpatsky, Anatoliy K.
2010-12-01
The analytical description of Lagrangian and Hamiltonian formalisms naturally arising from the invariance structure of given nonlinear dynamical systems on the infinite- dimensional functional manifold is presented. The basic ideas used to formulate the canonical symplectic structure are borrowed from the Cartan's theory of differential systems on associated jet-manifolds. The symmetry structure reduced on the invariant submanifolds of critical points of some nonlocal Euler-Lagrange functional is described thoroughly for both differential and differential-discrete dynamical systems. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integral-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Backlund transformation. The connection of this hierarchy with integrable by Lax spatially two-dimensional systems is studied. (author)
International Nuclear Information System (INIS)
Arsen'ev, A.A.
1979-01-01
Example of a classical dynamical system with the infinite-dimensional phase space, satisfying the analogue of the Kubo-Martin-Schwinger conditions for classical dynamics, is constructed explicitly. Connection between the system constructed and the Fock space dynamics is pointed out
Weakly infinite-dimensional spaces
International Nuclear Information System (INIS)
Fedorchuk, Vitalii V
2007-01-01
In this survey article two new classes of spaces are considered: m-C-spaces and w-m-C-spaces, m=2,3,...,∞. They are intermediate between the class of weakly infinite-dimensional spaces in the Alexandroff sense and the class of C-spaces. The classes of 2-C-spaces and w-2-C-spaces coincide with the class of weakly infinite-dimensional spaces, while the compact ∞-C-spaces are exactly the C-compact spaces of Haver. The main results of the theory of weakly infinite-dimensional spaces, including classification via transfinite Lebesgue dimensions and Luzin-Sierpinsky indices, extend to these new classes of spaces. Weak m-C-spaces are characterised by means of essential maps to Henderson's m-compacta. The existence of hereditarily m-strongly infinite-dimensional spaces is proved.
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Analysis of infinite dimensional diffusions
Maas, J.
2009-01-01
Stochastic processes in infinite dimensional state spaces provide a mathematical description of various phenomena in physics, population biology, finance, and other fields of science. Several aspects of these processes have been studied in this thesis by means of new analytic methods. Firstly,
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Teleportation schemes in infinite dimensional Hilbert spaces
International Nuclear Information System (INIS)
Fichtner, Karl-Heinz; Freudenberg, Wolfgang; Ohya, Masanori
2005-01-01
The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
Smooth controllability of infinite-dimensional quantum-mechanical systems
International Nuclear Information System (INIS)
Wu, Re-Bing; Tarn, Tzyh-Jong; Li, Chun-Wen
2006-01-01
Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies
Infinite Dimensional Differential Games with Hybrid Controls
Indian Academy of Sciences (India)
... zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the ...
Fractional supersymmetry and infinite dimensional lie algebras
International Nuclear Information System (INIS)
Rausch de Traubenberg, M.
2001-01-01
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed
On infinite-dimensional state spaces
International Nuclear Information System (INIS)
Fritz, Tobias
2013-01-01
It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V −1 U 2 V=U 3 , then finite-dimensionality entails the relation UV −1 UV=V −1 UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V −1 U 2 V=U 3 holds only up to ε and then yields a lower bound on the dimension.
On infinite-dimensional state spaces
Fritz, Tobias
2013-05-01
It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.
Two dimensional infinite conformal symmetry
International Nuclear Information System (INIS)
Mohanta, N.N.; Tripathy, K.C.
1993-01-01
The invariant discontinuous (discrete) conformal transformation groups, namely the Kleinian and Fuchsian groups Gamma (with an arbitrary signature) of H (the Poincare upper half-plane l) and the unit disc Delta are explicitly constructed from the fundamental domain D. The Riemann surface with signatures of Gamma and conformally invariant automorphic forms (functions) with Peterson scalar product are discussed. The functor, where the category of complex Hilbert spaces spanned by the space of cusp forms constitutes the two dimensional conformal field theory. (Author) 7 refs
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
Recursive tridiagonalization of infinite dimensional Hamiltonians
International Nuclear Information System (INIS)
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
Infinite dimensional groups and algebras in quantum physics
International Nuclear Information System (INIS)
Ottesen, J.T.
1995-01-01
This book is an introduction to the application of infite-dimensional groups and algebras in quantum physics. Especially considered are the spin representation of the infinite-dimensional orthogonal group, the metaplectic representation of the infinite-dimensional symplectic groups, and Loop and Virasoro algebras. (HSI)
One-dimensional gravity in infinite point distributions
Gabrielli, A.; Joyce, M.; Sicard, F.
2009-10-01
The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by “Jeans swindle” for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from “shuffled lattice” initial conditions. These show qualitative properties of the evolution (notably its “self-similarity”) like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.; Nurbekyan, Levon
2016-01-01
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.
2016-08-31
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables\\' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
Evolutionary dynamics on infinite strategy spaces
Oechssler, Jörg; Riedel, Frank
1998-01-01
The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications ...
Analysis of competitive equilibrium in an infinite dimensional ...
African Journals Online (AJOL)
This paper considered the cost of allocated goods and attaining maximal utility with such price in the finite dimensional commodity space and observed that there exist an equilibrium price. It goes further to establish that in an infinite dimensional commodity space with subsets as consumption and production set there exist a ...
Infinite dimensional differential games with hybrid controls
Indian Academy of Sciences (India)
The study of differential games with Elliott–Kalton strategies in the viscosity solution ... studied by Yong [6, 7]. ... Section 3 is devoted to the proof of the main uniqueness result for SQVI and the existence ...... Moreover, we have given explicit formulation of dynamic programming ... Financial support from NBHM is gratefully.
Lyapunov equation for infinite-dimensional discrete bilinear systems
International Nuclear Information System (INIS)
Costa, O.L.V.; Kubrusly, C.S.
1991-03-01
Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)
Infinite-dimensional Z2sup(k)-supermanifolds
International Nuclear Information System (INIS)
Molotkov, V.
1984-10-01
In this paper the theory of finite-dimensional supermanifolds of Berezin, Leites and Kostant is generalized in two directions. First, we introduce infinite-dimensional supermanifolds ''locally isomorphic'' to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassman superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex). As examples, flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces are constructed. Second, we define ''generalized'' supermanifolds, graded by Abelian groups Z 2 sup(k), instead of the group Z 2 (Z 2 sup(k)-supermanifolds). The corresponding superfields, describing, potentially, particles with more general statistics than Bose + Fermi, generally speaking, turn out to have an infinite number of components. (author)
Hilbert schemes of points and infinite dimensional Lie algebras
Qin, Zhenbo
2018-01-01
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes X^{[n]} of collections of n points (zero-dimensional subschemes) in a smooth algebraic surface X. Schemes X^{[n]} turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of X^{[n]}, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of X^{[n]} a...
An infinite-dimensional model of free convection
Energy Technology Data Exchange (ETDEWEB)
Iudovich, V.I. (Rostovskii Gosudarstvennyi Universitet, Rostov-on-Don (USSR))
1990-12-01
An infinite-dimensional model is derived from the equations of free convection in the Boussinesq-Oberbeck approximation. The velocity field is approximated by a single mode, while the heat-conduction equation is conserved fully. It is shown that, for all supercritical Rayleigh numbers, there exist exactly two secondary convective regimes. The case of ideal convection with zero viscosity and thermal conductivity is examined. The averaging method is used to study convection regimes at high Reynolds numbers. 10 refs.
An infinite-dimensional calculus for gauge theories
Mendes, Rui Vilela
2010-01-01
A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior ...
International Nuclear Information System (INIS)
Liu Guan-Ting; Yang Li-Ying
2017-01-01
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal. (paper)
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Symbolic Dynamics, Flower Automata and Infinite Traces
Foryś, Wit; Oprocha, Piotr; Bakalarski, Slawomir
Considering a finite alphabet as a set of allowed instructions, we can identify finite words with basic actions or programs. Hence infinite paths on a flower automaton can represent order in which these programs are executed and a flower shift related with it represents list of instructions to be executed at some mid-point of the computation.
New infinite-dimensional hidden symmetries for heterotic string theory
International Nuclear Information System (INIS)
Gao Yajun
2007-01-01
The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected
Stochastic optimal control in infinite dimension dynamic programming and HJB equations
Fabbri, Giorgio; Święch, Andrzej
2017-01-01
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...
Eisenstein series for infinite-dimensional U-duality groups
Fleig, Philipp; Kleinschmidt, Axel
2012-06-01
We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.
Riemann surfaces, Clifford algebras and infinite dimensional groups
International Nuclear Information System (INIS)
Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.
1990-01-01
We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)
Rare event simulation in finite-infinite dimensional space
International Nuclear Information System (INIS)
Au, Siu-Kui; Patelli, Edoardo
2016-01-01
Modern engineering systems are becoming increasingly complex. Assessing their risk by simulation is intimately related to the efficient generation of rare failure events. Subset Simulation is an advanced Monte Carlo method for risk assessment and it has been applied in different disciplines. Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial. Conventionally an independent-component Markov Chain Monte Carlo (MCMC) algorithm is used, which is applicable to high dimensional problems (i.e., a large number of random variables) without suffering from ‘curse of dimension’. Experience suggests that the algorithm may perform even better for high dimensional problems. Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of ‘hidden’ variables. We study analytically the limiting behavior of the algorithm as the number of hidden variables increases indefinitely. This leads to a new algorithm that is more generic and offers greater flexibility and control. It coincides with an algorithm recently suggested by independent researchers, where a joint Gaussian distribution is imposed between the current sample and the candidate. The present work provides theoretical reasoning and insights into the algorithm.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
Infinite-Dimensional Boundary Observer for Lithium-Ion Battery State Estimation
DEFF Research Database (Denmark)
Hasan, Agus; Jouffroy, Jerome
2017-01-01
This paper presents boundary observer design for state-of-charge (SOC) estimation of lithium-ion batteries. The lithium-ion battery dynamics are governed by thermal-electrochemical principles, which mathematically modeled by partial differential equations (PDEs). In general, the model is a reaction......-diffusion equation with time-dependent coefficients. A Luenberger observer is developed using infinite-dimensional backstepping method and uses only a single measurement at the boundary of the battery. The observer gains are computed by solving the observer kernel equation. A numerical example is performed to show...
International Nuclear Information System (INIS)
Xu Hao; Shi Tianjun
2011-01-01
In this article,the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one-dimensional infinite potential well and one-dimensional harmonic oscillator, and then the particular Wigner function of one-dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which,simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one-dimensional infinite potential well and one-dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. (authors)
Energy Dynamics of an Infinitely Large Offshore Wind Farm
DEFF Research Database (Denmark)
Frandsen, Sten Tronæs; Barthelmie, R.J.; Pryor, S.C.
, particularly in the near-term, can be expected in the higher resource, moderate water depths of the North Sea rather than the Mediterranean. There should therefore be significant interest in understanding the energy dynamics of the infinitely large wind farm – how wakes behave and whether the extraction...... of energy by wind turbines over a large area has a significant and lasting impact on the atmospheric boundary layer. Here we focus on developing understanding of the infinite wind farm through a combination of theoretical considerations, data analysis and modeling. Initial evaluation of power losses due...... is of about the same magnitude as for the infinitely large wind farm. We will examine whether this can be proved theoretically or is indicated by data currently available. We will also evaluate whether energy extraction at the likely scale of development in European Seas can be expected to modulate...
On the BRST charge over infinite-dimensional algebras
International Nuclear Information System (INIS)
Hlousek, Zvonimir.
1988-01-01
The author studies the BRST charge defined over an infinite algebra of gauged local symmetries. This is of great importance to string theories. The BRST charge of the gauge symmetry must be nilpotent. In string theories this implies the cancellation of conformal anomalies in critical dimension; 26 for bosonic string, 10 for superstring, and 2 for O(2) string. Furthermore, the O(2) symmetry of the O(2) string (a string theory with two, two-dimensional supersymmetries) is realized as a Kac-Moody symmetry. In general, the BRST quantization of the local, gauged KAC-Moody symmetry requires special care due to chiral anomaly. The chiral anomaly breaks the chiral gauge invariance, and the corresponding BRST charge is not nilpotent. To arrive at the nilpotent BRST charge for the gauged Kac-Moody symmetry, one has to modify the theory by adding a one-cocycle over the gauge group. A similar problem and its solution exist in the case of supersymmetric Kac-Moody algebras. The BRST charge of the first quantized string theory is a building block of the covariant string field theory. The BRST invariance of the first quantized theory generalizes to gauge invariance of string field theory. In Witten's open string field theory the BRST charge plays a role of exterior derivation on the space of string field functionals. The Fock space realization of the theory was given by Gross and Jevicki. For the consistency of the theory it is crucial that all the vertex operators are BRST invariant. The ghost part of the vertex comes in few varieties. The author has shown that all the versions of the ghost vertex are equivalent, as long as the total vertex is BRST invariant
Infinite dimensional gauge structure of Kaluza-Klein theories II: D>5
International Nuclear Information System (INIS)
Aulakh, C.S.; Sahdev, D.
1985-12-01
We carry out the dimensional reduction of the pure gravity sector of Kaluza Klein theories without making truncations of any sort. This generalizes our previous result for the 5-dimensional case to 4+d(>1) dimensions. The effective 4-dimensional action has the structure of an infinite dimensional gauge theory
International Nuclear Information System (INIS)
Guatteri, Giuseppina; Tessitore, Gianmario
2008-01-01
We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random.In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed
Infinite Dimensional Stochastic Analysis : in Honor of Hui-Hsiung Kuo
Sundar, Pushpa
2008-01-01
This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate
Energy Technology Data Exchange (ETDEWEB)
Vubangsi, M.; Tchoffo, M.; Fai, L. C. [Mesoscopic and Multilayer Structures Laboratory, Physics Department, University of Dschang, P.O. Box 417 Dschang (Cameroon); Pisma’k, Yu. M. [Department of Theoretical Physics, Saint Petersburg State University, Saint Petersburg (Russian Federation)
2015-12-15
The problem of a particle with position and time-dependent effective mass in a one-dimensional infinite square well is treated by means of a quantum canonical formalism. The dynamics of a launched wave packet of the system reveals a peculiar revival pattern that is discussed. .
To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space
International Nuclear Information System (INIS)
Khrennikov, Andrei
2007-01-01
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
Belitser, E.; Ghosal, S.
2003-01-01
We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a "smoothness condition," we first derive the convergence rate of the posterior distribution for a prior that
Renner, R; Cirac, J I
2009-03-20
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
The Analysis of Corporate Bond Valuation under an Infinite Dimensional Compound Poisson Framework
Directory of Open Access Journals (Sweden)
Sheng Fan
2014-01-01
Full Text Available This paper analyzes the firm bond valuation and credit spread with an endogenous model for the pure default and callable default corporate bond. Regarding the stochastic instantaneous forward rates and the firm value as an infinite dimensional Poisson process, we provide some analytical results for the embedded American options and firm bond valuations.
Classification of all solutions of the algebraic Riccati equations for infinite-dimensional systems
Iftime, O; Curtain, R; Zwart, H
2003-01-01
We obtain a complete classification of all self-adjoint solution of the control algebraic Riccati equation for infinite-dimensional systems under the following assumptions: the system is output stabilizable, strongly detectable and the filter Riccati equation has an invertible self-adjoint
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Logemann, H; Curtain, RF
2000-01-01
We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator
Infinite Dimensional Dynamical Systems and their Finite Dimensional Analogues.
1987-01-01
Rolla ____t___e ___o, __.Paul Steen Cornell Univ.Andrew Szeri Cornell Univ. ByEdriss Titi Univ. of Chicago _Distributi-on/ -S. Tsaltas Unvcrsity of...Cornell University Ithaca, NY 14853 Edriss Titi University of Chicago Dept. of Mathematics 5734 S. University Ave.Chicago, IL 60637 Spiros Tsaltas Dept
Multiscale implementation of infinite-swap replica exchange molecular dynamics.
Yu, Tang-Qing; Lu, Jianfeng; Abrams, Cameron F; Vanden-Eijnden, Eric
2016-10-18
Replica exchange molecular dynamics (REMD) is a popular method to accelerate conformational sampling of complex molecular systems. The idea is to run several replicas of the system in parallel at different temperatures that are swapped periodically. These swaps are typically attempted every few MD steps and accepted or rejected according to a Metropolis-Hastings criterion. This guarantees that the joint distribution of the composite system of replicas is the normalized sum of the symmetrized product of the canonical distributions of these replicas at the different temperatures. Here we propose a different implementation of REMD in which (i) the swaps obey a continuous-time Markov jump process implemented via Gillespie's stochastic simulation algorithm (SSA), which also samples exactly the aforementioned joint distribution and has the advantage of being rejection free, and (ii) this REMD-SSA is combined with the heterogeneous multiscale method to accelerate the rate of the swaps and reach the so-called infinite-swap limit that is known to optimize sampling efficiency. The method is easy to implement and can be trivially parallelized. Here we illustrate its accuracy and efficiency on the examples of alanine dipeptide in vacuum and C-terminal β-hairpin of protein G in explicit solvent. In this latter example, our results indicate that the landscape of the protein is a triple funnel with two folded structures and one misfolded structure that are stabilized by H-bonds.
Nambu, Y.
1967-01-01
The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
International Nuclear Information System (INIS)
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-01-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Energy Technology Data Exchange (ETDEWEB)
Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)
2016-03-15
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems
International Nuclear Information System (INIS)
Helin, T; Burger, M
2015-01-01
A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic and difficult to analyse. Current inverse problem literature often approaches the problem by considering suitable point estimators for the task. Typically the choice is made between the maximum a posteriori (MAP) or the conditional mean (CM) estimate. The benefits of either choice are not well-understood from the perspective of infinite-dimensional theory. Most importantly, there exists no general scheme regarding how to connect the topological description of a MAP estimate to a variational problem. The recent results by Dashti and others (Dashti et al 2013 Inverse Problems 29 095017) resolve this issue for nonlinear inverse problems in Gaussian framework. In this work we improve the current understanding by introducing a novel concept called the weak MAP (wMAP) estimate. We show that any MAP estimate in the sense of Dashti et al (2013 Inverse Problems 29 095017) is a wMAP estimate and, moreover, how the wMAP estimate connects to a variational formulation in general infinite-dimensional non-Gaussian problems. The variational formulation enables to study many properties of the infinite-dimensional MAP estimate that were earlier impossible to study. In a recent work by the authors (Burger and Lucka 2014 Maximum a posteriori estimates in linear inverse problems with logconcave priors are proper bayes estimators preprint) the MAP estimator was studied in the context of the Bayes cost method. Using Bregman distances, proper convex Bayes cost functions were introduced for which the MAP estimator is the Bayes estimator. Here, we generalize these results to the infinite-dimensional setting. Moreover, we discuss the implications of our results for some examples of prior models such as the Besov prior and hierarchical prior. (paper)
Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations
International Nuclear Information System (INIS)
Yuen, Manwai
2011-01-01
In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu → =0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. -- Highlights: → We construct a new class of solutions to the 3D compressible or incompressible Euler and Navier-Stokes equations. → The constructed solutions are similar to the famous Arnold-Beltrami-Childress flow. → The solutions with infinite energy can exhibit the interesting behaviors locally.
Infinite-Dimensional Observer for Process Monitoring in Managed Pressure Drilling
Hasan, Agus Ismail
2015-01-01
Utilizing flow rate and pressure data in and out of the mud circulation loop provides a driller with real-time trends for the early detection of well-control problems that impact the drilling efficiency. This paper presents state estimation for infinite-dimensional systems used in the process monitoring of oil well drilling. The objective is to monitor the key process variables associated with process safety by designing a model-based nonlinear observer that directly utilizes the available in...
Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process
International Nuclear Information System (INIS)
Maslowski, Bohdan; Pospisil, Jan
2008-01-01
Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise
Dynamics with infinitely many derivatives: variable coefficient equations
International Nuclear Information System (INIS)
Barnaby, Neil; Kamran, Niky
2008-01-01
Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also from cosmologists. Crucial to any application is a firm understanding of the mathematical structure of infinite order partial differential equations. In our previous work we developed a formalism to study the initial value problem for linear infinite order equations with constant coefficients. Our approach relied on the use of a contour integral representation for the functions under consideration. In many applications, including the study of cosmological perturbations in nonlocal inflation, one must solve linearized partial differential equations about some time-dependent background. This typically leads to variable coefficient equations, in which case the contour integral methods employed previously become inappropriate. In this paper we develop the theory of a particular class of linear infinite order partial differential equations with variable coefficients. Our formalism is particularly well suited to the types of equations that arise in nonlocal cosmological perturbation theory. As an example to illustrate our formalism we compute the leading corrections to the scalar field perturbations in p-adic inflation and show explicitly that these are small on large scales.
On an infinite-dimensional Lie algebra of Virasoro-type
International Nuclear Information System (INIS)
Pei Yufeng; Bai Chengming
2012-01-01
In this paper, we study an infinite-dimensional Lie algebra of Virasoro-type which is realized as an affinization of a two-dimensional Novikov algebra. It is a special deformation of the Lie algebra of differential operators on a circle of order at most 1. There is an explicit construction of a vertex algebra associated with the Lie algebra. We determine all derivations of this Lie algebra in terms of some derivations and centroids of the corresponding Novikov algebra. The universal central extension of this Lie algebra is also determined. (paper)
The w-categories associated with products of infinite-dimensional globes
International Nuclear Information System (INIS)
Cui, H.
2000-11-01
The results in this thesis are organised in four chapters. Chapter 1 is preliminary. We state the necessary definitions and results in w- complexes, atomic complexes and products of w-complexes. Some definitions are restated to meet the requirement for the following chapters. There is a new proof for the existence of 'natural homomorphism' (Theorem 1.3.6) and a new result for the decomposition of molecules in loop-free w-complexes (Theorem 1.4.13). In Chapter 2, we study the product of three infinite dimensional globes. The main result in this chapter is that a subcomplex in the product of three infinite dimensional globes is a molecule if and only if it is pairwise molecular (Theorem 2.1.6). The definition for pairwise molecular subcomplexes is given in section 1. One direction of the main theorem, molecules are necessarily pairwise molecular, is proved in section 2. Some properties of pairwise molecular subcomplexes are studied in section 3. These properties are the preparation for a more explicit description of pairwise molecular subcomplexes, which is given in section 4. The properties for the sources and targets of pairwise molecular subcomplexes are studied in section 5, where we prove that the class of pairwise molecular subcomplexes is closed under source and target operation; there are also algorithms to calculate the sources and targets of a pairwise molecular subcomplex. Section 6 deals with the composition of pairwise molecular subcomplexes. The proof of the main theorem is completed in section 7, where an algorithm for decomposing molecules into atoms is implied in the proof. The construction of molecules in the product of three infinite dimensional globes is studied in Chapter 3. The main result is that any molecule can be constructed inductively by a systematic approach. Section 1 gives another description for molecules in the product of three infinite dimensional globes which is the theoretical basis for the construction. Section 2 states the
Belkhatir, Zehor; Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem
2016-01-01
This paper deals with joint parameters and input estimation for coupled PDE-ODE system. The system consists of a damped wave equation and an infinite dimensional ODE. This model describes the spatiotemporal hemodynamic response in the brain
Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping
Lu, Jianfeng; Zhou, Zhennan
2018-02-01
To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.
Group theoretical construction of two-dimensional models with infinite sets of conservation laws
International Nuclear Information System (INIS)
D'Auria, R.; Regge, T.; Sciuto, S.
1980-01-01
We explicitly construct some classes of field theoretical 2-dimensional models associated with symmetric spaces G/H according to a general scheme proposed in an earlier paper. We treat the SO(n + 1)/SO(n) and SU(n + 1)/U(n) case, giving their relationship with the O(n) sigma-models and the CP(n) models. Moreover, we present a new class of models associated to the SU(n)/SO(n) case. All these models are shown to possess an infinite set of local conservation laws. (orig.)
Morozov, Oleg I.
2018-06-01
The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.
Classical r-matrices and Poisson bracket structures on infinite-dimensional groups
International Nuclear Information System (INIS)
Aratyn, H.; Nissimov, E.; Pacheva, S.
1992-01-01
Starting with a canonical symplectic structure defined on the contangent bundle T * G we derive, via Dirac hamiltonian reduction, Poisson brackets (PBs) on an arbitrary infinite-dimensional group G (admitting central extension). The PB structures are given in terms of an r-operator kernel related to the two-cocycle of the underlying Lie algebra and satisfying a differential classical Yang-Baxter equation. The explicit expressions of the PBs among the group variables for the (N, 0) for N=0, 1, ..., 4 (super-) Virasoro groups and the group of area-preserving diffeomorphisms on the torus are presented. (orig.)
On the infinite-dimensional spin-2 symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Hohm, O.; Hamburg Univ.
2005-11-01
We consider the couplings of an infinite number of spin-2 fields to gravity appearing in Kaluza-Klein theories. They are constructed as the broken phase of a massless theory possessing an infinite-dimensional spin-2 symmetry. Focusing on a circle compactification of four-dimensional gravity we show that the resulting gravity/spin-2 system in D=3 has in its unbroken phase an interpretation as a Chern-Simons theory of the Kac-Moody algebra iso(1,2) associated to the Poincare group and also fits into the geometrical framework of algebra-valued differential geometry developed by Wald. Assigning all degrees of freedom to scalar fields, the matter couplings in the unbroken phase are determined, and it is shown that their global symmetry algebra contains the Virasoro algebra together with an enhancement of the Ehlers group SL(2,R) to its affine extension. The broken phase is then constructed by gauging a subgroup of the global symmetries. It is shown that metric, spin-2 fields and Kaluza-Klein vectors combine into a Chern-Simons theory for an extended algebra, in which the affine Poincare subalgebra acquires a central extension. (orig.)
An infinite number of stationary soliton solutions to the five-dimensional vacuum Einstein equation
International Nuclear Information System (INIS)
Azuma, Takahiro; Koikawa, Takao
2006-01-01
We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2, 0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2, 2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical. (author)
Estimation Methods for Infinite-Dimensional Systems Applied to the Hemodynamic Response in the Brain
Belkhatir, Zehor
2018-05-01
Infinite-Dimensional Systems (IDSs) which have been made possible by recent advances in mathematical and computational tools can be used to model complex real phenomena. However, due to physical, economic, or stringent non-invasive constraints on real systems, the underlying characteristics for mathematical models in general (and IDSs in particular) are often missing or subject to uncertainty. Therefore, developing efficient estimation techniques to extract missing pieces of information from available measurements is essential. The human brain is an example of IDSs with severe constraints on information collection from controlled experiments and invasive sensors. Investigating the intriguing modeling potential of the brain is, in fact, the main motivation for this work. Here, we will characterize the hemodynamic behavior of the brain using functional magnetic resonance imaging data. In this regard, we propose efficient estimation methods for two classes of IDSs, namely Partial Differential Equations (PDEs) and Fractional Differential Equations (FDEs). This work is divided into two parts. The first part addresses the joint estimation problem of the state, parameters, and input for a coupled second-order hyperbolic PDE and an infinite-dimensional ordinary differential equation using sampled-in-space measurements. Two estimation techniques are proposed: a Kalman-based algorithm that relies on a reduced finite-dimensional model of the IDS, and an infinite-dimensional adaptive estimator whose convergence proof is based on the Lyapunov approach. We study and discuss the identifiability of the unknown variables for both cases. The second part contributes to the development of estimation methods for FDEs where major challenges arise in estimating fractional differentiation orders and non-smooth pointwise inputs. First, we propose a fractional high-order sliding mode observer to jointly estimate the pseudo-state and input of commensurate FDEs. Second, we propose a
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-10-01
The irreducible Racah basis for SU(N + 1|N) is introduced. An analytic continuation with respect to N leads to infinite-dimensional superalgebras su(υ + 1|υ). Large υ limit su(∞ + 1|∞) is calculated. The higher spin Sugawara construction leading to generalizations of the Virasoro algebra with infinite tower of higher spin currents is proposed and related WZNW and Toda models as well as possible applications in string theory are discussed. (author). 32 refs
Stiffness and Mass Matrices of FEM-Applicable Dynamic Infinite Element with Unified Shape Basis
International Nuclear Information System (INIS)
Kazakov, Konstantin
2009-01-01
This paper is devoted to the construction and evaluation of mass and stiffness matrices of elastodynamic four and five node infinite elements with unified shape functions (EIEUSF), recently proposed by the author. Such elements can be treated as a family of elastodynamic infinite elements appropriate for multi-wave soil-structure interaction problems. The common characteristic of the proposed infinite elements is the so-called unified shape function, based on finite number of wave shape functions. The idea and the construction of the unified shape basis are described in brief. This element belongs to the decay class of infinite elements. It is shown that by appropriate mapping functions the formulation of such an element can be easily transformed to a mapped form. The results obtained using the proposed infinite elements are in a good agreement with the superposed results obtained by a series of standard computational models. The continuity along the finite/infinite element line (artificial boundary) in two-dimensional substructure models is also discussed in brief. In this type of computational models such a line marks the artificial boundary between the near and the far field of the model.
Infinite-dimensional Lie algebras in 4D conformal quantum field theory
International Nuclear Information System (INIS)
Bakalov, Bojko; Nikolov, Nikolay M; Rehren, Karl-Henning; Todorov, Ivan
2008-01-01
The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of two-dimensional chiral conformal field theory, to a higher (even) dimensional spacetime. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V M (x, y), where the M span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite-dimensional Lie algebra: a central extension of sp(∞,R) corresponding to the field R of reals, of u(∞, ∞) associated with the field C of complex numbers, and of so*(4∞) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N) and U(N,H)=Sp(2N), respectively
Heyl, Markus; Vojta, Matthias
2015-09-01
In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.
Limitations of discrete-time quantum walk on a one-dimensional infinite chain
Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun
2018-04-01
How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form eiξ A ⊗1p, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form eiξ A ⊗1p. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σx.
International Nuclear Information System (INIS)
Ton-That, Tuong
2005-01-01
In a previous paper we gave a generalization of the notion of Casimir invariant differential operators for the infinite-dimensional Lie groups GL ∞ (C) (or equivalently, for its Lie algebra gj ∞ (C)). In this paper we give a generalization of the Casimir invariant differential operators for a class of infinite-dimensional Lie groups (or equivalently, for their Lie algebras) which contains the infinite-dimensional complex classical groups. These infinite-dimensional Lie groups, and their Lie algebras, are inductive limits of finite-dimensional Lie groups, and their Lie algebras, with some additional properties. These groups or their Lie algebras act via the generalized adjoint representations on projective limits of certain chains of vector spaces of universal enveloping algebras. Then the generalized Casimir operators are the invariants of the generalized adjoint representations. In order to be able to explicitly compute the Casimir operators one needs a basis for the universal enveloping algebra of a Lie algebra. The Poincare-Birkhoff-Witt (PBW) theorem gives an explicit construction of such a basis. Thus in the first part of this paper we give a generalization of the PBW theorem for inductive limits of Lie algebras. In the last part of this paper a generalization of the very important theorem in representation theory, namely the Chevalley-Racah theorem, is also discussed
International Nuclear Information System (INIS)
Porteus, E.
1982-01-01
The study of infinite-horizon nonstationary dynamic programs using the operator approach is continued. The point of view here differs slightly from that taken by others, in that Denardo's local income function is not used as a starting point. Infinite-horizon values are defined as limits of finite-horizon values, as the horizons get long. Two important conditions of an earlier paper are weakened, yet the optimality equations, the optimality criterion, and the existence of optimal ''structured'' strategies are still obtained
International Nuclear Information System (INIS)
Gonchar, N.S.
1986-01-01
This paper presents a mathematical method developed for investigating a class of systems of infinite-dimensional integral equations which have application in statistical mechanics. Necessary and sufficient conditions are obtained for the uniqueness and bifurcation of the solution of this class of systems of equations. Problems of equilibrium statistical mechanics are considered on the basis of this method
International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
Tutschke, W; Yang, C
2004-01-01
There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took place in Hanoi from August 8 - 12, 2001. This conference th was the 9 one in a series of conferences which take place alternately in China, Japan, Korea and Vietnam each year. The first one took place th at Pusan University in Korea in 1993. The preceding 8 conference was th held in Shandong in China in August 2000. The 9 conference of the was the first one which took place above mentioned series of conferences in Vietnam....
Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.
2018-04-01
This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.
Cumulative quantum work-deficit versus entanglement in the dynamics of an infinite spin chain
Energy Technology Data Exchange (ETDEWEB)
Dhar, Himadri Shekhar [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Ghosh, Rupamanjari [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); School of Natural Sciences, Shiv Nadar University, Gautam Budh Nagar, UP 203207 (India); Sen, Aditi [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019 (India); Sen, Ujjwal, E-mail: ujjwal@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019 (India)
2014-03-01
We find that the dynamical phase transition (DPT) in nearest-neighbor bipartite entanglement of time-evolved states of the anisotropic infinite quantum XY spin chain, in a transverse time-dependent magnetic field, can be quantitatively characterized by the dynamics of an information-theoretic quantum correlation measure, namely, quantum work-deficit (QWD). We show that only those nonequilibrium states exhibit entanglement resurrection after death, on changing the field parameter during the DPT, for which the cumulative bipartite QWD is above a threshold. The results point to an interesting inter-relation between two quantum correlation measures that are conceptualized from different perspectives.
Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2
International Nuclear Information System (INIS)
Babbitt, D.; Thomas, L.
1977-01-01
In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.) [de
International Nuclear Information System (INIS)
Li, P.D.; Li, X.Y.; Zheng, R.F.
2013-01-01
This Letter is concerned with thermo-elastic fundamental solutions of an infinite space, which is composed of two half-infinite bodies of different one-dimensional hexagonal quasi-crystals. A point thermal source is embedded in a half-space. The interface can be either perfectly bonded or smoothly contacted. On the basis of the newly developed general solution, the temperature-induced elastic field in full space is explicitly presented in terms of elementary functions. The interactions among the temperature, phonon and phason fields are revealed. The present work can play an important role in constructing farther analytical solutions for crack, inclusion and dislocation problems. -- Highlights: ► Green's functions are constructed in terms of 10 quasi-harmonic functions. ► Thermo-elastic field of a 1D hexagonal QC bi-material body is expressed explicitly. ► Both perfectly bonded and smoothly contacted interfaces are considered
DEFF Research Database (Denmark)
Domadiya, Parthkumar Gandalal; Manconi, Elisabetta; Vanali, Marcello
2016-01-01
Adding periodicity to structures leads to wavemode interaction, which generates pass- and stop-bands. The frequencies at which stop-bands occur are related to the periodic nature of the structure. Thus structural periodicity can be shaped in order to design vibro-acoustic filters for reducing...... method deals with the evaluation of a vibration level difference (VLD) in a finite periodic structure embedded within an infinite one-dimensional waveguide. This VLD is defined to predict the performance in terms of noise and vibration insulation of periodic cells embedded in an otherwise uniform...
Unitary representations of some infinite-dimensional Lie algebras motivated by string theory on AdS3
International Nuclear Information System (INIS)
Andreev, Oleg
1999-01-01
We consider some unitary representations of infinite-dimensional Lie algebras motivated by string theory on AdS 3 . These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS 3 exists
Belkhatir, Zehor
2016-08-05
This paper deals with joint parameters and input estimation for coupled PDE-ODE system. The system consists of a damped wave equation and an infinite dimensional ODE. This model describes the spatiotemporal hemodynamic response in the brain and the objective is to characterize brain regions using functional Magnetic Resonance Imaging (fMRI) data. For this reason, we propose an adaptive estimator and prove the asymptotic convergence of the state, the unknown input and the unknown parameters. The proof is based on a Lyapunov approach combined with a priori identifiability assumptions. The performance of the proposed observer is illustrated through some simulation results.
Validation of Infinite Impulse Response Multilayer Perceptron for Modelling Nuclear Dynamics
Directory of Open Access Journals (Sweden)
F. Cadini
2008-01-01
Full Text Available Artificial neural networks are powerful algorithms for constructing nonlinear empirical models from operational data. Their use is becoming increasingly popular in the complex modeling tasks required by diagnostic, safety, and control applications in complex technologies such as those employed in the nuclear industry. In this paper, the nonlinear modeling capabilities of an infinite impulse response multilayer perceptron (IIR-MLP for nuclear dynamics are considered in comparison to static modeling by a finite impulse response multilayer perceptron (FIR-MLP and a conventional static MLP. The comparison is made with respect to the nonlinear dynamics of a nuclear reactor as investigated by IIR-MLP in a previous paper. The superior performance of the locally recurrent scheme is demonstrated.
International Nuclear Information System (INIS)
Frese, M.F.
1991-01-01
This paper reports on computer simulations of the plasma flow in two-dimensionally symmetric railgun plasma arcs that were performed. The direction of symmetry is normal to the insulator surface, so that the rails are effectively infinite in width. The rail surface ablates according to one of two ablation models, in which either all absorbed energy flux, or only the excess over that which the rail material can conduct away, ablates mass. A number of combinations of initial conditions, boundary conditions and resistivity models were explored. The full ablation model produces an arc of continuously growing mass and length, in which the current distribution reaches from the projectile half-way to the breech. The conduction limited ablation model produces a compact arc approximately eight times the bore height in length, which ceases to ablate material from the rails before the projectile reaches a velocity of 1 km/s. There is need for further study in several areas. These include the arc initiation process, the ablation of the insulators, and three-dimensional effects
International Nuclear Information System (INIS)
De Santis, Emilio; Marinelli, Carlo
2007-01-01
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove 'fixation', i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-06-01
With any semisimple Lie algebra g we associate an infinite-dimensional Lie algebra AC(g) which is an analytic continuation of g from its root system to its root lattice. The manifest expressions for the structure constants of analytic continuations of the symplectic Lie algebras sp2 n are obtained by Poisson-bracket realizations method and AC(g) for g=sl n and so n are discussed. The representations, central extension, supersymmetric and higher spin generalizations are considered. The Virasoro theory is a particular case when g=sp 2 . (author). 9 refs
International Nuclear Information System (INIS)
Pal, Karoly F.; Vertesi, Tamas
2010-01-01
The I 3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I 3322 inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I 3322 inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.
Classical gauge theories on the coadjoint orbits of infinite dimensional groups
International Nuclear Information System (INIS)
Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung
1991-01-01
We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)
A Multiagent Cooperation Model Based on Trust Rating in Dynamic Infinite Interaction Environment
Directory of Open Access Journals (Sweden)
Sixia Fan
2018-01-01
Full Text Available To improve the liveness of agents and enhance trust and collaboration in multiagent system, a new cooperation model based on trust rating in dynamic infinite interaction environment (TR-DII is proposed. TR-DII model is used to control agent’s autonomy and selfishness and to make agent do the rational decision. TR-DII model is based on two important components. One is dynamic repeated interaction structure, and the other is trust rating. The dynamic repeated interaction structure is formed with multistage inviting and evaluating actions. It transforms agents’ interactions into an infinity task allocation environment, where controlled and renewable cycle is a component most agent models ignored. Additionally, it influences the expectations and behaviors of agents which may not appear in one-shot time but may appear in long-time cooperation. Moreover, with rewards and punishments mechanism (RPM, the trust rating (TR is proposed to control agent blindness in selection phase. However, RPM is the factor that directly influences decisions, not the reputation as other models have suggested. Meanwhile, TR could monitor agent’s statuses in which they could be trustworthy or untrustworthy. Also, it refines agent’s disrepute in a new way which is ignored by the others. Finally, grids puzzle experiment has been used to test TR-DII model and other five models are used as comparisons. The results show that TR-DII model can effectively adjust the trust level between agents and makes the solvers be more trustworthy and do choices that are more rational. Moreover, through interaction result feedback, TR-DII model could adjust the income function, to control cooperation reputation, and could achieve a closed-loop control.
Socolovsky, Eduardo A.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The cosine or correlation measures of similarity used to cluster high dimensional data are interpreted as projections, and the orthogonal components are used to define a complementary dissimilarity measure to form a similarity-dissimilarity measure pair. Using a geometrical approach, a number of properties of this pair is established. This approach is also extended to general inner-product spaces of any dimension. These properties include the triangle inequality for the defined dissimilarity measure, error estimates for the triangle inequality and bounds on both measures that can be obtained with a few floating-point operations from previously computed values of the measures. The bounds and error estimates for the similarity and dissimilarity measures can be used to reduce the computational complexity of clustering algorithms and enhance their scalability, and the triangle inequality allows the design of clustering algorithms for high dimensional distributed data.
An Integrated Approach to Parameter Learning in Infinite-Dimensional Space
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Wendelberger, Joanne Roth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-09-14
The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many user-set parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameter-space becomes highly non-trivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batch-parallel simulations, high-dimensional, derivative-free optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing user-guided, batch-parallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the time-varying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batch-parallelizable, random-walk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality of the problem using functional principal component analysis (fPCA), we are able to track the progress of the solver in a visually simple way as well as viewing the associated principle components. This allows a human to make reasonable guesses about which points in the state space the random walker should try next. Thus, by combining the random walker's ability to find descent directions with the human's understanding of the underlying physics, it is possible to use expensive simulations more efficiently and more quickly arrive at the
International Nuclear Information System (INIS)
Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio
1999-01-01
The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established
Infinite additional symmetries in the two-dimensional conformal quantum field theory
International Nuclear Information System (INIS)
Apikyan, S.A.
1987-01-01
Additional symmetries in the two-dimensional conformal field theory, generated by currents (2,3/2,5/2) and (2,3/2,3) have been studied. It has been shown that algebra (2,3/2,5/2) is the direct product of algebras (2,3/2) and (2,5/2), and algebra (2,3/2,3) is the direct product of algebras (2,3/2) and (2,3). Associative algebra, formed by multicomponent symmetry generators of spin 3 for SO(3) has also been found
Infinite additional symmetries in two-dimensional conformal quantum field theory
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1986-01-01
This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form associative algebras with quadratic determining relations. ''Minimal models'' of conforma field theory with such additional symmetries are considered. The space of local fields occurring in a conformal field theory with additional symmetry corresponds to a certain (in general, reducible) representation of the corresponding algebra of the symmetry
Wang, Lihua; Zeng, Yi; Shen, Aiguo; Zhou, Xiaodong; Hu, Jiming
2015-02-07
Novel three-dimensional (3D) nano-assemblies of noble metal nanoparticle (NP)-infinite coordination polymers (ICPs) are conveniently fabricated through the infiltration of HAuCl4 into hollow Au@Ag@ICPs core-shell nanostructures and its replacement reaction with Au@Ag NPs. The present 3D nano-assemblies exhibit highly efficient and specific intrinsic oxidase-like activity even without adding any cosubstrate.
Institute of Scientific and Technical Information of China (English)
Hua WANG; ALATANCANG; Junjie HUANG
2011-01-01
The authors investigate the completeness of the system of eigen or root vectors of the 2 x 2 upper triangular infinite-dimensional Hamiltonian operator H0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained. Finally,the obtained results are tested in several examples.
Wave function of an electron infinitely moving in the field of a one-dimensional layered structure
International Nuclear Information System (INIS)
Khachatrian, A.Zh.; Andreasyan, A.G.; Mgerian, G.G.; Badalyan, V.D.
2003-01-01
A method for finding the wave function of an electron infinitely moving in the field of an arbitrary layered structure bordered on both sides with two different semi infinite media is proposed. It is shown that this problem in the general form can be reduced to the solution of some system of linear finite-difference equations. The proposed approach is discussed in detail for the case of a periodic structure
International Nuclear Information System (INIS)
Elcoro, Luis; Etxebarria, Jesus
2011-01-01
The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used solid-state textbooks. Frequently, pair interaction is even considered to be the most general situation. In addition, it is shown that the demand of rotational invariance in an infinite crystal leads to inconsistencies in the symmetry of the elastic tensor. However, for finite crystals, no problems arise, and the Huang conditions are deduced using exclusively a microscopic approach for the elasticity theory, without making any reference to macroscopic parameters. This work may be useful in both undergraduate and graduate level courses to point out the crudeness of the pair-potential interaction and to explore the limits of the infinite-crystal approximation.
Infinite permutations vs. infinite words
Directory of Open Access Journals (Sweden)
Anna E. Frid
2011-08-01
Full Text Available I am going to compare well-known properties of infinite words with those of infinite permutations, a new object studied since middle 2000s. Basically, it was Sergey Avgustinovich who invented this notion, although in an early study by Davis et al. permutations appear in a very similar framework as early as in 1977. I am going to tell about periodicity of permutations, their complexity according to several definitions and their automatic properties, that is, about usual parameters of words, now extended to permutations and behaving sometimes similarly to those for words, sometimes not. Another series of results concerns permutations generated by infinite words and their properties. Although this direction of research is young, many people, including two other speakers of this meeting, have participated in it, and I believe that several more topics for further study are really promising.
International Nuclear Information System (INIS)
Khan, A.A.; Goeckeler, M.; Haegler, P.
2006-03-01
We present data for the axial coupling constant g A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point. (Orig.)
Energy Technology Data Exchange (ETDEWEB)
Khan, A.A.; Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Haegler, P. [Technische Univ. Muenchen (DE). Physik-Department, Theoretische Physik] (and others)
2006-03-15
We present data for the axial coupling constant g{sub A} of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g{sub A} based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point. (Orig.)
Jiang, Shidong; Xu, Minzhong
2005-01-01
The analytical solutions for the general-four-wave-mixing hyperpolarizabilities $\\chi^{(3)}(-(w_1+w_2+w_3);w_1,w_2,w_3)$ on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of DC Kerr effect $\\chi^{(3)}(-w;0,0,w)$, DC-induced second harmonic generation $\\chi^{(3)}(-2w;0,w,w)$, optical Kerr effect $\\chi^{(3)}(-w;w,-w,w)$ and DC-electric-field-induced optica...
International Nuclear Information System (INIS)
Davidson, R.; Kozak, J.J.
1978-01-01
In this paper we study the emission of a two-level atom in a radiation field in the case where one mode of the field is assumed to be excited initially, and where the system is assumed to be of infinite extent. (The restriction to a one-dimensional field, which has been made throughout this series, is not essential: It is made chiefly for ease of presentation of the mathematical methods.) An exact expression is obtained for the probability rho (t) that the two-level quantum system is in the excited state at time t. This problem, previously unsolved in radiation theory, is tackled by reformulating the expression found in VII [J. Math. Phys. 16, 1013 (1975)] of this series for the time evolution of rho (t) in a finite system in the presence of an extra photon, and then constructing the infinite-system limit. A quantitative assessment of the role of the extra photon and of the coupling constant in influencing the dynamics is obtained by studying numerically the expression derived for rho (t) for a particular choice of initial condition. The study presented here casts light on the problem of time-reversal invariance and clarifies the sense in which exponential decay is universal; in particular, we find that: (1) It is the infinite-system limit which converts the time-reversible solutions of VII into the irreversible solution obtained here, and (2) it is the weak-coupling limit that imposes exponential form on the time dependence of the evolution of the system. The anticipated generalization of our methods to more complicated radiation-matter problems is discussed, and finally, several problems in radiation chemistry and physics, already accessible to exact analysis given the approach introduced here, are cited
Molecular dynamics simulation of melting of finite and infinite size silicene
Min, Tjun Kit; Yoon, Tiem Leong; Lim, Thong Leng
2017-01-01
We report the melting temperature of free-standing silicene by carrying out molecular dynamics (MD) simulation experiments using optimzed Stillinger-Weber (SW) potential by Zhang {\\it et al.}. The melting scenario of a free-standing silicene is well captured visually in our MD simulations. The data are systematically analyzed using a few qualitatively different indicators, including caloric curve, radial distribution function and a numerical indicator known as `global similarity index'. The o...
Hirschman, Isidore Isaac
2014-01-01
This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the app
On the limit dynamics of systems with infinite multiple degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Braun, W A
1977-01-01
By using N/sup -2/ phi (g sub i - g sub j) regular pair interactions, it is shown that, for n approaching infinity, the Vlasovdynamics is the omega meson resonances -limit of the classical canonical N-particle-dynamics. Propagation of molecular chaos holds in this limit and the fluctuations converge to a Gaussian stochastic process, which is, however, non-Markovian. A model of a nerve membrane is studied in the limit of singular interaction with Fermion reservoirs. The resulting axon equations have the same structure as the Hodgkin Huxley equations. Recently proven theorems are used on nonlinear diffusion equations to show the existance of a propagating pulse solution.
Positive operator semigroups from finite to infinite dimensions
Bátkai, András; Rhandi, Abdelaziz
2017-01-01
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate t...
International Nuclear Information System (INIS)
Zio, Enrico; Pedroni, Nicola; Broggi, Matteo; Golea, Lucia Roxana
2009-01-01
In this paper, an infinite impulse response locally recurrent neural network (IIR-LRNN) is employed for modelling the dynamics of the Lead Bismuth Eutectic eXperimental Accelerator Driven System (LBE-XADS). The network is trained by recursive back-propagation (RBP) and its ability in estimating transients is tested under various conditions. The results demonstrate the robustness of the locally recurrent scheme in the reconstruction of complex nonlinear dynamic relationships
Idier, D.; Farine, M.; Remaud, B.; Sébille, F.
For one decade, several fields in physics as well microscopic as macroscopic benefit from the computational particle-models (astrophysics, electronics, fluids mechanics...). In particular, the nuclear matter offers an interesting challenge as many body problem, owing to the quantal nature of its components and the complexity of the in-medium interaction. Using a model derived from semi-classical Vlasov equation and the projection of the Wigner function on a Gaussian coherent states basis (pseudo-particles), static and dynamical properties of nuclear matter are studied, featuring the growing of bulk instabilities in dilute matter. Using different zero and finite range effective interactions, the effect of the model parameters upon the relation total energy - density - temperature and surface energy of the pseudo-particles fluid is pointed out. The dynamical feature is first based upon a model of the 2-body Uehling-Ulhenbeck collisionnal term. A study of the relaxation of a nucleonic system is performed. At last, the pseudo-particle model is used in order to extract time scale for the growing of density fluctuations. This process is supposed to be a possible way to clusterization during heavy nuclei collisions. Depuis une dizaine d'années, plusieurs domaines de la physique aussi bien microscopiques que macroscopiques bénéficient des modèles à particules pour ordinateurs (astrophysique, électronique, plasmas...). En particulier, la matière nucléaire constitue un objet intéressant pour le problème à N corps ; tant par la nature quantique des nucléons que par la complexité des interactions dans ce milieu. A travers un modèle dérivant de l'équation de Vlasov semi-classique et de la projection de la fonction de Wigner sur une base d'état cohérents gaussiens (les pseudo-particules), on étudie les propriétés statiques et dynamiques de la matière nucléaire dont en particulier le développement des instabilités de volume en milieu dilué. Pour diff
Some problems of dynamical systems on three dimensional manifolds
International Nuclear Information System (INIS)
Dong Zhenxie.
1985-08-01
It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)
Small random perturbations of infinite dimensional dynamical systems and nucleation theory
International Nuclear Information System (INIS)
Cassandro, M.; Olivieri, E.; Picco, P.
1985-06-01
We consider a stochastic differential equation with a standard space-time white noise and a double well non symmetric potential. The equation without the white noise term exhibits several equilibria two of which are stable. We study, in the double limit zero noise and thermodynamic limit the large fluctuations and compute the transition probability between the two stable equilibria (tunnelling). The unique stationary measure associated to the stochastic process described by our equation is strictly related to the Gibbs measure for a ferromagnetic spin system subject to a Kac interaction. Our double limit corresponds to the one considered by Lobowitz and Penrose in their rigorous version of the mean field theory of the first order phase transitions. The tunnelling between the two (non equivalent) equilibrium configurations is interpreted as the decay from the metastable to the stable state. Our results are in qualitative agreement with the usual nucleation theory
International Nuclear Information System (INIS)
Prentice, H. J.; Proud, W. G.
2006-01-01
A technique has been developed to determine experimentally the three-dimensional displacement field on the rear surface of a dynamically deforming plate. The technique combines speckle analysis with stereoscopy, using a modified angular-lens method: this incorporates split-frame photography and a simple method by which the effective lens separation can be adjusted and calibrated in situ. Whilst several analytical models exist to predict deformation in extended or semi-infinite targets, the non-trivial nature of the wave interactions complicates the generation and development of analytical models for targets of finite depth. By interrogating specimens experimentally to acquire three-dimensional strain data points, both analytical and numerical model predictions can be verified more rigorously. The technique is applied to the quasi-static deformation of a rubber sheet and dynamically to Mild Steel sheets of various thicknesses
Low-power low-noise mixed-mode VLSI ASIC for infinite dynamic range imaging applications
Turchetta, Renato; Hu, Y.; Zinzius, Y.; Colledani, C.; Loge, A.
1998-11-01
Solid state solutions for imaging are mainly represented by CCDs and, more recently, by CMOS imagers. Both devices are based on the integration of the total charge generated by the impinging radiation, with no processing of the single photon information. The dynamic range of these devices is intrinsically limited by the finite value of noise. Here we present the design of an architecture which allows efficient, in-pixel, noise reduction to a practically zero level, thus allowing infinite dynamic range imaging. A detailed calculation of the dynamic range is worked out, showing that noise is efficiently suppressed. This architecture is based on the concept of single-photon counting. In each pixel, we integrate both the front-end, low-noise, low-power analog part and the digital part. The former consists of a charge preamplifier, an active filter for optimal noise bandwidth reduction, a buffer and a threshold comparator, and the latter is simply a counter, which can be programmed to act as a normal shift register for the readout of the counters' contents. Two different ASIC's based on this concept have been designed for different applications. The first one has been optimized for silicon edge-on microstrips detectors, used in a digital mammography R and D project. It is a 32-channel circuit, with a 16-bit binary static counter.It has been optimized for a relatively large detector capacitance of 5 pF. Noise has been measured to be equal to 100 + 7*Cd (pF) electron rms with the digital part, showing no degradation of the noise performances with respect to the design values. The power consumption is 3.8mW/channel for a peaking time of about 1 microsecond(s) . The second circuit is a prototype for pixel imaging. The total active area is about (250 micrometers )**2. The main differences of the electronic architecture with respect to the first prototype are: i) different optimization of the analog front-end part for low-capacitance detectors, ii) in- pixel 4-bit comparator
International Nuclear Information System (INIS)
Hassan, M.H.A.; Eltayeb, I.A.
1992-07-01
The previous study (Eltayeb and Hassan, 1992) of the two-dimensional diffusion equation of dust over a rough ground surface, which acts as a dust source of variable strength, under the influence of horizontal wind and gravitational attraction is here extended to all finite values of the roughness height Z 0 . An analytic expression is obtained for the concentration of dust for a general strength of the source. The result reduces to the previously known solutions as special cases. The expression for the concentration has been evaluated for some representative example of the source strength g(X). It is found that the concentration decreases with roughness height at any fixed point above ground level. (author). 4 refs, 2 figs
Photoinduced charge-order melting dynamics in a one-dimensional interacting Holstein model
Hashimoto, Hiroshi; Ishihara, Sumio
2017-07-01
Transient quantum dynamics in an interacting fermion-phonon system are investigated with a focus on a charge order (CO) melting after a short optical-pulse irradiation and the roles of the quantum phonons in the transient dynamics. A spinless-fermion model in a one-dimensional chain coupled with local phonons is analyzed numerically. The infinite time-evolving block decimation algorithm is adopted as a reliable numerical method for one-dimensional quantum many-body systems. Numerical results for the photoinduced CO melting dynamics without phonons are well interpreted by the soliton picture for the CO domains. This interpretation is confirmed by numerical simulation of an artificial local excitation and the classical soliton model. In the case of large phonon frequencies corresponding to the antiadiabatic condition, CO melting is induced by propagations of the polaronic solitons with the renormalized soliton velocity. On the other hand, in the case of small phonon frequencies corresponding to the adiabatic condition, the first stage of the CO melting dynamics occurs due to the energy transfer from the fermionic to phononic systems, and the second stage is brought about by the soliton motions around the bottom of the soliton band. The analyses provide a standard reference for photoinduced CO melting dynamics in one-dimensional many-body quantum systems.
Three-dimensional dynamics of protostellar evolution
International Nuclear Information System (INIS)
Cook, T.L.
1977-06-01
A three-dimensional finite difference numerical methodology was developed for self-gravitating, rotating gaseous systems. The fully nonlinear equations for time-varying fluid dynamics are solved by high speed computer in a cylindrical coordinate system rotating with an instantaneous angular velocity, selected such that the net angular momentum relative to the rotating frame is zero. The time-dependent adiabatic collapse of gravitationally bound, rotating, protostellar clouds is studied for specified uniform and nonuniform initial conditions. Uniform clouds can form axisymmetric, rotating toroidal configurations. If the thermal pressure is high, nonuniform clouds can also collapse to axisymmetric toroids. For low thermal pressures, however, the collapsing cloud is unstable to initial perturbations. The fragmentation of protostellar clouds is investigated by studying the response of rotating, self-gravitating, equilibrium toroids to non-axisymmetric perturbations. The detailed evolution of the fragmenting toroid depends upon a non-dimensional function of the initial entropy, the total mass in the toroid, the angular velocity of rotation, and the number of perturbation wavelengths around the circumference of the toroid. For low and intermediate entropies, the configuration develops into co-rotating components with spiral streamers. In the spiral regions retrograde vortices are observed in some examples. For high levels of entropy, barred spirals can exist as intermediate states of the fragmentation
Directory of Open Access Journals (Sweden)
Yakovenko Larisa Aleksandrovna
2014-06-01
Full Text Available The article studies the functioning of stylistically marked verbal lexis in the infinitive form in literary critical articles of Russian publicists of the middle and second half of the 19th century. The critical texts of that period are characterized by the use of different functional, stylistic and expressive emotional coloring verbal lexemes. The author reveals the lexical content of infinitive forms, determines the markedness character (functional and stylistic, or expressive and emotional. The article presents the dynamics of using infinitive forms which shows that in the texts of 19th century they are used to express critics' attitude to fiction works, litetrary images, and this attitude is determined by publicists' ideas about the ways of reality depiction. It is revealed that in the second half of 19th century this form reflects the urge to evaluate the social maturity and fiction skills of a writer, and that serves to increasing number of stylistically marked lexemes in the texts of that period.
Quantum control in infinite dimensions
International Nuclear Information System (INIS)
Karwowski, Witold; Vilela Mendes, R.
2004-01-01
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite-dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators
Three-dimensional dynamics of protostellar evolution
International Nuclear Information System (INIS)
Cook, T.L.; Harlow, F.H.
1978-01-01
A three-dimensional finite difference numerical methodology has been developed for self-gravitating, rotating gaseous systems. The fully nonlinear equations for time-varying fluid dynamics are solved by high-speed computer in a cylindrical coordinate system rotating with an instantaneous angular velocity. The time-dependent adiabatic collapse of gravitationally bound, rotating, protostellar clouds is studied for specified uniform and nonuniform initial conditions. Uniform clouds can form axisymmetric, rotating toroidal configurations. If the thermal pressure is high, nonuniform clouds can also collapse to axisymmetric ellipsoids. For low thermal pressures, however, the collapsing cloud is unstable to perturbations. The resulting fragmentation of unstable protostellar clouds is investigated by studying the response of rotating, self-gravitating, equilibrium toroids to nonaxisymmetric perturbations. The detailed evolution of the fragmentation toroid depends upon a nondimensional function of the initial entropy, the total mass in the toroid, the angular velocity of rotation, and the number of perturbation wave-lengths around the circumference of the toroid. For low and intermediate entropies, the configuration develops into corotating components with spiral streamers. In the spiral regions retrograde vortices are observed in some examples. For high levels of entropy, barred spirals can exist as intermediate states of the fragmentation
Multimodal three-dimensional dynamic signature
Directory of Open Access Journals (Sweden)
Yury E. Kozlov
2017-11-01
Full Text Available Reliable authentication in mobile applications is among the most important information security challenges. Today, we can hardly imagine a person who would not own a mobile device that connects to the Internet. Mobile devices are being used to store large amounts of confidential information, ranging from personal photos to electronic banking tools. In 2009, colleagues from Rice University together with their collaborators from Motorola, proposed an authentication through in-air gestures. This and subsequent work contributing to the development of the method are reviewed in our introduction. At the moment, there exists a version of the gesture-based authentication software available for Android mobile devices. This software has not become widespread yet. One of likely reasons for that is the insufficient reliability of the method, which involves similar to its earlier analogs the use of only one device. Here we discuss the authentication based on the multimodal three-dimensional dynamic signature (MTDS performed by two independent mobile devices. The MTDS-based authentication technique is an advanced version of in-air gesture authentication. We describe the operation of a prototype of MTDS-based authentication, including the main implemented algorithms, as well as some preliminary results of testing the software. We expect that our method can be used in any mobile application, provided a number of additional improvements discussed in the conclusion are made.
Analysing spatially extended high-dimensional dynamics by recurrence plots
Energy Technology Data Exchange (ETDEWEB)
Marwan, Norbert, E-mail: marwan@pik-potsdam.de [Potsdam Institute for Climate Impact Research, 14412 Potsdam (Germany); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, 14412 Potsdam (Germany); Humboldt Universität zu Berlin, Institut für Physik (Germany); Nizhny Novgorod State University, Department of Control Theory, Nizhny Novgorod (Russian Federation); Foerster, Saskia [GFZ German Research Centre for Geosciences, Section 1.4 Remote Sensing, Telegrafenberg, 14473 Potsdam (Germany)
2015-05-08
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analysing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world. - Highlights: • We use recurrence plots for analysing partially extended dynamics. • We investigate the high-dimensional chaos of the Lorenz96 model. • The approach distinguishes different spatio-temporal dynamics. • We use the method for studying vegetation cover time series.
Discretization model for nonlinear dynamic analysis of three dimensional structures
International Nuclear Information System (INIS)
Hayashi, Y.
1982-12-01
A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt
PREFACE: Dynamics of low-dimensional systems Dynamics of low-dimensional systems
Bernasconi, M.; Miret-Artés, S.; Toennies, J. P.
2012-03-01
With the development of techniques for high-resolution inelastic helium atom scattering (HAS), electron scattering (EELS) and neutron spin echo spectroscopy, it has become possible, within approximately the last thirty years, to measure the dispersion curves of surface phonons in insulators, semiconductors and metals. In recent years, the advent of new experimental techniques such as 3He spin-echo spectroscopy, scanning inelastic electron tunnel spectroscopy, inelastic x-ray scattering spectroscopy and inelastic photoemission have extended surface phonon spectroscopy to a variety of systems. These include ultra-thin metal films, adsorbates at surface and elementary processes where surface phonons play an important role. Other important directions have been actively pursued in the past decade: the dynamics of stepped surfaces and clusters grown on metal surfaces, due to their relevance in many dynamical and chemical processes at surfaces, including heterogeneous catalysis; clusters; diffusion etc. The role of surface effects in these processes has been conjectured since the early days of surface dynamics, although only now is the availability of ab initio approaches providing those conjectures with a microscopic basis. Last but not least, the investigation of non-adiabatic effects, originating for instance from the hybridization (avoided crossing) of the surface phonons branches with the quasi 1D electron-hole excitation branch, is also a challenging new direction. Furthermore, other elementary oscillations such as surface plasmons are being actively investigated. The aforementioned experimental breakthroughs have been accompanied by advances in the theoretical study of atom-surface interaction. In particular, in the past decade first principles calculations based on density functional perturbation theory have boosted the theoretical study of the dynamics of low-dimensional systems. Phonon dispersion relations of clean surfaces, the dynamics of adsorbates, and the
Riggs, Peter J.
2013-01-01
Students often wrestle unsuccessfully with the task of correctly calculating momentum probability densities and have difficulty in understanding their interpretation. In the case of a particle in an "infinite" potential well, its momentum can take values that are not just those corresponding to the particle's quantised energies but…
Dynamic colloidal assembly pathways via low dimensional models
Energy Technology Data Exchange (ETDEWEB)
Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu [Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Thyagarajan, Raghuram; Ford, David M. [Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
2016-05-28
Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterized by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.
Waiting Time Dynamics in Two-Dimensional Infrared Spectroscopy
Jansen, Thomas L. C.; Knoester, Jasper
We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example,
Inference in High-dimensional Dynamic Panel Data Models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Tang, Haihan
We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities are derived for the fixed effects. Next, we show how one can...
On infinitely divisible semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Rosiński, Jan
2015-01-01
to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker's theorem fails to hold. Then, as the main result, we prove that an infinitely divisible semimartingale relative to the filtration generated...... by a random measure admits a unique decomposition into an independent increment process and an infinitely divisible process of finite variation. Consequently, the natural analog of Stricker's theorem holds for all strictly representable processes (as defined in this paper). Since Gaussian processes...... are strictly representable due to Hida's multiplicity theorem, the classical Stricker's theorem follows from our result. Another consequence is that the question when an infinitely divisible process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible...
Structures in dynamics finite dimensional deterministic studies
Broer, HW; van Strien, SJ; Takens, F
1991-01-01
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic
Dynamical class of a two-dimensional plasmonic Dirac system.
Silva, Érica de Mello
2015-10-01
A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.
International Nuclear Information System (INIS)
Leznov, A.N.; Saveliev, M.V.
1982-01-01
An investigation of two-dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary Lie algebra g whose grading is consistent with an arbitrary integral embedding of 3d-subalgebra in g has been carried out. The corresponding systems of nonlinear partial differential equations of the second order h been constructed in an explicit form and their genral solutions in the sense of a Goursat problem have been obtained. A method for the construction of a wide class of infinite-dimensional Lie algebras of finite growth has been proposed
Chaotic dynamics in two-dimensional noninvertible maps
Mira, Christian; Cathala, Jean-Claude; Gardini, Laura
1996-01-01
This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this resea
Energy Technology Data Exchange (ETDEWEB)
Kirtman, Bernard [Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106 (United States); Springborg, Michael [Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken (Germany); Rérat, Michel [Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l' Adour, 64000 Pau (France); Ferrero, Mauro; Lacivita, Valentina; Dovesi, Roberto [Departimeno di Chimica, IFM, Università di Torino and NIS - Nanostructure Interfaces and Surfaces - Centre of Excellence, Via P. Giuria 7, 10125 Torino (Italy); Orlando, Roberto [Departimento di Scienze e Tecnologie Avanzati, Università del Piemonte Orientale, Viale T. Michel 11, 15121 Alessandria (Italy)
2015-01-22
An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.
Spin dynamics in a two-dimensional quantum gas
DEFF Research Database (Denmark)
Pedersen, Poul Lindholm; Gajdacz, Miroslav; Deuretzbacher, Frank
2014-01-01
We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimp......We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions...
Three-Dimensional Computational Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Haworth, D.C.; O' Rourke, P.J.; Ranganathan, R.
1998-09-01
Computational fluid dynamics (CFD) is one discipline falling under the broad heading of computer-aided engineering (CAE). CAE, together with computer-aided design (CAD) and computer-aided manufacturing (CAM), comprise a mathematical-based approach to engineering product and process design, analysis and fabrication. In this overview of CFD for the design engineer, our purposes are three-fold: (1) to define the scope of CFD and motivate its utility for engineering, (2) to provide a basic technical foundation for CFD, and (3) to convey how CFD is incorporated into engineering product and process design.
Squashed entanglement in infinite dimensions
International Nuclear Information System (INIS)
Shirokov, M. E.
2016-01-01
We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.
Simulations of four-dimensional simplicial quantum gravity as dynamical triangulation
International Nuclear Information System (INIS)
Agishtein, M.E.; Migdal, A.A.
1992-01-01
In this paper, Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. The authors studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: the authors reached about 5 x 10 4 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. The authors varied the gravitational constant, and they found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). The authors studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths
Electromagnetic interactions in relativistic infinite component wave equations
International Nuclear Information System (INIS)
Gerry, C.C.
1979-01-01
The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group
Complex dynamical invariants for two-dimensional complex potentials
Indian Academy of Sciences (India)
Abstract. Complex dynamical invariants are searched out for two-dimensional complex poten- tials using rationalization method within the framework of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. It is found that the cubic oscillator and shifted harmonic oscillator ...
Nonlinear dynamic characterization of two-dimensional materials
Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.
2017-01-01
Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's
Hadronic currents in the infinite momentum frame
International Nuclear Information System (INIS)
Toth, K.
1975-01-01
The problem of the transformation properties of hadronic currents in the infinite momentum frame (IMF) is investigated. A general method is proposed to deal with the problem which is based upon the concept of group contraction. The two-dimensional aspects of the IMF description are studied in detail, and the current matrix elements of a three-dimensional Poincare covariant theory are reduced to those of a two-dimensional one. It is explicitlyshown that the covariance group of the two-dimensional theory may either be a 'non-relativistic' (Galilei) group, or a 'relativistic' (Poincare) one depending on the value of a parameter reminiscent of the light velocity in the three-dimensional theory. The value of this parameter cannot be determined by kinematical argument. These results offer a natural generalization of models which assume Galilean symmetry in the infinite momentum frame
Remarks on the existence of non equilibrium dynamics
International Nuclear Information System (INIS)
Marchioro, C.; Pellegrinotti, A.; Pulvirenti, M.
1981-01-01
The authors give an existence theorem for the dynamics of an infinite system of anharmonic oscillators. They obtain another proof of the existence of the dynamics in the case of one-dimensional system of infinitely many particles interacting via a bounded potential. The case of very singular potential is also solved. (Auth.)
Gumral, Hasan
Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.
Supporting Dynamic Quantization for High-Dimensional Data Analytics.
Guzun, Gheorghi; Canahuate, Guadalupe
2017-05-01
Similarity searches are at the heart of exploratory data analysis tasks. Distance metrics are typically used to characterize the similarity between data objects represented as feature vectors. However, when the dimensionality of the data increases and the number of features is large, traditional distance metrics fail to distinguish between the closest and furthest data points. Localized distance functions have been proposed as an alternative to traditional distance metrics. These functions only consider dimensions close to query to compute the distance/similarity. Furthermore, in order to enable interactive explorations of high-dimensional data, indexing support for ad-hoc queries is needed. In this work we set up to investigate whether bit-sliced indices can be used for exploratory analytics such as similarity searches and data clustering for high-dimensional big-data. We also propose a novel dynamic quantization called Query dependent Equi-Depth (QED) quantization and show its effectiveness on characterizing high-dimensional similarity. When applying QED we observe improvements in kNN classification accuracy over traditional distance functions. Gheorghi Guzun and Guadalupe Canahuate. 2017. Supporting Dynamic Quantization for High-Dimensional Data Analytics. In Proceedings of Ex-ploreDB'17, Chicago, IL, USA, May 14-19, 2017, 6 pages. https://doi.org/http://dx.doi.org/10.1145/3077331.3077336.
Poincare' maps of impulsed oscillators and two-dimensional dynamics
International Nuclear Information System (INIS)
Lupini, R.; Lenci, S.; Gardini, L.; Urbino Univ.
1996-01-01
The Poincare' map of one-dimensional linear oscillators subject to periodic, non-linear and time-delayed impulses is shown to reduce to a family of plane maps with possible non-uniqueness of the inverse. By restricting the analysis to a convenient form of the impulse function, a variety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical curves of two-dimensional endomorphisms are used to identify the structure of absorbing areas and their bifurcations
Dynamic characteristics of lead rubber bearings with dynamic two-dimensional test equipment
International Nuclear Information System (INIS)
Ohtori, Y.; Ishida, K.; Mazda, T.
1994-01-01
Although studies have previously been done on the static mechanical properties of lead rubber bearings, this study aims to grasp the dynamic characteristics of lead rubber bearings from experimental results, using two-dimensional dynamic test equipment which is designed to grasp in detail such dynamic characteristics as deformation capacity and proof stress. This paper describes the results from three types of tests: (1) dynamic mechanical properties tests, (2) cyclic loading tests, and (3) dynamic ultimate tests. Through these tests, it was confirmed that the dynamic characteristics of lead rubber bearings are independent of strain rate
Numerical and spectral investigations of novel infinite elements
International Nuclear Information System (INIS)
Barai, P.; Harari, I.; Barbonet, P.E.
1998-01-01
Exterior problems of time-harmonic acoustics are addressed by a novel infinite element formulation, defined on a bounded computational domain. For two-dimensional configurations with circular interfaces, the infinite element results match Quell both analytical values and those obtained from. other methods like DtN. Along 1uith the numerical performance of this formulation, of considerable interest are its complex-valued eigenvalues. Hence, a spectral analysis of the present scheme is also performed here, using various infinite elements
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...
Kantowski-Sachs multidimensional cosmological models and dynamical dimensional reduction
International Nuclear Information System (INIS)
Demianski, M.; Rome Univ.; Golda, Z.A.; Heller, M.; Szydlowski, M.
1988-01-01
Einstein's field equations are solved for a multidimensional spacetime (KS) x Tsup(m), where (KS) is a four-dimensional Kantowski-Sachs spacetime and Tsup(m) is an m-dimensional torus. Among all possible vacuum solutions there is a large class of spacetimes in which the macroscopic space expands and the microscopic space contracts to a finite volume. We also consider a non-vacuum case and we explicitly solve the field equations for the matter satisfying the Zel'dovich equation of state. In non-vacuum models, with matter satisfying an equation of state p = γρ, O ≤ γ < 1, at a sufficiently late stage of evolution the microspace always expands and the dynamical dimensional reduction does not occur. (author)
Canonical and symplectic analysis for three dimensional gravity without dynamics
Energy Technology Data Exchange (ETDEWEB)
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48 72570, Puebla, Pue. (Mexico); Osmart Ochoa-Gutiérrez, H. [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado postal 1152, 72001 Puebla, Pue. (Mexico)
2017-03-15
In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev–Jackiw symplectic approach is developed; we report the complete set of Faddeev–Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev–Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw and Dirac’s formalism are briefly discussed. - Highlights: • We report the symplectic analysis for three dimensional gravity without dynamics. • We report the Faddeev–Jackiw constraints. • A pure Dirac’s analysis is performed. • The complete structure of Dirac’s constraints is reported. • We show that symplectic and Dirac’s brackets coincide to each other.
Scaling analyses of the spectral dimension in 3-dimensional causal dynamical triangulations
Cooperman, Joshua H.
2018-05-01
The spectral dimension measures the dimensionality of a space as witnessed by a diffusing random walker. Within the causal dynamical triangulations approach to the quantization of gravity (Ambjørn et al 2000 Phys. Rev. Lett. 85 347, 2001 Nucl. Phys. B 610 347, 1998 Nucl. Phys. B 536 407), the spectral dimension exhibits novel scale-dependent dynamics: reducing towards a value near 2 on sufficiently small scales, matching closely the topological dimension on intermediate scales, and decaying in the presence of positive curvature on sufficiently large scales (Ambjørn et al 2005 Phys. Rev. Lett. 95 171301, Ambjørn et al 2005 Phys. Rev. D 72 064014, Benedetti and Henson 2009 Phys. Rev. D 80 124036, Cooperman 2014 Phys. Rev. D 90 124053, Cooperman et al 2017 Class. Quantum Grav. 34 115008, Coumbe and Jurkiewicz 2015 J. High Energy Phys. JHEP03(2015)151, Kommu 2012 Class. Quantum Grav. 29 105003). I report the first comprehensive scaling analysis of the small-to-intermediate scale spectral dimension for the test case of the causal dynamical triangulations of 3-dimensional Einstein gravity. I find that the spectral dimension scales trivially with the diffusion constant. I find that the spectral dimension is completely finite in the infinite volume limit, and I argue that its maximal value is exactly consistent with the topological dimension of 3 in this limit. I find that the spectral dimension reduces further towards a value near 2 as this case’s bare coupling approaches its phase transition, and I present evidence against the conjecture that the bare coupling simply sets the overall scale of the quantum geometry (Ambjørn et al 2001 Phys. Rev. D 64 044011). On the basis of these findings, I advance a tentative physical explanation for the dynamical reduction of the spectral dimension observed within causal dynamical triangulations: branched polymeric quantum geometry on sufficiently small scales. My analyses should facilitate attempts to employ the spectral
Blended particle filters for large-dimensional chaotic dynamical systems
Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.
2014-01-01
A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886
Collision dynamics of two-dimensional non-Abelian vortices
Mawson, Thomas; Petersen, Timothy C.; Simula, Tapio
2017-09-01
We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation—an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.
International Nuclear Information System (INIS)
Sprung, D.W.L.
1975-01-01
This paper is a brief review of those aspects of the effective interaction problem that can be grouped under the heading of infinite partial summations of the perturbation series. After a brief mention of the classic examples of infinite summations, the author turns to the effective interaction problem for two extra core particles. Their direct interaction is summed to produce the G matrix, while their indirect interaction through the core is summed in a variety of ways under the heading of core polarization. (orig./WL) [de
Dynamic screening and electron dynamics in low-dimensional metal systems
International Nuclear Information System (INIS)
Silkin, V.M.; Quijada, M.; Vergniory, M.G.; Alducin, M.; Borisov, A.G.; Diez Muino, R.; Juaristi, J.I.; Sanchez-Portal, D.; Chulkov, E.V.; Echenique, P.M.
2007-01-01
Recent advances in the theoretical description of dynamic screening and electron dynamics in metallic media are reviewed. The time-dependent building-up of screening in different situations is addressed. Perturbative and non-perturbative theories are used to study electron dynamics in low-dimensional systems, such as metal clusters, image states, surface states and quantum wells. Modification of the electronic lifetimes due to confinement effects is analyzed as well
Are low-dimensional dynamics typical in magnetically confined plasmas?
International Nuclear Information System (INIS)
Ball, R.; Dewar, R.L.
2000-01-01
Full text: Since 1988 there have been many serious attempts to construct low-dimensional dynamical systems that model L-H transitions and associated oscillatory phenomena in magnetically confined plasmas. Such models usually consist of coupled ordinary differential equations in a few dynamical state variables and several parameters that represent physical properties or external controls. The advantages of a unified, low-dimensional approach to modelling plasma behaviour are multifold. Most importantly, the qualitative analysis of nonlinear ODE and algebraic systems is supported by a substantial body of theory. The toolkits of singularity and stability theory are well-developed and accessible, and contain the right tools for the job of charting the state and parameter space. One of the driving forces behind the development of low-dimensional dynamical models is the predictive potential of a parameter map. For example, a model that talks of the shape and extent of hysteresis in the L-H transition would help engineers who are interested in controlling access to H-mode. We can express this problem another way: given the enormous number of variables and parameters that could be varied around a hysteretic regime, it would be cheaper to know in advance which ones actually do influence the quality and quantity of the hysteresis. The quest for a low-dimensional state space that contains the qualitative dynamics of L-H transitions also introduces other problems. We need to identify the essential (few) dynamical variables and the essential (few) independent parameter groups, clarify the mechanisms for the feedback that is modelled by nonlinear terms, and identify symmetries in the physics. Before jumping the gun on these questions the fundamental issue should be addressed of whether a confined plasma, having many important length and time scales, steep gradients, strong anisotropy, and an uncountable multiplicity of states, can indeed exhibit low-dimensional dynamics. In this
DEFF Research Database (Denmark)
Srba, Jiří
2002-01-01
This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page http://www.brics.dk/~srba/roadmap....
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
Wanko, Jeffrey J.
2009-01-01
This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…
Dynamics of an impurity in a one-dimensional lattice
International Nuclear Information System (INIS)
Massel, F; Kantian, A; Giamarchi, T; Daley, A J; Törmä, P
2013-01-01
We study the non-equilibrium dynamics of an impurity in a harmonic trap that is kicked with a well-defined quasi-momentum, and interacts with a bath of free fermions or interacting bosons in a one-dimensional lattice configuration. Using numerical and analytical techniques we investigate the full dynamics beyond linear response, which allows us to quantitatively characterize states of the impurity in the bath for different parameter regimes. These vary from a tightly bound molecular state in a strongly interacting limit to a polaron (dressed impurity) and a free particle for weak interactions, with composite behaviour in the intermediate regime. These dynamics and different parameter regimes should be readily realizable in systems of cold atoms in optical lattices. (paper)
Gauge theory for finite-dimensional dynamical systems
International Nuclear Information System (INIS)
Gurfil, Pini
2007-01-01
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory
REVIEW One-Dimensional Dynamical Modeling of Earthquakes: A Review
Directory of Open Access Journals (Sweden)
Jeen-Hwa Wang
2008-01-01
Full Text Available Studies of the power-law relations of seismicity and earthquake source parameters based on the one-dimensional (1-D Burridge-Knopoff¡¦s (BK dynamical lattice model, especially those studies conducted by Taiwan¡¦s scientists, are reviewed in this article. In general, velocity- and/or state-dependent friction is considered to control faulting. A uniform distribution of breaking strengths (i.e., the static friction strength is taken into account in some studies, and inhomogeneous distributions in others. The scaling relations in these studies include: Omori¡¦s law, the magnitude-frequency or energy-frequency relation, the relation between source duration time and seismic moment, the relation between rupture length and seismic moment, the frequency-length relation, and the source power spectra. The main parameters of the one-dimensional (1-D Burridge-Knopoff¡¦s (BK dynamical lattice model include: the decreasing rate (r of dynamic friction strength with sliding velocity; the type and degree of heterogeneous distribution of the breaking strengths, the stiffness ratio (i.e., the ratio between the stiffness of the coil spring connecting two mass elements and that of the leaf spring linking a mass element and the moving plate; the frictional drop ratio of the minimum dynamic friction strength to the breaking strength; and the maximum breaking strength. For some authors, the distribution of the breaking strengths was considered to be a fractal function. Hence, the fractal dimension of such a distribution is also a significant parameter. Comparison between observed scaling laws and simulation results shows that the 1-D BK dynamical lattice model acceptably approaches fault dynamics.
A low dimensional dynamical system for the wall layer
Aubry, N.; Keefe, L. R.
1987-01-01
Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.
Quantum diffusion in semi-infinite periodic and quasiperiodic systems
International Nuclear Information System (INIS)
Zhang Kaiwang
2008-01-01
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C(t) ∼ t −δ and d(t) ∼ t β . However, it finds that 0 < δ < 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed
Dynamics of vortex interactions in two-dimensional flows
DEFF Research Database (Denmark)
Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.
2002-01-01
The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...... a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 ... is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection...
Probabilistic Infinite Secret Sharing
Csirmaz, László
2013-01-01
The study of probabilistic secret sharing schemes using arbitrary probability spaces and possibly infinite number of participants lets us investigate abstract properties of such schemes. It highlights important properties, explains why certain definitions work better than others, connects this topic to other branches of mathematics, and might yield new design paradigms. A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a colle...
Static and dynamic properties of two-dimensional Coulomb clusters.
Ash, Biswarup; Chakrabarti, J; Ghosal, Amit
2017-10-01
We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the crossover from solid- to liquid-like behaviors. While static correlations that investigate the translational and bond orientational order in the confinements show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase, reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations in irregular traps. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries.
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...
Measuring protein dynamics with ultrafast two-dimensional infrared spectroscopy
International Nuclear Information System (INIS)
Adamczyk, Katrin; Candelaresi, Marco; Hunt, Neil T; Robb, Kirsty; Hoskisson, Paul A; Tucker, Nicholas P; Gumiero, Andrea; Walsh, Martin A; Parker, Anthony W
2012-01-01
Recent advances in the methodology and application of ultrafast two-dimensional infrared (2D-IR) spectroscopy to biomolecular systems are reviewed. A description of the 2D-IR technique and the molecular contributions to the observed spectra are presented followed by a discussion of recent literature relating to the use of 2D-IR and associated approaches for measuring protein dynamics. In particular, these include the use of diatomic ligand groups for measuring haem protein dynamics, isotopic labelling strategies and the use of vibrational probe groups. The final section reports on the current state of the art regarding the use of 2D-IR methods to provide insights into biological reaction mechanisms. (topical review)
Oscillatory Dynamics of One-Dimensional Homogeneous Granular Chains
Starosvetsky, Yuli; Jayaprakash, K. R.; Hasan, Md. Arif; Vakakis, Alexander F.
The acoustics of the homogeneous granular chains has been studied extensively both numerically and experimentally in the references cited in the previous chapters. This chapter focuses on the oscillatory behavior of finite dimensional homogeneous granular chains. It is well known that normal vibration modes are the building blocks of the vibrations of linear systems due to the applicability of the principle of superposition. One the other hand, nonlinear theory is deprived of such a general superposition principle (although special cases of nonlinear superpositions do exist), but nonlinear normal modes ‒ NNMs still play an important role in the forced and resonance dynamics of these systems. In their basic definition [1], NNMs were defined as time-periodic nonlinear oscillations of discrete or continuous dynamical systems where all coordinates (degrees-of-freedom) oscillate in-unison with the same frequency; further extensions of this definition have been considered to account for NNMs of systems with internal resonances [2]...
High dimensional model representation method for fuzzy structural dynamics
Adhikari, S.; Chowdhury, R.; Friswell, M. I.
2011-03-01
Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.
Dynamic masquerade with morphing three-dimensional skin in cuttlefish.
Panetta, Deanna; Buresch, Kendra; Hanlon, Roger T
2017-03-01
Masquerade is a defence tactic in which a prey resembles an inedible or inanimate object thus causing predators to misclassify it. Most masquerade colour patterns are static although some species adopt postures or behaviours to enhance the effect. Dynamic masquerade in which the colour pattern can be changed is rare. Here we report a two-step sensory process that enables an additional novel capability known only in cuttlefish and octopus: morphing three-dimensional physical skin texture that further enhances the optical illusions created by coloured skin patterns. Our experimental design incorporated sequential sensory processes: addition of a three-dimensional rock to the testing arena, which attracted the cuttlefish to settle next to it; then visual processing by the cuttlefish of physical textures on the rock to guide expression of the skin papillae, which can range from fully relaxed (smooth skin) to fully expressed (bumpy skin). When a uniformly white smooth rock was presented, cuttlefish moved to the rock and deployed a uniform body pattern with mostly smooth skin. When a rock with small-scale fragments of contrasting shells was presented, the cuttlefish deployed mottled body patterns with strong papillae expression. These robust and reversible responses indicate a sophisticated visual sensorimotor system for dynamic masquerade. © 2017 The Author(s).
A qualitative numerical study of high dimensional dynamical systems
Albers, David James
Since Poincare, the father of modern mathematical dynamical systems, much effort has been exerted to achieve a qualitative understanding of the physical world via a qualitative understanding of the functions we use to model the physical world. In this thesis, we construct a numerical framework suitable for a qualitative, statistical study of dynamical systems using the space of artificial neural networks. We analyze the dynamics along intervals in parameter space, separating the set of neural networks into roughly four regions: the fixed point to the first bifurcation; the route to chaos; the chaotic region; and a transition region between chaos and finite-state neural networks. The study is primarily with respect to high-dimensional dynamical systems. We make the following general conclusions as the dimension of the dynamical system is increased: the probability of the first bifurcation being of type Neimark-Sacker is greater than ninety-percent; the most probable route to chaos is via a cascade of bifurcations of high-period periodic orbits, quasi-periodic orbits, and 2-tori; there exists an interval of parameter space such that hyperbolicity is violated on a countable, Lebesgue measure 0, "increasingly dense" subset; chaos is much more likely to persist with respect to parameter perturbation in the chaotic region of parameter space as the dimension is increased; moreover, as the number of positive Lyapunov exponents is increased, the likelihood that any significant portion of these positive exponents can be perturbed away decreases with increasing dimension. The maximum Kaplan-Yorke dimension and the maximum number of positive Lyapunov exponents increases linearly with dimension. The probability of a dynamical system being chaotic increases exponentially with dimension. The results with respect to the first bifurcation and the route to chaos comment on previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss. Moreover, results regarding the high-dimensional
Infinite matrices and sequence spaces
Cooke, Richard G
2014-01-01
This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi
Knopp, Konrad
1956-01-01
One of the finest expositors in the field of modern mathematics, Dr. Konrad Knopp here concentrates on a topic that is of particular interest to 20th-century mathematicians and students. He develops the theory of infinite sequences and series from its beginnings to a point where the reader will be in a position to investigate more advanced stages on his own. The foundations of the theory are therefore presented with special care, while the developmental aspects are limited by the scope and purpose of the book. All definitions are clearly stated; all theorems are proved with enough detail to ma
Non-equilibrium dynamics of one-dimensional Bose gases
International Nuclear Information System (INIS)
Langen, T.
2013-01-01
Understanding the non-equilibrium dynamics of isolated quantum many-body systems is an open problem on vastly different energy, length, and time scales. Examples range from the dynamics of the early universe and heavy-ion collisions to the subtle coherence and transport properties in condensed matter physics. However, realizations of such quantum many-body systems, which are both well isolated from the environment and accessible to experimental study are scarce. This thesis presents a series of experiments with ultracold one-dimensional Bose gases. These gases combine a nearly perfect isolation from the environment with many well-established methods to manipulate and probe their quantum states. This makes them an ideal model system to explore the physics of quantum many body systems out of equilibrium. In the experiments, a well-defined non-equilibrium state is created by splitting a single one-dimensional gas coherently into two parts. The relaxation of this state is probed using matter-wave interferometry. The Observations reveal the emergence of a prethermalized steady state which differs strongly from thermal equilibrium. Such thermal-like states had previously been predicted for a large variety of systems, but never been observed directly. Studying the relaxation process in further detail shows that the thermal correlations of the prethermalized state emerge locally in their final form and propagate through the system in a light-cone-like evolution. This provides first experimental evidence for the local relaxation conjecture, which links relaxation processes in quantum many-body systems to the propagation of correlations. Furthermore, engineering the initial state of the evolution demonstrates that the prethermalized state is described by a generalized Gibbs ensemble, an observation which substantiates the importance of this ensemble as an extension of standard statistical mechanics. Finally, an experiment is presented, where pairs of gases with an atom
Three-dimensional particle tracking velocimetry using dynamic vision sensors
Borer, D.; Delbruck, T.; Rösgen, T.
2017-12-01
A fast-flow visualization method is presented based on tracking neutrally buoyant soap bubbles with a set of neuromorphic cameras. The "dynamic vision sensors" register only the changes in brightness with very low latency, capturing fast processes at a low data rate. The data consist of a stream of asynchronous events, each encoding the corresponding pixel position, the time instant of the event and the sign of the change in logarithmic intensity. The work uses three such synchronized cameras to perform 3D particle tracking in a medium sized wind tunnel. The data analysis relies on Kalman filters to associate the asynchronous events with individual tracers and to reconstruct the three-dimensional path and velocity based on calibrated sensor information.
Semi-infinite Weil complex and the Virasoro algebra
International Nuclear Information System (INIS)
Feigin, B.; Frenkel, E.
1991-01-01
We define a semi-infinite analogue of the Weil algebra associated with an infinite-dimensional Lie algebra. It can be used for the definition of semi-infinite characteristic classes by analogy with the Chern-Weil construction. The second term of a spectral sequence of this Weil complex consists of the semi-infinite cohomology of the Lie algebra with coefficients in its 'adjoint semi-infinite symmetric powers'. We compute this cohomology for the Virasoro algebra. This is just the BRST cohomology of the bosonic βγ-system with the central charge 26. We give a complete description of the Fock representations of this bosonic system as modules over the Virasoro algebra, using Friedan-Martinec-Shenker bosonization. We derive a combinatorial identity from this result. (orig.)
Rare events in finite and infinite dimensions
Reznikoff, Maria G.
Thermal noise introduces stochasticity into deterministic equations and makes possible events which are never seen in the zero temperature setting. The driving force behind the thesis work is a desire to bring analysis and probability to bear on a class of relevant and intriguing physical problems, and in so doing, to allow applications to drive the development of new mathematical theory. The unifying theme is the study of rare events under the influence of small, random perturbations, and the manifold mathematical problems which ensue. In the first part, we apply large deviation theory and prefactor estimates to a coherent rotation micromagnetic model in order to analyze thermally activated magnetic switching. We consider recent physical experiments and the mathematical questions "asked" by them. A stochastic resonance type phenomenon is discovered, leading to the definition of finite temperature astroids. Non-Arrhenius behavior is discussed. The analysis is extended to ramped astroids. In addition, we discover that for low damping and ultrashort pulses, deterministic effects can override thermal effects, in accord with very recent ultrashort pulse experiments. Even more interesting, perhaps, is the study of large deviations in the infinite dimensional context, i.e. in spatially extended systems. Inspired by recent numerical investigations, we study the stochastically perturbed Allen Cahn and Cahn Hilliard equations. For the Allen Cahn equation, we study the action minimization problem (a deterministic variational problem) and prove the action scaling in four parameter regimes, via upper and lower bounds. The sharp interface limit is studied. We formally derive a reduced action functional which lends insight into the connection between action minimization and curvature flow. For the Cahn Hilliard equation, we prove upper and lower bounds for the scaling of the energy barrier in the nucleation and growth regime. Finally, we consider rare events in large or infinite
Ambiguities about infinite nuclear matter
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1978-01-01
Exact solutions of the harmonic-oscillator and infinite hyperspherical well are given for the ground state of a infinitely heavy (N=Z) nucleus. The density of matter is a steadily decreasing function. The kinetic energy per particle is 12% smaller than the one predicted by the Fermi sea
The Infinitive Marker across Scandinavian
DEFF Research Database (Denmark)
Christensen, Ken Ramshøj
2007-01-01
In this paper I argue that the base-position of the infinitive marker in the Scandinavian languages and English share a common origin site. It is inserted as the top-most head in the VP-domain. The cross-linguistic variation in the syntactic distribution of the infinitive marker can be accounted...
Static and dynamic properties of three-dimensional dot-type magnonic crystals
International Nuclear Information System (INIS)
Maksymov, Artur; Spinu, Leonard
2016-01-01
The static and dynamic magnetization of three-dimensional magnonic metamaterials has been investigated. By numerical means it was analyzed the impact of space dimensionality on the properties of magnonic crystal with unit cell consisting of four dots. It is find out the possibility of multi-vortex core formation which is related to the increasing of the crystal height by three-dimensional periodicity of single crystal layer. Additionally is provided the analysis of ferromagnetic resonance phenomenon for two-dimensional and three-dimensional structures. For the unsaturated magnetization of three-dimensional crystal the several pronounced resonance frequencies were detected.
Static and dynamic properties of three-dimensional dot-type magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Maksymov, Artur, E-mail: maxyartur@gmail.com [Advanced Materials Research Institute, University of New Orleans, LA 70148 (United States); Department of General Physics, Chernivtsi National University, Chernivtsi 58012 (Ukraine); Spinu, Leonard [Advanced Materials Research Institute, University of New Orleans, LA 70148 (United States); Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)
2016-04-01
The static and dynamic magnetization of three-dimensional magnonic metamaterials has been investigated. By numerical means it was analyzed the impact of space dimensionality on the properties of magnonic crystal with unit cell consisting of four dots. It is find out the possibility of multi-vortex core formation which is related to the increasing of the crystal height by three-dimensional periodicity of single crystal layer. Additionally is provided the analysis of ferromagnetic resonance phenomenon for two-dimensional and three-dimensional structures. For the unsaturated magnetization of three-dimensional crystal the several pronounced resonance frequencies were detected.
Two dimensional kicked quantum Ising model: dynamical phase transitions
International Nuclear Information System (INIS)
Pineda, C; Prosen, T; Villaseñor, E
2014-01-01
Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two-dimensional lattice, which is periodically driven by a δ-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality. (paper)
Infinite families of superintegrable systems separable in subgroup coordinates
International Nuclear Information System (INIS)
Lévesque, Daniel; Post, Sarah; Winternitz, Pavel
2012-01-01
A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials. (paper)
Is the Free Vacuum Energy Infinite?
International Nuclear Information System (INIS)
Shirazi, S. M.; Razmi, H.
2015-01-01
Considering the fundamental cutoff applied by the uncertainty relations’ limit on virtual particles’ frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the fourth power of the dimensional distance of the space under consideration and thus the corresponding vacuum energy automatically regularized to zero value for an infinitely large free space. This can be used in regularizing a number of unwanted infinities that happen in the Casimir effect, the cosmological constant problem, and so on without using already known mathematical (not so reasonable) techniques and tricks
International Nuclear Information System (INIS)
Doroshkevich, A.G.; Kotok, E.V.; Novikov, I.D.; Polyudov, A.N.; Shandarin, S.F.; Sigov, Y.S.
1980-01-01
The results of a numerical experiment are given that describe the non-linear stages of the development of perturbations in gravitating matter density in the expanding Universe. This process simulates the formation of the large-scale structure of the Universe from an initially almost homogeneous medium. In the one- and two-dimensional cases of this numerical experiment the evolution of the system from 4096 point masses that interact gravitationally only was studied with periodic boundary conditions (simulation of the infinite space). The initial conditions were chosen that resulted from the theory of the evolution of small perturbations in the expanding Universe. The results of numerical experiments are systematically compared with the approximate analytic theory. The results of the calculations show that in the case of collisionless particles, as well as in the gas-dynamic case, the cellular structure appeared at the non-linear stage in the case of the adiabatic perturbations. The greater part of the matter is in thin layers that separate vast regions of low density. In a Robertson-Walker universe the cellular structure exists for a finite time and then fragments into a few compact objects. In the open Universe the cellular structure also exists if the amplitude of initial perturbations is large enough. But the following disruption of the cellular structure is more difficult because of too rapid an expansion of the Universe. The large-scale structure is frozen. (author)
DEFF Research Database (Denmark)
Vendrell, Oriol; Gatti, Fabien; Meyer, Hans-Dieter
2007-01-01
The infrared absorption spectrum of the protonated water dimer (H5O2+) is simulated in full dimensionality (15 dimensional) in the spectral range of 0-4000 cm(-1). The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method for propagation of wavepackets. All...
Dirac and Weyl fermion dynamics on two-dimensional surface
International Nuclear Information System (INIS)
Kavalov, A.R.; Sedrakyan, A.G.; Kostov, I.K.
1986-01-01
Fermions on 2-dimensional surface, embedded into a 3-dimensional space are investigated. The determinant of induced Dirac operator for the Dirac and Weyl fermions is calculated. The reparametrization-invariant effective action is determined by conformal anomaly (giving Liouville action) and also by Lorentz anomaly leading to Wess-Zumino term, the structure of which at d=3 is determined by the Hopf topological invariant of the S 3 → S 2 map
Hsieh, K S; Lin, C C; Liu, W S; Chen, F L
1996-01-01
Two-dimensional echocardiography had long been a standard diagnostic modality for congenital heart disease. Further attempts of three-dimensional reconstruction using two-dimensional echocardiographic images to visualize stereotypic structure of cardiac lesions have been successful only recently. So far only very few studies have been done to display three-dimensional anatomy of the heart through two-dimensional image acquisition because such complex procedures were involved. This study introduced a recently developed image acquisition and processing system for dynamic three-dimensional visualization of various congenital cardiac lesions. From December 1994 to April 1995, 35 cases were selected in the Echo Laboratory here from about 3000 Echo examinations completed. Each image was acquired on-line with specially designed high resolution image grazmber with EKG and respiratory gating technique. Off-line image processing using a window-architectured interactive software package includes construction of 2-D ehcocardiographic pixel to 3-D "voxel" with conversion of orthogonal to rotatory axial system, interpolation, extraction of region of interest, segmentation, shading and, finally, 3D rendering. Three-dimensional anatomy of various congenital cardiac defects was shown, including four cases with ventricular septal defects, two cases with atrial septal defects, and two cases with aortic stenosis. Dynamic reconstruction of a "beating heart" is recorded as vedio tape with video interface. The potential application of 3D display of the reconstruction from 2D echocardiographic images for the diagnosis of various congenital heart defects has been shown. The 3D display was able to improve the diagnostic ability of echocardiography, and clear-cut display of the various congenital cardiac defects and vavular stenosis could be demonstrated. Reinforcement of current techniques will expand future application of 3D display of conventional 2D images.
Quantization of a Hamiltonian system with an infinite number of degrees of freedom
International Nuclear Information System (INIS)
Zhidkov, P.E.
1994-01-01
We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schroedinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. In the paper rigorous mathematical methods are used. 9 refs. (author)
Turnpike phenomenon and infinite horizon optimal control
Zaslavski, Alexander J
2014-01-01
This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value intergrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis, and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Resea...
Selfadjointness of the Liouville operator for infinite classical systems
Energy Technology Data Exchange (ETDEWEB)
Marchioro, C [Camerino Univ. (Italy). Istituto di Matematica; Pellegrinotti, A [Rome Univ. (Italy). Istituto di Matematica; Pulvirenti, M [Ancona Univ. (Italy). Istituto di Matematica
1978-02-01
We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed.
Selfadjointness of the Liouville operator for infinite classical systems
International Nuclear Information System (INIS)
Marchioro, C.; Pellegrinotti, A.; Pulvirenti, M.
1978-01-01
We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed. (orig.) [de
Zero Divisors in Associative Algebras over Infinite Fields
Schweitzer, Michael; Finch, Steven
1999-01-01
Let F be an infinite field. We prove that the right zero divisors of a three-dimensional associative F-algebra A must form the union of at most finitely many linear subspaces of A. The proof is elementary and written with students as the intended audience.
Cylindrical continuous martingales and stochastic integration in infinite dimensions
Veraar, M.C.; Yaroslavtsev, I.S.
2016-01-01
In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local
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
Semi-infinite fractional programming
Verma, Ram U
2017-01-01
This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research envi...
Quantitative hyperbolicity estimates in one-dimensional dynamics
International Nuclear Information System (INIS)
Day, S; Kokubu, H; Pilarczyk, P; Luzzatto, S; Mischaikow, K; Oka, H
2008-01-01
We develop a rigorous computational method for estimating the Lyapunov exponents in uniformly expanding regions of the phase space for one-dimensional maps. Our method uses rigorous numerics and graph algorithms to provide results that are mathematically meaningful and can be achieved in an efficient way
Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow
Gonzalez, M.
2018-04-01
The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.
Energy Technology Data Exchange (ETDEWEB)
Tahira, Rabia; Ikram, Manzoor; Zubairy, M Suhail [Centre for Quantum Physics, COMSATS Institute of Information Technology, Islamabad (Pakistan); Bougouffa, Smail [Department of Physics, Faculty of Science, Taibah University, PO Box 30002, Madinah (Saudi Arabia)
2010-02-14
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
International Nuclear Information System (INIS)
Tahira, Rabia; Ikram, Manzoor; Zubairy, M Suhail; Bougouffa, Smail
2010-01-01
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
Approximate Dynamic Programming Solving the Curses of Dimensionality
Powell, Warren B
2011-01-01
Praise for the First Edition "Finally, a book devoted to dynamic programming and written using the language of operations research (OR)! This beautiful book fills a gap in the libraries of OR specialists and practitioners."-Computing Reviews This new edition showcases a focus on modeling and computation for complex classes of approximate dynamic programming problems Understanding approximate dynamic programming (ADP) is vital in order to develop practical and high-quality solutions to complex industrial problems, particularly when those problems involve making decisions in the presence of unce
Three-dimensional reactor dynamics code for VVER type nuclear reactors
Energy Technology Data Exchange (ETDEWEB)
Kyrki-Rajamaeki, R. [VTT Energy, Espoo (Finland)
1995-10-01
A three-dimensional reactor dynamics computer code has been developed, validated and applied for transient and accident analyses of VVER type nuclear reactors. This code, HEXTRAN, is a part of the reactor physics and dynamics calculation system of the Technical Research Centre of Finland, VTT. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and the two-phase flow equations of hydraulics. It includes all the experience of VTT from 20 years on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics. The dynamic coupling with the thermal hydraulic system code SMABRE also allows the VVER circuit-modelling experience to be included in the analyses. (79 refs.).
Three-dimensional reactor dynamics code for VVER type nuclear reactors
International Nuclear Information System (INIS)
Kyrki-Rajamaeki, R.
1995-10-01
A three-dimensional reactor dynamics computer code has been developed, validated and applied for transient and accident analyses of VVER type nuclear reactors. This code, HEXTRAN, is a part of the reactor physics and dynamics calculation system of the Technical Research Centre of Finland, VTT. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and the two-phase flow equations of hydraulics. It includes all the experience of VTT from 20 years on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics. The dynamic coupling with the thermal hydraulic system code SMABRE also allows the VVER circuit-modelling experience to be included in the analyses. (79 refs.)
Truccolo, Wilson
2016-11-01
This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. Published by Elsevier Ltd.
Brane dynamics and four-dimensional quantum field theory
International Nuclear Information System (INIS)
Lambert, N.D.; West, P.C.
1999-01-01
We review the relation between the classical dynamics of the M-fivebrane and the quantum low energy effective action for N = 2 Yang-Mills theories. We also discuss some outstanding issues in this correspondence. (author)
Infinite time interval backward stochastic differential equations with continuous coefficients.
Zong, Zhaojun; Hu, Feng
2016-01-01
In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).
Infinite Spin Fields in d = 3 and Beyond
Directory of Open Access Journals (Sweden)
Yurii M. Zinoviev
2017-08-01
Full Text Available In this paper, we consider the frame-like formulation for the so-called infinite (continuous spin representations of the Poincare algebra. In the three-dimensional case, we give explicit Lagrangian formulation for bosonic and fermionic infinite spin fields (including the complete sets of the gauge-invariant objects and all the necessary extra fields. Moreover, we find the supertransformations for the supermultiplet containing one bosonic and one fermionic field, leaving the sum of their Lagrangians invariant. Properties of such fields and supermultiplets in four and higher dimensions are also briefly discussed.
Approximate dynamic programming solving the curses of dimensionality
Powell, Warren B
2007-01-01
Warren B. Powell, PhD, is Professor of Operations Research and Financial Engineering at Princeton University, where he is founder and Director of CASTLE Laboratory, a research unit that works with industrial partners to test new ideas found in operations research. The recipient of the 2004 INFORMS Fellow Award, Dr. Powell has authored over 100 refereed publications on stochastic optimization, approximate dynamic programming, and dynamic resource management.
Multi spin-flip dynamics: a solution of the one-dimensional Ising model
International Nuclear Information System (INIS)
Novak, I.
1990-01-01
The Glauber dynamics of interacting Ising spins (the single spin-flip dynamics) is generalized to p spin-flip dynamics with a simultaneous flip of up to p spins in a single configuration move. The p spin-flip dynamics is studied of the one-dimensional Ising model with uniform nearest-neighbour interaction. For this case, an exact relation is given for the time dependence of magnetization. It was found that the critical slowing down in this model could be avoided when p spin-flip dynamics with p>2 was considered. (author). 17 refs
Dynamics and Control of Three-Dimensional Perching Maneuver under Dynamic Stall Influence
Feroskhan, Mir Alikhan Bin Mohammad
Perching is a type of aggressive maneuver performed by the class 'Aves' species to attain precision point landing with a generally short landing distance. Perching capability is desirable on unmanned aerial vehicles (UAVs) due to its efficient deceleration process that potentially expands the functionality and flight envelope of the aircraft. This dissertation extends the previous works on perching, which is mostly limited to two-dimensional (2D) cases, to its state-of-the-art threedimensional (3D) variety. This dissertation presents the aerodynamic modeling and optimization framework adopted to generate unprecedented variants of the 3D perching maneuver that include the sideslip perching trajectory, which ameliorates the existing 2D perching concept by eliminating the undesirable undershoot and reliance on gravity. The sideslip perching technique methodically utilizes the lateral and longitudinal drag mechanisms through consecutive phases of yawing and pitching-up motion. Since perching maneuver involves high rates of change in the angles of attack and large turn rates, introduction of three internal variables thus becomes necessary for addressing the influence of dynamic stall delay on the UAV's transient post-stall behavior. These variables are then integrated into a static nonlinear aerodynamic model, developed using empirical and analytical methods, and into an optimization framework that generates a trajectory of sideslip perching maneuver, acquiring over 70% velocity reduction. An impact study of the dynamic stall influence on the optimal perching trajectories suggests that consideration of dynamic stall delay is essential due to the significant discrepancies in the corresponding control inputs required. A comparative study between 2D and 3D perching is also conducted to examine the different drag mechanisms employed by 2D and 3D perching respectively. 3D perching is presented as a more efficient deceleration technique with respect to spatial costs and
Automated Analysis of Infinite Scenarios
DEFF Research Database (Denmark)
Buchholtz, Mikael
2005-01-01
The security of a network protocol crucially relies on the scenario in which the protocol is deployed. This paper describes syntactic constructs for modelling network scenarios and presents an automated analysis tool, which can guarantee that security properties hold in all of the (infinitely many...
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
Gini estimation under infinite variance
A. Fontanari (Andrea); N.N. Taleb (Nassim Nicholas); P. Cirillo (Pasquale)
2018-01-01
textabstractWe study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α∈(1,2)). We show that, in such a case, the Gini coefficient
Algebra of orthofermions and equivalence of their thermodynamics to the infinite U Hubbard model
International Nuclear Information System (INIS)
Kishore, R.; Mishra, A.K.
2006-01-01
The equivalence of thermodynamics of independent orthofermions to the infinite U Hubbard model, shown earlier for the one-dimensional infinite lattice, has been extended to a finite system of two lattice sites. Regarding the algebra of orthofermions, the algebraic expressions for the number operator for a given spin and the spin raising (lowering) operators in the form of infinite series are rearranged in such a way that the ith term, having the form of an infinite series, of the number (spin raising (lowering)) operator represents the number (spin raising (lowering)) operator at the ith lattice site
Cui, Yiqian; Shi, Junyou; Wang, Zili
2017-11-01
Built-in tests (BITs) are widely used in mechanical systems to perform state identification, whereas the BIT false and missed alarms cause trouble to the operators or beneficiaries to make correct judgments. Artificial neural networks (ANN) are previously used for false and missed alarms identification, which has the features such as self-organizing and self-study. However, these ANN models generally do not incorporate the temporal effect of the bottom-level threshold comparison outputs and the historical temporal features are not fully considered. To improve the situation, this paper proposes a new integrated BIT design methodology by incorporating a novel type of dynamic neural networks (DNN) model. The new DNN model is termed as Forward IIR & Recurrent FIR DNN (FIRF-DNN), where its component neurons, network structures, and input/output relationships are discussed. The condition monitoring false and missed alarms reduction implementation scheme based on FIRF-DNN model is also illustrated, which is composed of three stages including model training, false and missed alarms detection, and false and missed alarms suppression. Finally, the proposed methodology is demonstrated in the application study and the experimental results are analyzed.
Confinement and dynamical regulation in two-dimensional convective turbulence
DEFF Research Database (Denmark)
Bian, N.H.; Garcia, O.E.
2003-01-01
In this work the nature of confinement improvement implied by the self-consistent generation of mean flows in two-dimensional convective turbulence is studied. The confinement variations are linked to two distinct regulation mechanisms which are also shown to be at the origin of low......-frequency bursting in the fluctuation level and the convective heat flux integral, both resulting in a state of large-scale intermittency. The first one involves the control of convective transport by sheared mean flows. This regulation relies on the conservative transfer of kinetic energy from tilted fluctuations...
Perturbations of dynamics of homogeneous two-dimensional cellular automata
Energy Technology Data Exchange (ETDEWEB)
Makowiec, D [Gdansk Univ. (Poland)
1993-04-01
The probabilistic approach provides a useful tool for understanding the nature of dynamics of cellular automata. It allows not only clarification of different results of the evolution but also gives explanation to the physical meaning of the rules. (author). 11 refs, 4 figs.
Counting and classifying attractors in high dimensional dynamical systems.
Bagley, R J; Glass, L
1996-12-07
Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.
Bayesian Inference of High-Dimensional Dynamical Ocean Models
Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.
2015-12-01
This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.
Nambu-Poisson reformulation of the finite dimensional dynamical systems
International Nuclear Information System (INIS)
Baleanu, D.; Makhaldiani, N.
1998-01-01
A system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system is introduced. We found in two simplest cases the complete sets of the integrals of motion using Nambu-Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures
Dynamics of a two-dimensional order-disorder transition
International Nuclear Information System (INIS)
Sahni, P.S.; Dee, G.; Gunton, J.D.; Phani, M.; Lebowitz, J.L.; Kalos, M.
1981-01-01
We present results of a Monte Carlo study of the time development of a two-dimensional order-disorder model binary alloy following a quench to low temperature from a disordered, high-temperature state. The behavior is qualitatively quite similar to that seen in a recent study of a three-dimensional system. The structure function exhibits a scaling of the form K 2 (t)S(k,t) = G(k/K(t)) where the moment K(t) decreases with time approximately like t/sup -1/2/. If one interprets this moment as being inversely proportional to the domain size, the characteristic domain growth rate is proportional to t/sup -1/2/. Additional insight into this time evolution is obtained from studying the development of the short-range order, as well as from monitoring the growth of a compact ordered domain embedded in a region of opposite order. All these results are consistent with the picture of domain growth as proposed by Lifshitz and by Cahn and Allen
Intense field stabilization in circular polarization: Three-dimensional time-dependent dynamics
International Nuclear Information System (INIS)
Choi, Dae-Il; Chism, Will
2002-01-01
We investigate the stabilization of hydrogen atoms in a circularly polarized laser field. We use a three-dimensional, time-dependent approach to study the quantum dynamics of hydrogen atoms subject to high-intensity, short-wavelength, laser pulses. We find an enhanced survival probability as the field is increased under fixed envelope conditions. We also confirm wave packet behaviors previously seen in two-dimensional time-dependent computations
Approximate Dynamic Programming Based on High Dimensional Model Representation
Czech Academy of Sciences Publication Activity Database
Pištěk, Miroslav
2013-01-01
Roč. 49, č. 5 (2013), s. 720-737 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP102/11/0437 Institutional support: RVO:67985556 Keywords : approximate dynamic programming * Bellman equation * approximate HDMR minimization * trust region problem Subject RIV: BC - Control Systems Theory Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/pistek-0399560.pdf
The dynamical structure of higher dimensional Chern-Simons theory
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G x U(1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion. (orig.)
Cortical dynamics of three-dimensional figure-ground perception of two-dimensional pictures.
Grossberg, S
1997-07-01
This article develops the FACADE theory of 3-dimensional (3-D) vision and figure-ground separation to explain data concerning how 2-dimensional pictures give rise to 3-D percepts of occluding and occluded objects. The model describes how geometrical and contrastive properties of a picture can either cooperate or compete when forming the boundaries and surface representation that subserve conscious percepts. Spatially long-range cooperation and spatially short-range competition work together to separate the boundaries of occluding figures from their occluded neighbors. This boundary ownership process is sensitive to image T junctions at which occluded figures contact occluding figures. These boundaries control the filling-in of color within multiple depth-sensitive surface representations. Feedback between surface and boundary representations strengthens consistent boundaries while inhibiting inconsistent ones. Both the boundary and the surface representations of occluded objects may be amodally completed, while the surface representations of unoccluded objects become visible through modal completion. Functional roles for conscious modal and amodal representations in object recognition, spatial attention, and reaching behaviors are discussed. Model interactions are interpreted in terms of visual, temporal, and parietal cortices.
Dynamical properties of magnetized two-dimensional one-component plasma
Dubey, Girija S.; Gumbs, Godfrey; Fessatidis, Vassilios
2018-05-01
Molecular dynamics simulation are used to examine the effect of a uniform perpendicular magnetic field on a two-dimensional interacting electron system. In this simulation we include the effect of the magnetic field classically through the Lorentz force. Both the Coulomb and the magnetic forces are included directly in the electron dynamics to study their combined effect on the dynamical properties of the 2D system. Results are presented for the velocity autocorrelation function and the diffusion constants in the presence and absence of an external magnetic field. Our simulation results clearly show that the external magnetic field has an effect on the dynamical properties of the system.
Directory of Open Access Journals (Sweden)
Marshall Naylor
2018-01-01
Full Text Available Prominent approaches to the problems of evil assume that even if the Anselmian God exists, some worlds are better than others, all else being equal. But the assumptions that the Anselmian God exists and that some worlds are better than others cannot be true together. One description, by Mark Johnston and Georg Cantor, values God’s existence as exceeding any transfinite cardinal value. For any finite or infinite amount of goodness in any possible world, God’s value infinitely exceeds that amount. This conception is not obviously inconsistent with the Anselmian God. As a result, the prominent approaches to the problems of evil are mistaken. The elimination of evil does not, in fact, improve the value of any world as commonly thought. Permitting evil does not, in fact, diminish the value of any world as commonly thought.
Agravity up to infinite energy
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [CERN, Theoretical Physics Department, Geneva (Switzerland); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); INFN, Pisa (Italy)
2018-02-15
The self-interactions of the conformal mode of the graviton are controlled, in dimensionless gravity theories (agravity), by a coupling f{sub 0} that is not asymptotically free. We show that, nevertheless, agravity can be a complete theory valid up to infinite energy. When f{sub 0} grows to large values, the conformal mode of the graviton decouples from the rest of the theory and does not hit any Landau pole provided that scalars are asymptotically conformally coupled and all other couplings approach fixed points. Then agravity can flow to conformal gravity at infinite energy. We identify scenarios where the Higgs mass does not receive unnaturally large physical corrections. We also show a useful equivalence between agravity and conformal gravity plus two extra conformally coupled scalars, and we give a simpler form for the renormalization group equations of dimensionless couplings as well as of massive parameters in the presence of the most general matter sector. (orig.)
Lizana, L; Ambjörnsson, T
2009-11-01
We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rhoT(yT,t|yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N -particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T , we arrive at an exact expression for rhoT(yT,t|yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N , maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rhoT(yT,t|yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time tparticle concentration and D is the diffusion constant for each particle, the tagged particle undergoes a normal diffusion; (B) for times much larger than the collision time t >taucoll but times smaller than the equilibrium time ttaue , rhoT(yT,t|yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.
On Landauer's Principle and Bound for Infinite Systems
Longo, Roberto
2018-04-01
Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. Here we set up a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view. By the Tomita-Takesaki modular theory, we can indeed describe a canonical evolution associated with a quantum channel state transfer. Such evolution is implemented both by a modular Hamiltonian and a physical Hamiltonian, the latter being determined by its functoriality properties. This allows us to make an intrinsic analysis, extending our QFT index formula, but without any a priori given dynamics; the associated incremental free energy is related to the logarithm of the Jones index and is thus quantised. This leads to a general lower bound for the incremental free energy of an irreversible quantum channel which is half of the Landauer bound, and to further bounds corresponding to the discrete series of the Jones index. In the finite dimensional context, or in the case of DHR charges in QFT, where the dimension is a positive integer, our lower bound agrees with Landauer's bound.
Infinite games with uncertain moves
Directory of Open Access Journals (Sweden)
Nicholas Asher
2013-03-01
Full Text Available We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore what happens to sets in various levels of the Borel hierarchy under such a situation. We show that the sets at every alternate level of the hierarchy jump to the next higher level.
Hole growth dynamics in a two dimensional Leidenfrost droplet
Raufaste, Christophe; Celestini, Franck; Barzyk, Alexandre; Frisch, Thomas
2015-03-01
We studied the behaviors of Leidenfrost droplets confined in a Hele-Shaw cell. These droplets are unstable above a critical size and a hole grows at their center. We experimentally investigate two different systems for which the hole growth dynamics exhibits peculiar features that are driven by capillarity and inertia. We report a first regime characterized by the liquid reorganization from a liquid sheet to a liquid torus with similarities to the burst of micron-thick soap films. In the second regime, the liquid torus expands and thins before fragmentation. Finally, we propose models to account for the experimental results.
Semi-infinite assignment and transportation games
Timmer, Judith B.; Sánchez-Soriano, Joaqu´ın; Llorca, Navidad; Tijs, Stef; Goberna, Miguel A.; López, Marco A.
2001-01-01
Games corresponding to semi-infinite transportation and related assignment situations are studied. In a semi-infinite transportation situation, one aims at maximizing the profit from the transportation of a certain good from a finite number of suppliers to an infinite number of demanders. An
On infinite regular and chiral maps
Arredondo, John A.; Valdez, Camilo Ramírez y Ferrán
2015-01-01
We prove that infinite regular and chiral maps take place on surfaces with at most one end. Moreover, we prove that an infinite regular or chiral map on an orientable surface with genus can only be realized on the Loch Ness monster, that is, the topological surface of infinite genus with one end.
3-Dimensional simulations of storm dynamics on Saturn
Hueso, R.; Sanchez-Lavega, A.
2000-10-01
The formation and evolution of convective clouds in the atmosphere of Saturn is investigated using an anelastic three-dimensional time-dependent model with parameterized microphysics. The model is designed to study the development of moist convection on any of the four giant planets and has been previously used to investigate the formation of water convective storms in the jovian atmosphere. The role of water and ammonia in moist convection is investigated with varying deep concentrations. Results imply that most of the convective activity observed at Saturn may occur at the ammonia cloud deck while the formation of water moist convection may happen only when very strong constraints on the lower troposphere are met. Ammonia storms can ascend to the 300 mb level with vertical velocities around 30 ms-1. The seasonal effect on the thermal profile at the upper troposphere may have important effects on the development of ammonia storms. In the cases where water storms can develop they span many scale heights with peak vertical velocities around 160 ms-1 and cloud particles can be transported up to the 150 mb level. These predicted characteristics are similar to the Great White Spots observed in Saturn which, therefore, could be originated at the water cloud base level. This work has been supported by Gobierno Vasco PI 1997-34. R. Hueso acknowledges a PhD fellowship from Gobierno Vasco.
Topological phase transition in the quench dynamics of a one-dimensional Fermi gas
Wang, Pei; Yi, Wei; Xianlong, Gao
2014-01-01
We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of t...
Krivov, Sergei V
2011-07-01
Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game--the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.
Patriarca, M.; Kuronen, A.; Robles, M.; Kaski, K.
2007-01-01
The study of crystal defects and the complex processes underlying their formation and time evolution has motivated the development of the program ALINE for interactive molecular dynamics experiments. This program couples a molecular dynamics code to a Graphical User Interface and runs on a UNIX-X11 Window System platform with the MOTIF library, which is contained in many standard Linux releases. ALINE is written in C, thus giving the user the possibility to modify the source code, and, at the same time, provides an effective and user-friendly framework for numerical experiments, in which the main parameters can be interactively varied and the system visualized in various ways. We illustrate the main features of the program through some examples of detection and dynamical tracking of point-defects, linear defects, and planar defects, such as stacking faults in lattice-mismatched heterostructures. Program summaryTitle of program:ALINE Catalogue identifier:ADYJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYJ_v1_0 Program obtainable from: CPC Program Library, Queen University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers:DEC ALPHA 300, Intel i386 compatible computers, G4 Apple Computers Installations:Laboratory of Computational Engineering, Helsinki University of Technology, Helsinki, Finland Operating systems under which the program has been tested:True64 UNIX, Linux-i386, Mac OS X 10.3 and 10.4 Programming language used:Standard C and MOTIF libraries Memory required to execute with typical data:6 Mbytes but may be larger depending on the system size No. of lines in distributed program, including test data, etc.:16 901 No. of bytes in distributed program, including test data, etc.:449 559 Distribution format:tar.gz Nature of physical problem:Some phenomena involving defects take place inside three-dimensional crystals at times which can be hardly predicted. For this reason they are
Murad-Regadas, S M; Regadas, F S P; Barreto, R G L; Rodrigues, L V; de Souza, M H L P
2009-10-01
The aim of this prospective study was to test two-dimensional dynamic anorectal ultrasonography (2D-DAUS) in the assessment of anismus and compare it with echodefecography (ECD). Fifty consecutive female patients with outlet delay were submitted to 2D and 3D-DAUS, measuring the relaxing or contracting puborectalis muscle angle during straining. The patients were assigned to one of two groups based on ECD findings. Group I consisted of 29 patients without anismus and group II included 21 patients diagnosed with anismus. Subsequently 2D-DAUS images were checked for anismus and compared with ECD findings. Upon straining, the angle produced by the movement of the puborectalis muscle decreased in 26 out of the 29 (89.6%) patients of group I and increased 19 out of the 21 (90.4%) patients of group II. The mean angle during straining differed significantly between group I and group II. The index of agreement between the two scanning modes was 89.6% (26/29) for group I (Kappa: 0.796; CI: 95%; range: 0.51-1.0) and 90.4% (19/21) for group II (Kappa: 0.796; CI: 95%; range: 0.51-1.0). Two-dimensional dynamic anal ultrasonography can be used as an alternative method to assess patients with anismus, although the 3-D modality is more precise to evaluate the PR angle as the sphincters integrity as the whole muscle length is clearly visualized.
International Nuclear Information System (INIS)
Brunie, L.
1992-12-01
The object of this thesis is to put in correspondence images coming from different ways. The area of application is biomedical imaging, particularly dynamic imaging in three dimensional calculations of spinal cord. The use of computers allows modeling. Then a study of validation by clinical experimentation on spinal cord proves the efficiency of the simulation
DEFF Research Database (Denmark)
Hvam, Jørn Märcher; Langbein, Wolfgang; Borri, Paola
1999-01-01
Coherent optical spectroscopy in the form of nonlinear transient four-wave mixing (TFWM) and linear resonant Rayleigh scattering (RRS) has been applied to investigate the exciton dynamics of low-dimensional semiconductor heterostructures. The dephasing times of excitons are determined from...
Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics
Gaudillière, A.; Hollander, den W.Th.F.; Nardi, F.R.; Olivieri, E.; Scoppola, E.
2009-01-01
In this paper we consider a two-dimensional lattice gas under Kawasaki dynamics, i.e., particles hop around randomly subject to hard-core repulsion and nearest-neighbor attraction. We show that, at fixed temperature and in the limit as the particle density tends to zero, such a gas evolves in a way
Dynamic Three-Dimensional Geometry of the Aortic Valve Apparatus-A Feasibility Study
Khamooshian, Arash; Amador, Yannis; Hai, Ting; Jeganathan, Jelliffe; Saraf, Maria; Mahmood, Eitezaz; Matyal, Robina; Khabbaz, Kamal R.; Mariani, Massimo; Mahmood, Feroze
OBJECTIVE: To provide (1) an overview of the aortic valve (AV) apparatus anatomy and nomenclature, and (2) data regarding the normal AV apparatus geometry and dynamism during the cardiac cycle obtained from three-dimensional transesophageal echocardiography (3D TEE). DESIGN: Retrospective
Dynamic model of organic pollutant degradation in three dimensional packed bed electrode reactor.
Pang, Tianting; Wang, Yan; Yang, Hui; Wang, Tianlei; Cai, Wangfeng
2018-04-21
A dynamic model of semi-batch three-dimensional electrode reactor was established based on the limiting current density, Faraday's law, mass balance and a series of assumptions. Semi-batch experiments of phenol degradation were carried out in a three-dimensional electrode reactor packed with activated carbon under different conditions to verify the model. The factors such as the current density, the electrolyte concentration, the initial pH value, the flow rate of organic and the initial organic concentration were examined to know about the pollutant degradation in the three-dimensional electrode reactor. The various concentrations and logarithm of concentration of phenol with time were compared with the dynamic model. It was shown that the calculated data were in good agreement with experimental data in most cases. Copyright © 2018 Elsevier Ltd. All rights reserved.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
Energy Technology Data Exchange (ETDEWEB)
Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Shiro, Masanori [Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan); Takahashi, Nozomu; Mas, Paloma [Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193 (Spain)
2015-01-15
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
International Nuclear Information System (INIS)
Hirata, Yoshito; Aihara, Kazuyuki; Suzuki, Hideyuki; Shiro, Masanori; Takahashi, Nozomu; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data
Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Three-Dimensional Dynamics of Baroclinic Tides Over a Seamount
Vlasenko, Vasiliy; Stashchuk, Nataliya; Nimmo-Smith, W. Alex M.
2018-02-01
The Massachusetts Institute of Technology general circulation model is used for the analysis of baroclinic tides over Anton Dohrn Seamount (ADS), in the North Atlantic. The model output is validated against in situ data collected during the 136th cruise of the RRS "James Cook" in May-June 2016. The observational data set includes velocity time series recorded at two moorings as well as temperature, salinity, and velocity profiles collected at 22 hydrological stations. Synthesis of observational and model data enabled the reconstruction of the details of baroclinic tidal dynamics over ADS. It was found that the baroclinic tidal waves are generated in the form of tidal beams radiating from the ADS periphery to its center, focusing tidal energy in a surface layer over the seamount's summit. This energy focusing enhances subsurface water mixing and the local generation of internal waves. The tidal beams interacting with the seasonal pycnocline generate short-scale internal waves radiating from the ADS center. An important ecological outcome from this study concerns the pattern of residual currents generated by tides. The rectified flows over ADS have the form of a pair of dipoles, cyclonic and anticyclonic eddies located at the seamount's periphery. These eddies are potentially an important factor in local larvae dispersion and their escape from ADS.
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
Dimensionality crossover in vortex dynamics of magnetically coupled F-S-F hybrids
International Nuclear Information System (INIS)
Karapetrov, G; Belkin, A; Iavarone, M; Yefremenko, V; Pearson, J E; Novosad, V; Divan, R; Cambel, V
2011-01-01
We report on the vortex dynamics in magnetically coupled F-S-F trilayers extracted from the analysis of the resistance-current isotherms. The superconducting thin film that is conventionally in the 2D vortex limit exhibits quite different behavior when sandwiched between ferromagnetic layers. The value of the dynamic critical exponent strongly increases in the F-S-F case due to screening of the stray vortex field by the adjacent ferromagnetic layers, leading to an effective dimensional crossover in vortex dynamics. Furthermore, the directional pinning by the magnetic stripe domains induces anisotropy in the vortex glass transition temperature and causes metastable avalanche behavior at strong driving currents.
Newton's law in braneworlds with an infinite extra dimension
Ito, Masato
2001-01-01
We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.
Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models
Martin Burda; Artem Prokhorov
2012-01-01
Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling scenarios. In economics, they have been particularly useful in estimating nonparametric distributions of latent variables. However, these models have been rarely applied in more than one dimension. Indeed, the multivariate case suffers from the curse of dimensionality, with a rapidly increas...
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...... of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped...... narrow spikes. The influence of the point impurities on this dynamics is also investigated....
Compactified cosmological simulations of the infinite universe
Rácz, Gábor; Szapudi, István; Csabai, István; Dobos, László
2018-06-01
We present a novel N-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically projected cosmological simulations. It uses stereographic projection for space compactification and naive O(N^2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 running matching initial conditions.
Compactified Cosmological Simulations of the Infinite Universe
Rácz, Gábor; Szapudi, István; Csabai, István; Dobos, László
2018-03-01
We present a novel N-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically Projected Cosmological Simulations. It uses stereographic projection for space compactification and naive O(N^2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 running matching initial conditions.
Gils, S; Hoveijn, I; Takens, F; Nonlinear Dynamical Systems and Chaos
1996-01-01
Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
An algorithm for engineering regime shifts in one-dimensional dynamical systems
Tan, James P. L.
2018-01-01
Regime shifts are discontinuous transitions between stable attractors hosting a system. They can occur as a result of a loss of stability in an attractor as a bifurcation is approached. In this work, we consider one-dimensional dynamical systems where attractors are stable equilibrium points. Relying on critical slowing down signals related to the stability of an equilibrium point, we present an algorithm for engineering regime shifts such that a system may escape an undesirable attractor into a desirable one. We test the algorithm on synthetic data from a one-dimensional dynamical system with a multitude of stable equilibrium points and also on a model of the population dynamics of spruce budworms in a forest. The algorithm and other ideas discussed here contribute to an important part of the literature on exercising greater control over the sometimes unpredictable nature of nonlinear systems.
Rhythmic dynamics and synchronization via dimensionality reduction: application to human gait.
Directory of Open Access Journals (Sweden)
Jie Zhang
Full Text Available Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system.
Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model
Reid, Daniel A. P.; Hildenbrandt, H.; Hemelrijk, C. K.; Padding, J.T.
2012-01-01
The fluid dynamics of animal locomotion, such as that of an undulating fish, are of great interest to both biologists and engineers. However, experimentally studying these fluid dynamics is difficult and time consuming. Model studies can be of great help because of their simpler and more detailed
International Nuclear Information System (INIS)
Sarmento, E.F.
1981-01-01
Results are found for the dynamical correlation functions (or its corresponding Green's functions) among any combination including operator pairs of electronic and nuclear spins in an antiferromagnet semi-infinite medium, at low temperatures T [pt
Directory of Open Access Journals (Sweden)
David T. Williams
1995-03-01
Full Text Available The idea of the infinity of God has recently come under pressure due to the modern world-view, and due to the difficulty of proving the doctrine. However, the idea of the infinite, as qualitatively different from the merely very large, has properties which may be applied to some traditional difficulties in Christian theology, such as the ideas of the Trinity and the Incarnation, particularly in regard to the limitation and subordination of the Son. Predication of infinity to God may then make the doctrine of God more comprehensible and rational At the same time, however, this has implications fo r the nature of God, particularly in his relation to the material and to time. Not to be overlooked is the value of the idea from a pastoral perspective.
Study of fission dynamics with the three-dimensional Langevin equations
Energy Technology Data Exchange (ETDEWEB)
Eslamizadeh, H. [Persian Gulf University, Department of Physics, Bushehr (Iran, Islamic Republic of)
2011-11-15
The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei {sup 210}Po and {sup 224}Th formed in the fusion-fission reactions {sup 4}He+{sup 206}Pb, {sup 16}O+{sup 208}Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data. (orig.)
Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system
International Nuclear Information System (INIS)
He Zhizhu; Liu, Jing
2010-01-01
This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.
Self-diffusion in monodisperse three-dimensional magnetic fluids by molecular dynamics simulations
Energy Technology Data Exchange (ETDEWEB)
Dobroserdova, A.B. [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); Kantorovich, S.S., E-mail: alla.dobroserdova@urfu.ru [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); University of Vienna, Sensengasse 8, Vienna (Austria)
2017-06-01
In the present work we study the self-diffusion behaviour in the three-dimensional monodisperse magnetic fluids using the Molecular Dynamics Simulation and Density Functional Theory. The peculiarity of computer simulation is to study two different systems: dipolar and soft sphere ones. In the theoretical method, it is important to choose the approximation for the main structures, which are chains. We compare the theoretical results and the computer simulation data for the self-diffusion coefficient as a function of the particle volume fraction and magnetic dipole-dipole interaction parameter and find the qualitative and quantitative agreement to be good. - Highlights: • The paper deals with the study of the self-diffusion in monodisperse three-dimensional magnetic fluids. • The theoretical approach contains the free energy density functional minimization. • Computer simulations are performed by the molecular dynamics method. • We have a good qualitative and quantitative agreement between the theoretical results and computer simulation data.
Non-equilibrium coherence dynamics in one-dimensional Bose gases
DEFF Research Database (Denmark)
Hofferberth, S.; Lesanovsky, Igor; Fischer, B.
2007-01-01
Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However......, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide...... range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena....
Three-dimensional display and measurement of cardiac dynamic indexes from MR images
International Nuclear Information System (INIS)
Kono, M.; Matsuo, M.; Yamasaki, K.; Banno, T.; Toriwaki, J.; Yokoi, S.; Oshita, H.
1986-01-01
The cardiac dynamic index, to which such variables as cardiac output, ejection fraction, and wall motion contribute, is routinely determined using various modalities such as angiography, radionuclide imaging, US, and x-ray CT. Each of these modalities, however, has some disadvantages in regard to evaluating the cardiac dynamic index. The authors have obtained precise multidirectional projection images of the heart by means of computer graphics and reformatted data of cardiac MR images obtained with cardiac gating. The contiguous coronal MR images of the heart are made at an interimage distance of 5 mm. In each section, five or six cardiac images can be obtained, depending on the systolic or diastolic phase. These images are stored in a computer, and a three-dimensional display of the heart with biocular observation and with multiplex holograms is made possible with computer graphics. Three-dimensional measurement of the cardiac index is now being attempted, including cardiac output, ejection fraction, and wall motion
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
Hărăguş-Courcelle, M.; Schneider, G.
We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.
Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz
Directory of Open Access Journals (Sweden)
Jan C. Zill, Tod M. Wright, Karen V. Kheruntsyan, Thomas Gasenzer, Matthew J. Davis
2018-02-01
Full Text Available We use the coordinate Bethe ansatz to study the Lieb-Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.
Signatures of chaos and non-integrability in two-dimensional gravity with dynamical boundary
Directory of Open Access Journals (Sweden)
Fitkevich Maxim
2016-01-01
Full Text Available We propose a model of two-dimensional dilaton gravity with a boundary. In the bulk our model coincides with the classically integrable CGHS model; the dynamical boundary cuts of the CGHS strong-coupling region. As a result, classical dynamics in our model reminds that in the spherically-symmetric gravity: wave packets of matter fields either reflect from the boundary or form black holes. We find large integrable sector of multisoliton solutions in this model. At the same time, we argue that the model is globally non-integrable because solutions at the verge of black hole formation display chaotic properties.
Study of journal bearing dynamics using 3-dimensional motion picture graphics
Brewe, D. E.; Sosoka, D. J.
1985-01-01
Computer generated motion pictures of three dimensional graphics are being used to analyze journal bearings under dynamically loaded conditions. The motion pictures simultaneously present the motion of the journal and the pressures predicted within the fluid film of the bearing as they evolve in time. The correct prediction of these fluid film pressures can be complicated by the development of cavitation within the fluid. The numerical model that is used predicts the formation of the cavitation bubble and its growth, downstream movement, and subsequent collapse. A complete physical picture is created in the motion picture as the journal traverses through the entire dynamic cycle.
The magnetic flux dynamics in the critical state of one-dimensional discrete superconductor
International Nuclear Information System (INIS)
Ginzburg, S.L.; Nakin, A.V.; Savitskaya, N.E.
2006-01-01
We give a theoretical description of avalanche-like dynamics of magnetic flux in the critical state of discrete superconductors using a one-dimensional model of a multijunction SQUID. We show that the system under consideration demonstrates the self-organized criticality. The avalanches of vortices manifest themselves as jumps of the total magnetic flux in the sample. The sizes of these jumps have a power-law distribution. We argue that similarities in the behavior of discrete and usual type-II superconductors allows to extend our results for description of avalanche-like dynamics in type-II superconductors with strong pinning
Non-equilibrium coherence dynamics in one-dimensional Bose gases.
Hofferberth, S; Lesanovsky, I; Fischer, B; Schumm, T; Schmiedmayer, J
2007-09-20
Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.
Energy Technology Data Exchange (ETDEWEB)
Kohnert, Aaron A.; Wirth, Brian D. [University of Tennessee, Knoxville, Tennessee 37996-2300 (United States)
2015-04-21
The black dot damage features which develop in iron at low temperatures exhibit significant mobility during in situ irradiation experiments via a series of discrete, intermittent, long range hops. By incorporating this mobility into cluster dynamics models, the temperature dependence of such damage structures can be explained with a surprising degree of accuracy. Such motion, however, is one dimensional in nature. This aspect of the physics has not been fully considered in prior models. This article describes one dimensional reaction kinetics in the context of cluster dynamics and applies them to the black dot problem. This allows both a more detailed description of the mechanisms by which defects execute irradiation-induced hops while allowing a full examination of the importance of kinetic assumptions in accurately assessing the development of this irradiation microstructure. Results are presented to demonstrate whether one dimensional diffusion alters the dependence of the defect population on factors such as temperature and defect hop length. Finally, the size of interstitial loops that develop is shown to depend on the extent of the reaction volumes between interstitial clusters, as well as the dimensionality of these interactions.
Exactly integrable two-dimensional dynamical systems related with supersymmetric algebras
International Nuclear Information System (INIS)
Leznov, A.N.
1983-01-01
A wide class of exactly integrable dynamical systems in two-dimensional space related with superalgebras, which generalize supersymmetric Liouville equation, is constructed. The equations can be interpretated as nonlinearly interacting Bose and Fermi fields belonging within classical limit to even and odd parts of the Grassman space. Explicit expressions for the solutions of the constructed systems are obtained on the basis of standard perturbation theory
Sirmas, Nick; Radulescu, Matei I.
2016-01-01
The problem of thermal ignition in a homogeneous gas is revisited from a molecular dynamics perspective. A two-dimensional model is adopted, which assumes reactive disks of type A and B in a fixed area that react to form type C products if an activation threshold for impact is surpassed. Such a reaction liberates kinetic energy to the product particles, representative of the heat release. The results for the ignition delay are compared with those obtained from the continuum description assumi...
International Nuclear Information System (INIS)
Moura, A.R.; Pereira, A.R.; Moura-Melo, W.A.; Pires, A.S.T.
2008-01-01
We develop an effective theory to study the skyrmion dynamics in the presence of a hole (removed spins from the lattice) in Neel ordered two-dimensional antiferromagnets with arbitrary spin value S. The general equation of motion for the 'mass center' of this structure is obtained. The frequency of small amplitude oscillations of pinned skyrmions around the defect center is calculated. It is proportional to the hole size and inversely proportional to the square of the skyrmion size
International Nuclear Information System (INIS)
Taguchi, K; Okada, J; Nomura, Y; Tamura, K
2012-01-01
In this paper, chemically etched fiber probe was proposed for laser trapping and manipulation of cells. We fabricated tapered fiber probe by dynamic chemical etching technique. Three-Dimensional optical trap of a yeast cell dispersed in water solution could be formed by the fiber tip with 17deg tip. Optical forces were sufficient to move the yeast cell for trapping and manipulation. From these experimental results, it was found that our proposed tapered fiber tip was a promising tool for cell isolation.
Ghosts in high dimensional non-linear dynamical systems: The example of the hypercycle
International Nuclear Information System (INIS)
Sardanyes, Josep
2009-01-01
Ghost-induced delayed transitions are analyzed in high dimensional non-linear dynamical systems by means of the hypercycle model. The hypercycle is a network of catalytically-coupled self-replicating RNA-like macromolecules, and has been suggested to be involved in the transition from non-living to living matter in the context of earlier prebiotic evolution. It is demonstrated that, in the vicinity of the saddle-node bifurcation for symmetric hypercycles, the persistence time before extinction, T ε , tends to infinity as n→∞ (being n the number of units of the hypercycle), thus suggesting that the increase in the number of hypercycle units involves a longer resilient time before extinction because of the ghost. Furthermore, by means of numerical analysis the dynamics of three large hypercycle networks is also studied, focusing in their extinction dynamics associated to the ghosts. Such networks allow to explore the properties of the ghosts living in high dimensional phase space with n = 5, n = 10 and n = 15 dimensions. These hypercyclic networks, in agreement with other works, are shown to exhibit self-maintained oscillations governed by stable limit cycles. The bifurcation scenarios for these hypercycles are analyzed, as well as the effect of the phase space dimensionality in the delayed transition phenomena and in the scaling properties of the ghosts near bifurcation threshold
Strong Coupling Dynamics of Four-Dimensional N=1 Gauge Theories from M Theory Fivebrane
International Nuclear Information System (INIS)
Hori, K.; Ooguri, H.; Oz, Y.
1997-01-01
It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N c ) gauge group and N f quarks. For N c > N f , we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N c and f , we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N c = N f . We also prove the type II s-rule in M theory and find new non-renormalization theorems for N = 1 superpotentials
International Nuclear Information System (INIS)
Kornreich, D.E.; Ganapol, B.D.
1997-01-01
The linear Boltzmann equation for the transport of neutral particles is investigated with the objective of generating benchmark-quality evaluations of solutions for homogeneous infinite media. In all cases, the problems are stationary, of one energy group, and the scattering is isotropic. The solutions are generally obtained through the use of Fourier transform methods with the numerical inversions constructed from standard numerical techniques such as Gauss-Legendre quadrature, summation of infinite series, and convergence acceleration. Consideration of the suite of benchmarks in infinite homogeneous media begins with the standard one-dimensional problems: an isotropic point source, an isotropic planar source, and an isotropic infinite line source. The physical and mathematical relationships between these source configurations are investigated. The progression of complexity then leads to multidimensional problems with source configurations that also emit particles isotropically: the finite line source, the disk source, and the rectangular source. The scalar flux from the finite isotropic line and disk sources will have a two-dimensional spatial variation, whereas a finite rectangular source will have a three-dimensional variation in the scalar flux. Next, sources emitting particles anisotropically are considered. The most basic such source is the point beam giving rise to the Green's function, which is physically the most fundamental transport problem, yet may be constructed from the isotropic point source solution. Finally, the anisotropic plane and anisotropically emitting infinite line sources are considered. Thus, a firm theoretical and numerical base is established for the most fundamental neutral particle benchmarks in infinite homogeneous media
Statistical inference using weak chaos and infinite memory
International Nuclear Information System (INIS)
Welling, Max; Chen Yutian
2010-01-01
We describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These 'herding systems' combine learning and inference into one algorithm, where moments or data-items are converted directly into an arbitrarily long sequence of pseudo-samples. This sequence has infinite range correlations and as such is highly structured. We show that its information content, as measured by sub-extensive entropy, can grow as fast as K log T, which is faster than the usual 1/2 K log T for exchangeable sequences generated by random posterior sampling from a Bayesian model. In one dimension we prove that herding sequences are equivalent to Sturmian sequences which have complexity exactly log(T + 1). More generally, we advocate the application of the rich theoretical framework around nonlinear dynamical systems, chaos theory and fractal geometry to statistical learning.
Statistical inference using weak chaos and infinite memory
Energy Technology Data Exchange (ETDEWEB)
Welling, Max; Chen Yutian, E-mail: welling@ics.uci.ed, E-mail: yutian.chen@uci.ed [Donald Bren School of Information and Computer Science, University of California Irvine CA 92697-3425 (United States)
2010-06-01
We describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These 'herding systems' combine learning and inference into one algorithm, where moments or data-items are converted directly into an arbitrarily long sequence of pseudo-samples. This sequence has infinite range correlations and as such is highly structured. We show that its information content, as measured by sub-extensive entropy, can grow as fast as K log T, which is faster than the usual 1/2 K log T for exchangeable sequences generated by random posterior sampling from a Bayesian model. In one dimension we prove that herding sequences are equivalent to Sturmian sequences which have complexity exactly log(T + 1). More generally, we advocate the application of the rich theoretical framework around nonlinear dynamical systems, chaos theory and fractal geometry to statistical learning.
International Nuclear Information System (INIS)
Kaczmarek, J.
2002-01-01
Elementary processes responsible for phenomena in material are frequently related to scale close to atomic one. Therefore atomistic simulations are important for material sciences. On the other hand continuum mechanics is widely applied in mechanics of materials. It seems inevitable that both methods will gradually integrate. A multiscale method of integration of these approaches called collection of dynamical systems with dimensional reduction is introduced in this work. The dimensional reduction procedure realizes transition between various scale models from an elementary dynamical system (EDS) to a reduced dynamical system (RDS). Mappings which transform variables and forces, skeletal dynamical system (SDS) and a set of approximation and identification methods are main components of this procedure. The skeletal dynamical system is a set of dynamical systems parameterized by some constants and has variables related to the dimensionally reduced model. These constants are identified with the aid of solutions of the elementary dynamical system. As a result we obtain a dimensionally reduced dynamical system which describes phenomena in an averaged way in comparison with the EDS. Concept of integration of atomistic simulations with continuum mechanics consists in using a dynamical system describing evolution of atoms as an elementary dynamical system. Then, we introduce a continuum skeletal dynamical system within the dimensional reduction procedure. In order to construct such a system we have to modify a continuum mechanics formulation to some degree. Namely, we formalize scale of averaging for continuum theory and as a result we consider continuum with finite-dimensional fields only. Then, realization of dimensional reduction is possible. A numerical example of realization of the dimensional reduction procedure is shown. We consider a one dimensional chain of atoms interacting by Lennard-Jones potential. Evolution of this system is described by an elementary
Chen, Yong; Yan, Zhenya; Li, Xin
2018-02-01
The influence of spatially-periodic momentum modulation on beam dynamics in parity-time (PT) symmetric optical lattice is systematically investigated in the one- and two-dimensional nonlinear Schrödinger equations. In the linear regime, we demonstrate that the momentum modulation can alter the first and second PT thresholds of the classical lattice, periodically or regularly change the shapes of the band structure, rotate and split the diffraction patterns of beams leading to multiple refraction and emissions. In the Kerr-nonlinear regime for one-dimension (1D) case, a large family of fundamental solitons within the semi-infinite gap can be found to be stable, even beyond the second PT threshold; it is shown that the momentum modulation can shrink the existing range of fundamental solitons and not change their stability. For two-dimension (2D) case, most solitons with higher intensities are relatively unstable in their existing regions which are narrower than those in 1D case, but we also find stable fundamental solitons corroborated by linear stability analysis and direct beam propagation. More importantly, the momentum modulation can also utterly change the direction of the transverse power flow and control the energy exchange among gain or loss regions.
Dynamics of the two-dimensional directed Ising model in the paramagnetic phase
Godrèche, C.; Pleimling, M.
2014-05-01
We consider the nonconserved dynamics of the Ising model on the two-dimensional square lattice, where each spin is influenced preferentially by its east and north neighbours. The single-spin flip rates are such that the stationary state is Gibbsian with respect to the usual ferromagnetic Ising Hamiltonian. We show the existence, in the paramagnetic phase, of a dynamical transition between two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite, when the asymmetry parameter is less than a threshold value, and a regime of strong violation where this ratio vanishes asymptotically above the threshold. This study suggests that this novel kind of dynamical transition in nonequilibrium stationary states, already found for the directed Ising chain and the spherical model with asymmetric dynamics, might be quite general. In contrast with the latter models, the equal-time correlation function for the two-dimensional directed Ising model depends on the asymmetry.
Quantum walks with infinite hitting times
International Nuclear Information System (INIS)
Krovi, Hari; Brun, Todd A.
2006-01-01
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well
Improving the Instruction of Infinite Series
Lindaman, Brian; Gay, A. Susan
2012-01-01
Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…
On the Infinite Loch Ness monster
Arredondo, John A.; Maluendas, Camilo Ramírez
2017-01-01
In this paper we present in a topological way the construction of the orientable surface with only one end and infinite genus, called \\emph{The Infinite Loch Ness Monster}. In fact, we introduce a flat and hyperbolic construction of this surface. We discuss how the name of this surface has evolved and how it has been historically understood.
Properties of semi-infinite nuclei
International Nuclear Information System (INIS)
El-Jaick, L.J.; Kodama, T.
1976-04-01
Several relations among density distributions and energies of semi-infinite and infinite nuclei are iventigated in the framework of Wilets's statistical model. The model is shown to be consistent with the theorem of surface tension given by Myers and Swiatecki. Some numerical results are shown by using an appropriate nuclear matter equation of state
Degrees of infinite words, polynomials and atoms
J. Endrullis; J. Karhumaki; J.W. Klop (Jan Willem); A. Saarela
2016-01-01
textabstractOur objects of study are finite state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite automata for recognising and
Degrees of infinite words, polynomials and atoms
Endrullis, Jörg; Karhumäki, Juhani; Klop, Jan Willem; Saarela, Aleksi
2016-01-01
Our objects of study are finite state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite automata for recognising and transforming
Proving productivity in infinite data structures
Zantema, H.; Raffelsieper, M.; Lynch, C.
2010-01-01
For a general class of infinite data structures including streams, binary trees, and the combination of finite and infinite lists, we investigate the notion of productivity. This generalizes stream productivity. We develop a general technique to prove productivity based on proving context-sensitive
Negating the Infinitive in Biblical Hebrew
DEFF Research Database (Denmark)
Ehrensvärd, Martin Gustaf
1999-01-01
The article examines the negating of the infinitive in biblical and post-biblical Hebrew. The combination of the negation ayin with infinitive is widely claimed to belong to the linguistic layer commonly referred to as late biblical Hebrew and scholars use it to late-date texts. The article showa...
Variational Infinite Hidden Conditional Random Fields
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja; Ghahramani, Zoubin
2015-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of
Understanding the Behaviour of Infinite Ladder Circuits
Ucak, C.; Yegin, K.
2008-01-01
Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…
Xu, Kui; Lin, Zifeng; Merlet, Céline; Taberna, Pierre-Louis; Miao, Ling; Jiang, Jianjun; Simon, Patrice
2017-12-06
We present a molecular dynamics simulation study achieved on two-dimensional (2D) Ti 3 C 2 T x MXenes in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM] + [TFSI] - ) electrolyte. Our simulations reproduce the different patterns of volumetric change observed experimentally for both the negative and positive electrodes. The analysis of ionic fluxes and structure rearrangements in the 2D material provide an atomic scale insight into the charge and discharge processes in the layer pore and confirm the existence of two different charge-storage mechanisms at the negative and positive electrodes. The ionic number variation and the structure rearrangement contribute to the dynamic volumetric changes of both electrodes: negative electrode expansion and positive electrode contraction. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Lecca, Paola; Mura, Ivan; Re, Angela; Barker, Gary C; Ihekwaba, Adaoha E C
2016-01-01
Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering
Energy Technology Data Exchange (ETDEWEB)
Weber, Carsten
2008-07-01
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo- dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and
Slow quench dynamics of a one-dimensional Bose gas confined to an optical lattice.
Bernier, Jean-Sébastien; Roux, Guillaume; Kollath, Corinna
2011-05-20
We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.
Wavepacket dynamics in one-dimensional system with long-range correlated disorder
Yamada, Hiroaki S.
2018-03-01
We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum 1 /fα (α: spectrum exponent) generated by Fourier filtering method. For relatively small α MSD) of the initially localized wavepacket shows ballistic spread and localizes as time elapses. It is shown that α-dependence of the dynamical localization length determined by the MSD exhibits a simple scaling law in the localization regime for the relatively weak disorder strength W. Furthermore, scaled MSD by the dynamical localization length almost obeys an universal function from the ballistic to the localization regime in the various combinations of the parameters α and W.
IMSF: Infinite Methodology Set Framework
Ota, Martin; Jelínek, Ivan
Software development is usually an integration task in enterprise environment - few software applications work autonomously now. It is usually a collaboration of heterogeneous and unstable teams. One serious problem is lack of resources, a popular result being outsourcing, ‘body shopping’, and indirectly team and team member fluctuation. Outsourced sub-deliveries easily become black boxes with no clear development method used, which has a negative impact on supportability. Such environments then often face the problems of quality assurance and enterprise know-how management. The used methodology is one of the key factors. Each methodology was created as a generalization of a number of solved projects, and each methodology is thus more or less connected with a set of task types. When the task type is not suitable, it causes problems that usually result in an undocumented ad-hoc solution. This was the motivation behind formalizing a simple process for collaborative software engineering. Infinite Methodology Set Framework (IMSF) defines the ICT business process of adaptive use of methods for classified types of tasks. The article introduces IMSF and briefly comments its meta-model.
Are There Infinite Irrigation Trees?
Bernot, M.; Caselles, V.; Morel, J. M.
2006-08-01
In many natural or artificial flow systems, a fluid flow network succeeds in irrigating every point of a volume from a source. Examples are the blood vessels, the bronchial tree and many irrigation and draining systems. Such systems have raised recently a lot of interest and some attempts have been made to formalize their description, as a finite tree of tubes, and their scaling laws [25], [26]. In contrast, several mathematical models [5], [22], [10], propose an idealization of these irrigation trees, where a countable set of tubes irrigates any point of a volume with positive Lebesgue measure. There is no geometric obstruction to this infinitesimal model and general existence and structure theorems have been proved. As we show, there may instead be an energetic obstruction. Under Poiseuille law R(s) = s -2 for the resistance of tubes with section s, the dissipated power of a volume irrigating tree cannot be finite. In other terms, infinite irrigation trees seem to be impossible from the fluid mechanics viewpoint. This also implies that the usual principle analysis performed for the biological models needs not to impose a minimal size for the tubes of an irrigating tree; the existence of the minimal size can be proven from the only two obvious conditions for such irrigation trees, namely the Kirchhoff and Poiseuille laws.
Dynamical observations on the crack tip zone and stress corrosion of two-dimensional MoS2
Ly, Thuc Hue; Zhao, Jiong; Cichocka, Magdalena Ola; Li, Lain-Jong; Lee, Young Hee
2017-01-01
Whether and how fracture mechanics needs to be modified for small length scales and in systems of reduced dimensionality remains an open debate. Here, employing in situ transmission electron microscopy, atomic structures and dislocation dynamics
International Nuclear Information System (INIS)
Gauvrit, Jean-Yves; Oppenheim, Catherine; Naggara, Olivier; Trystram, Denis; Fredy, Daniel; Meder, Jean-Francois; Nataf, Francois; Roux, Francois-Xavier; Munier, Thierry; Pruvo, Jean-Pierre; Leclerc, Xavier
2006-01-01
We assessed the value of three-dimensional (3D) dynamic magnetic resonance angiography (MRA) for the follow-up of patients with radiosurgically treated cerebral arteriovenous malformations (AVMs). Fifty-four patients with cerebral AVMs treated by radiosurgery (RS) were monitored using conventional catheter angiography (CCA) and 3D dynamic MRA with sensitivity encoding based on the parallel imaging. Cerebral AVM was qualitatively classified by two radiologists into one of five categories in terms of residual nidus size and persistence of early draining vein (I, >6 cm; II, 3-6 cm; III, <3 cm; IV, isolated early draining vein; V, complete obliteration). 3D MRA findings showed a good agreement with CCA in 40 cases (κ=0.62). Of 23 nidus detected on CCA, 3D dynamic MRA showed 14 residual nidus. Of 28 occluded nidus on 3D dynamic MRA, 22 nidus were occluded on CCA. The sensitivity and specificity of 3D dynamic MRA for the detection of residual AVM were 81% and 100%. 3D dynamic MRA after RS may therefore be useful in association with MRI and can be repeated as long as opacification of the nidus or early venous drainage persists, one CCA remaining indispensable to affirm the complete occlusion at the end of follow-up. (orig.)
Dynamics in a one-dimensional ferrogel model: relaxation, pairing, shock-wave propagation.
Goh, Segun; Menzel, Andreas M; Löwen, Hartmut
2018-05-23
Ferrogels are smart soft materials, consisting of a polymeric network and embedded magnetic particles. Novel phenomena, such as the variation of the overall mechanical properties by external magnetic fields, emerge consequently. However, the dynamic behavior of ferrogels remains largely unveiled. In this paper, we consider a one-dimensional chain consisting of magnetic dipoles and elastic springs between them as a simple model for ferrogels. The model is evaluated by corresponding simulations. To probe the dynamics theoretically, we investigate a continuum limit of the energy governing the system and the corresponding equation of motion. We provide general classification scenarios for the dynamics, elucidating the touching/detachment dynamics of the magnetic particles along the chain. In particular, it is verified in certain cases that the long-time relaxation corresponds to solutions of shock-wave propagation, while formations of particle pairs underlie the initial stage of the dynamics. We expect that these results will provide insight into the understanding of the dynamics of more realistic models with randomness in parameters and time-dependent magnetic fields.
Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model
Energy Technology Data Exchange (ETDEWEB)
Ito, Yuta [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Graduate University for Advanced Studies (SOKENDAI),1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Tsuchiya, Asato [Department of Physics, Shizuoka University,836 Ohya, Suruga-ku, Shizuoka 422-8529 (Japan)
2017-03-27
The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing “infrared” cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power (2p) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of p and hence universal for p≳1.3. For p as large as 2.0, however, we find that large-N scaling behaviors do not show up, and we cannot take a sensible large-N limit. Thus we find that there is a certain range of p in which a universal large-N limit can be taken. Within this range of p, the dynamical space-time dimensionality turns out to be (3+1), while for p=2.0, where we cannot take a sensible large-N limit, we observe a (5+1)d structure.
Treatment of dynamical processes in two-dimensional models of the troposphere and stratosphere
International Nuclear Information System (INIS)
Wuebbles, D.J.
1980-07-01
The physical structure of the troposphere and stratosphere is the result of an intricate interplay among a large number of radiative, chemical, and dynamical processes. Because it is not possible to model the global environment in the laboratory, theoretical models must be relied on, subject to observational verification, to simulate atmospheric processes. Of particular concern in recent years has been the modeling of those processes affecting the structure of ozone and other trace species in the stratosphere and troposphere. Zonally averaged two-dimensional models with spatial resolution in the vertical and meridional directions can provide a much more realistic representation of tracer transport than one-dimensional models, yet are capable of the detailed representation of chemical and radiative processes contained in the one-dimensional models. The purpose of this study is to describe and analyze existing approaches to representing global atmospheric transport processes in two-dimensional models and to discuss possible alternatives to these approaches. A general description of the processes controlling the transport of trace constituents in the troposphere and stratosphere is given
Dynamic critical phenomena in two-dimensional fully frustrated Coulomb gas model with disorder
International Nuclear Information System (INIS)
Zhang Wei; Luo Mengbo
2008-01-01
The dynamic critical phenomena near depinning transition in two-dimensional fully frustrated square lattice Coulomb gas model with disorders was studied using Monte Carlo technique. The ground state of the model system with disorder σ=0.3 is a disordered state. The dependence of charge current density J on electric field E was investigated at low temperatures. The nonlinear J-E behavior near critical depinning field can be described by a scaling function proposed for three-dimensional flux line system [M.B. Luo, X. Hu, Phys. Rev. Lett. 98 (2007) 267002]. We evaluated critical exponents and found an Arrhenius creep motion for field region E c /2 c . The scaling law of the depinning transition is also obtained from the scaling function
Dynamical response of local magnons: single impurity limit in one dimensional magnets
International Nuclear Information System (INIS)
Koiller, B.; Rezende, S.M.
1979-11-01
The dynamic response of local magnon modes associated with a single impurity spin in one-dimensional ferro and antiferromagnetic insulators is studied theoretically with the use of a Green's function formulation solved exactly, by transfer matrix techniques, for zero temperature. The calculations are applied to the typical 1 - d ferromagnet CsNiF 3 and the antiferromagnet TMMC as functions of the impurity parameters in a way to allow the interpretation of possible future measurements of defect modes in these materials. The theory also explains qualitatively recent measurements in the three dimensional defect antiferromagnets FeF 2 : Mn 2+ , CoF 2 : Mn 2+ and FeF 2 : Co 2+ . (Author) [pt
Directory of Open Access Journals (Sweden)
Z. Peric
2012-04-01
Full Text Available In this paper high dynamic range nonuniform two-dimensional vector quantization model for Laplacean source was provided. Semilogarithmic A-law compression characteristic was used as radial scalar compression characteristic of two-dimensional vector quantization. Optimal number value of concentric quantization domains (amplitude levels is expressed in the function of parameter A. Exact distortion analysis with obtained closed form expressions is provided. It has been shown that proposed model provides high SQNR values in wide range of variances, and overachieves quality obtained by scalar A-law quantization at same bit rate, so it can be used in various switching and adaptation implementations for realization of high quality signal compression.
Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
Sid, S.; Terrapon, V. E.; Dubief, Y.
2018-02-01
The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed
Polarization dynamics and polarization time of random three-dimensional electromagnetic fields
International Nuclear Information System (INIS)
Voipio, Timo; Setaelae, Tero; Shevchenko, Andriy; Friberg, Ari T.
2010-01-01
We investigate the polarization dynamics of random, stationary three-dimensional (3D) electromagnetic fields. For analyzing the time evolution of the instantaneous polarization state, two intensity-normalized polarization autocorrelation functions are introduced, one based on a geometric approach with the Poincare vectors and the other on energy considerations with the Jones vectors. Both approaches lead to the same conclusions on the rate and strength of the polarization dynamics and enable the definition of a polarization time over which the state of polarization remains essentially unchanged. For fields obeying Gaussian statistics, the two correlation functions are shown to be expressible in terms of quantities characterizing partial 3D polarization and electromagnetic coherence. The 3D degree of polarization is found to have the same meaning in the 3D polarization dynamics as the usual two-dimensional (2D) degree of polarization does with planar fields. The formalism is demonstrated with several examples, and it is expected to be useful in applications dealing with polarization fluctuations of 3D light.
Approaches to determining the reliability of a multimodal three-dimensional dynamic signature
Directory of Open Access Journals (Sweden)
Yury E. Kozlov
2018-03-01
Full Text Available The market of modern mobile applications has increasingly strict requirements for the authentication system reliability. This article examines an authentication method using a multimodal three-dimensional dynamic signature (MTDS, that can be used both as a main and additional method of user authentication in mobile applications. It is based on the use of gesture in the air performed by two independent mobile devices as an identifier. The MTDS method has certain advantages over currently used biometric methods, including fingerprint authentication, face recognition and voice recognition. A multimodal three-dimensional dynamic signature allows quickly changing an authentication gesture, as well as concealing the authentication procedure using gestures that do not attract attention. Despite all its advantages, the MTDS method has certain limitations, the main one is building functionally dynamic complex (FDC skills required for accurate repeating an authentication gesture. To correctly create MTDS need to have a system for assessing the reliability of gestures. Approaches to the solution of this task are grouped in this article according to methods of their implementation. Two of the approaches can be implemented only with the use of a server as a centralized MTDS processing center and one approach can be implemented using smartphone's own computing resources. The final part of the article provides data of testing one of these methods on a template performing the MTDS authentication.
Dynameomics: a multi-dimensional analysis-optimized database for dynamic protein data.
Kehl, Catherine; Simms, Andrew M; Toofanny, Rudesh D; Daggett, Valerie
2008-06-01
The Dynameomics project is our effort to characterize the native-state dynamics and folding/unfolding pathways of representatives of all known protein folds by way of molecular dynamics simulations, as described by Beck et al. (in Protein Eng. Des. Select., the first paper in this series). The data produced by these simulations are highly multidimensional in structure and multi-terabytes in size. Both of these features present significant challenges for storage, retrieval and analysis. For optimal data modeling and flexibility, we needed a platform that supported both multidimensional indices and hierarchical relationships between related types of data and that could be integrated within our data warehouse, as described in the accompanying paper directly preceding this one. For these reasons, we have chosen On-line Analytical Processing (OLAP), a multi-dimensional analysis optimized database, as an analytical platform for these data. OLAP is a mature technology in the financial sector, but it has not been used extensively for scientific analysis. Our project is further more unusual for its focus on the multidimensional and analytical capabilities of OLAP rather than its aggregation capacities. The dimensional data model and hierarchies are very flexible. The query language is concise for complex analysis and rapid data retrieval. OLAP shows great promise for the dynamic protein analysis for bioengineering and biomedical applications. In addition, OLAP may have similar potential for other scientific and engineering applications involving large and complex datasets.
Generation of dark solitons and their instability dynamics in two-dimensional condensates
Verma, Gunjan; Rapol, Umakant D.; Nath, Rejish
2017-04-01
We analyze numerically the formation and the subsequent dynamics of two-dimensional matter wave dark solitons in a Thomas-Fermi rubidium condensate using various techniques. An initially imprinted sharp phase gradient leads to the dynamical formation of a stationary soliton as well as very shallow gray solitons, whereas a smooth gradient only creates gray solitons. The depth and hence, the velocity of the soliton is provided by the spatial width of the phase gradient, and it also strongly influences the snake-instability dynamics of the two-dimensional solitons. The vortex dipoles stemming from the unstable soliton exhibit rich dynamics. Notably, the annihilation of a vortex dipole via a transient dark lump or a vortexonium state, the exchange of vortices between either a pair of vortex dipoles or a vortex dipole and a single vortex, and so on. For sufficiently large width of the initial phase gradient, the solitons may decay directly into vortexoniums instead of vortex pairs, and also the decay rate is augmented. Later, we discuss alternative techniques to generate dark solitons, which involve a Gaussian potential barrier and time-dependent interactions, both linear and periodic. The properties of the solitons can be controlled by tuning the amplitude or the width of the potential barrier. In the linear case, the number of solitons and their depths are determined by the quench time of the interactions. For the periodic modulation, a transient soliton lattice emerges with its periodicity depending on the modulation frequency, through a wave number selection governed by the local Bogoliubov spectrum. Interestingly, for sufficiently low barrier potential, both Faraday pattern and soliton lattice coexist. The snake instability dynamics of the soliton lattice is characteristically modified if the Faraday pattern is present.
Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model
Reid, Daniel A. P.; Hildenbrandt, H.; Padding, J. T.; Hemelrijk, C. K.
2012-02-01
The fluid dynamics of animal locomotion, such as that of an undulating fish, are of great interest to both biologists and engineers. However, experimentally studying these fluid dynamics is difficult and time consuming. Model studies can be of great help because of their simpler and more detailed analysis. Their insights may guide empirical work. Particularly the recently introduced multiparticle collision dynamics method may be suitable for the study of moving organisms because it is computationally fast, simple to implement, and has a continuous representation of space. As regards the study of hydrodynamics of moving organisms, the method has only been applied at low Reynolds numbers (below 120) for soft, permeable bodies, and static fishlike shapes. In the present paper we use it to study the hydrodynamics of an undulating fish at Reynolds numbers 1100-1500, after confirming its performance for a moving insect wing at Reynolds number 75. We measure (1) drag, thrust, and lift forces, (2) swimming efficiency and spatial structure of the wake, and (3) distribution of forces along the fish body. We confirm the resemblance between the simulated undulating fish and empirical data. In contrast to theoretical predictions, our model shows that for steadily undulating fish, thrust is produced by the rear 2/3 of the body and that the slip ratio U/V (with U the forward swimming speed and V the rearward speed of the body wave) correlates negatively (instead of positively) with the actual Froude efficiency of swimming. Besides, we show that the common practice of modeling individuals while constraining their sideways acceleration causes them to resemble unconstrained fish with a higher tailbeat frequency.
Light detection and ranging measurements of wake dynamics. Part II: two-dimensional scanning
DEFF Research Database (Denmark)
Trujillo, Juan-José; Bingöl, Ferhat; Larsen, Gunner Chr.
2011-01-01
the instantaneous transversal wake position which is quantitatively compared with the prediction of the Dynamic Wake Meandering model. The results, shown for two 10-min time series, suggest that the conjecture of the wake behaving as a passive tracer is a fair approximation; this corroborates and expands...... the results of one-dimensional measurements already presented in the first part of this paper. Consequently, it is now possible to separate the deterministic and turbulent parts of the wake wind field, thus enabling capturing the wake in the meandering frame of reference. The results correspond, qualitatively...
International Nuclear Information System (INIS)
Huang Feng; Wang Xue-Jin; Liu Yan-Hong; Ye Mao-Fu; Wang Long
2010-01-01
Structures and dynamics of two-dimensional dust lattices with and without Coulomb molecules in plasmas are investigated. The experimental results show that the lattices have the crystal-like hexagonal structures, i.e. most particles have six nearest-neighboring particles. However, the lattice points can be occupied by the individual particles or by a pair of particles called Coulomb molecules. The pair correlation function is used to compare the structures between the lattices with or without the Coulomb molecules. In the experiments, the Coulomb molecules can also decompose and recombine with another individual particle to form a new molecule. (physics of gases, plasmas, and electric discharges)
Renormalization group flows in σ-models coupled to two-dimensional dynamical gravity
International Nuclear Information System (INIS)
Penati, S.; Santambrogio, A.; Zanon, D.
1997-01-01
We consider a bosonic σ-model coupled to two-dimensional gravity. In the semiclassical limit, c→-∞, we compute the gravity dressing of the β-functions at two-loop order in the matter fields. We find that the corrections due to the presence of dynamical gravity are not expressible simply in terms of a multiplicative factor as previously obtained at the one-loop level. Our result indicates that the critical points of the theory are non-trivially influenced and modified by the induced gravity. (orig.)
Gritsev, Vladimir; Demler, Eugene; Lukin, Mikhail; Polkovnikov, Anatoli
2007-11-16
We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.
Phase slip process and charge density wave dynamics in a one dimensional conductor
Habiballah, N.; Zouadi, M.; Arbaoui, A.; Qjani, M.; Dumas, J.
In this paper, we study the phase slip effect on the charge density wave (CDW) dynamics in a one-dimensional conductor in the weak pinning limit. A considerable enhancement of JCDW is observed in the presence of phase slips. In addition, a spatial dependence of the CDW current density JCDW is also studied showing that a decrease of JCDW with distance from the current contact occurs. The results are discussed in terms the relationship between additional phase slips and the mobility of phase dislocations nucleated at electrical contacts.
Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence
Yu, Pei; Zhang, Wenjing; Wahl, Lindi M.
2016-08-01
In this paper, a previously developed 2-dimensional disease model is studied, which can be used for both epidemiologic modeling and in-host disease modeling. The main attention of this paper is focused on various dynamical behaviors of the system, including Hopf and generalized Hopf bifurcations which yield bistability and tristability, Bogdanov-Takens bifurcation, and homoclinic bifurcation. It is shown that the Bogdanov-Takens bifurcation and homoclinic bifurcation provide a new mechanism for generating disease recurrence, that is, cycles of remission and relapse such as the viral blips observed in HIV infection.
Dynamics of toroidal spiral strings around five-dimensional black holes
International Nuclear Information System (INIS)
Igata, Takahisa; Ishihara, Hideki
2010-01-01
We examine the separability of the Nambu-Goto equation for test strings in a shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In particular, for a 'Hopf loop' string which is a special class of the toroidal spiral strings, we show the complete separation of variables occurs in two cases, Kerr background and Kerr-AdS background with equal angular momenta. We also obtain the dynamical solution for the Hopf loop around a black hole and for the general toroidal spiral in Minkowski background.
Energy Technology Data Exchange (ETDEWEB)
Jiang, Bin; Guo, Hua, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States)
2013-12-14
Dynamics of the title reaction is investigated on an ab initio based potential energy surface using a full-dimensional quantum wave packet method within the centrifugal sudden approximation. It is shown that the reaction between H and HCN leads to both the hydrogen exchange and hydrogen abstraction channels. The exchange channel has a lower threshold and larger cross section than the abstraction channel. It also has more oscillations due apparently to quantum resonances. Both channels are affected by long-lived resonances supported by potential wells. Comparison with experimental cross sections indicates underestimation of the abstraction barrier height.
Anomalous current in periodic Lorentz gases with infinite horizon
Energy Technology Data Exchange (ETDEWEB)
Dolgopyat, Dmitrii I [University of Maryland, College Park (United States); Chernov, Nikolai I [University of Alabama at Birmingham, Birmingham, Alabama (United States)
2009-08-31
Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, that is, J=1/2 D*E+o(||E||), where D* is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by J=1/2 DE| log||E|| | + O(||E||), where D is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju. Bibliography: 31 titles.
Anomalous current in periodic Lorentz gases with infinite horizon
International Nuclear Information System (INIS)
Dolgopyat, Dmitrii I; Chernov, Nikolai I
2009-01-01
Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, that is, J=1/2 D*E+o(||E||), where D* is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by J=1/2 DE| log||E|| | + O(||E||), where D is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju. Bibliography: 31 titles.
Quantum infinite square well with an oscillating wall
International Nuclear Information System (INIS)
Glasser, M.L.; Mateo, J.; Negro, J.; Nieto, L.M.
2009-01-01
A linear matrix equation is considered for determining the time dependent wave function for a particle in a one-dimensional infinite square well having one moving wall. By a truncation approximation, whose validity is checked in the exactly solvable case of a linearly contracting wall, we examine the cases of a simple harmonically oscillating wall and a non-harmonically oscillating wall for which the defining parameters can be varied. For the latter case, we examine in closer detail the dependence on the frequency changes, and we find three regimes: an adiabatic behabiour for low frequencies, a periodic one for high frequencies, and a chaotic behaviour for an intermediate range of frequencies.
Infinite-horizon optimal control problems in economics
Energy Technology Data Exchange (ETDEWEB)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-04-30
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
Infinite-horizon optimal control problems in economics
International Nuclear Information System (INIS)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-01-01
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
International Nuclear Information System (INIS)
Nie, Qing-Miao; Zhang, Sha-Sha; Chen, Qing-Hu; Zhou, Wei
2012-01-01
On the basis of resistively-shunted junction dynamics, we study vortex dynamics in two-dimensional Josephson junction arrays with asymmetrically single and bimodulated periodic pinning potential for the full range of vortex density f. The ratchet effect occurring at a certain range of temperature, current, and f, is observed in our simulation. We explain the microscopic behavior behind this effect by analyzing the vortex distribution and interaction. The reversal of the ratchet effect can be observed at several f values for a small driven current. This effect is stronger when the asymmetric potential is simultaneously introduced in two directions. -- Highlights: ► The ratchet effect in Josephson junction arrays strongly depends on vortex density. ► The reversed ratchet effect can be observed at several f for a small current. ► The interaction between vortices can explain the reversed ratchet effect. ► The ratchet effect is enhanced by injecting the bimodulated asymmetric potential.
Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond
Vitali, Ettore; Shi, Hao; Qin, Mingpu; Zhang, Shiwei
2017-12-01
Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles such as neutrons or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging and extremely valuable. In this paper, we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.
International Nuclear Information System (INIS)
Jiang, Bin; Song, Hongwei; Yang, Minghui; Guo, Hua
2016-01-01
The quantum dynamics of water dissociative chemisorption on the rigid Ni(111) surface is investigated using a recently developed nine-dimensional potential energy surface. The quantum dynamical model includes explicitly seven degrees of freedom of D 2 O at fixed surface sites, and the final results were obtained with a site-averaging model. The mode specificity in the site-specific results is reported and analyzed. Finally, the approximate sticking probabilities for various vibrationally excited states of D 2 O are obtained considering surface lattice effects and formally all nine degrees of freedom. The comparison with experiment reveals the inaccuracy of the density functional theory and suggests the need to improve the potential energy surface.
Magnetic field line random walk in two-dimensional dynamical turbulence
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article, by using the field line tracing method, the mean square displacement (MSD) of FLRW is calculated on all possible length scales for pure two-dimensional turbulence with the damping dynamical model. We demonstrate that in order to describe FLRW with the damping dynamical model, a new dimensionless quantity R is needed to be introduced. On different length scales, dimensionless MSD shows different relationships with the dimensionless quantity R. Although the temporal effect affects the MSD of FLRW and even changes regimes of FLRW, it does not affect the relationship between the dimensionless MSD and dimensionless quantity R on all possible length scales.
Ten dimensional SO(10) G.U.T. models with dynamical symmetry breaking
International Nuclear Information System (INIS)
Hanlon, B.E.; Joshi, G.C.
1993-01-01
To date, considerations on SO (10) models within Coset Space Dimensional Reduction (CSDR) have been diagonalized to the standard model or rely upon imaginative applications of Wilson lines so as to avoid the problem of the nonexistence of an intermediate Higgs mechanism. However, there is an alternative approach involving four fermion condensates, breaking symmetries by a dynamical mechanism. Indeed, dynamical symmetry breaking has been the direction taken in some SU(5) models within this framework in order to avoid the problems of electroweak symmetry breaking at the compactification scale. This paper presents realistic models which utilize this mechanism. It is shown that the appropriate fermionic representations can emerge from CSDR and the construction of such condensates within the constraints of this scheme is presented. By introducing discrete symmetries onto the internal manifold a strong breaking of the SO(10) G.U.T. is produced and, more importantly, eliminate Higgs fields of geometrical origin. 31 refs
Directory of Open Access Journals (Sweden)
Vivian M. Hsu, MD
2014-09-01
Conclusions: This pilot study illustrates that the face can be objectively and quantitatively evaluated using dynamic major strain analysis. The technology of 3-dimensional optical imaging can be used to advance our understanding of facial soft-tissue dynamics and the effects of animation on facial strain over time.
Geraci, Joseph; Dharsee, Moyez; Nuin, Paulo; Haslehurst, Alexandria; Koti, Madhuri; Feilotter, Harriet E; Evans, Ken
2014-03-01
We introduce a novel method for visualizing high dimensional data via a discrete dynamical system. This method provides a 2D representation of the relationship between subjects according to a set of variables without geometric projections, transformed axes or principal components. The algorithm exploits a memory-type mechanism inherent in a certain class of discrete dynamical systems collectively referred to as the chaos game that are closely related to iterative function systems. The goal of the algorithm was to create a human readable representation of high dimensional patient data that was capable of detecting unrevealed subclusters of patients from within anticipated classifications. This provides a mechanism to further pursue a more personalized exploration of pathology when used with medical data. For clustering and classification protocols, the dynamical system portion of the algorithm is designed to come after some feature selection filter and before some model evaluation (e.g. clustering accuracy) protocol. In the version given here, a univariate features selection step is performed (in practice more complex feature selection methods are used), a discrete dynamical system is driven by this reduced set of variables (which results in a set of 2D cluster models), these models are evaluated for their accuracy (according to a user-defined binary classification) and finally a visual representation of the top classification models are returned. Thus, in addition to the visualization component, this methodology can be used for both supervised and unsupervised machine learning as the top performing models are returned in the protocol we describe here. Butterfly, the algorithm we introduce and provide working code for, uses a discrete dynamical system to classify high dimensional data and provide a 2D representation of the relationship between subjects. We report results on three datasets (two in the article; one in the appendix) including a public lung cancer
Infinite genus surfaces and irrational polygonal billiards
Valdez, Ferrán
2009-01-01
We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological real surface with exactly one end.
Approach to equilibrium in infinite quantum systems
International Nuclear Information System (INIS)
Haag, R.
1975-01-01
Ergodic theory of infinite quantum systems is discussed. The framework of this theory is based in an algebra of quasi-local observables. Nonrelativistic situation, i.e., Galilei invariance and Clifford algebra, is used [pt
Directory of Open Access Journals (Sweden)
Kravets Victor V.
2016-05-01
Full Text Available One-dimensional dynamic design of a component characterized by inertia coefficient, elastic coefficient, and coefficient of energy dispersion. The component is affected by external action in the form of time-independent initial kinematic disturbances and varying ones. Mathematical model of component dynamics as well as a new form of analytical representation of transient in terms of one-dimensional problem of kinematic effect is provided. Dynamic design of a component is being carried out according to a theory of modal control.
Stable biexcitons in two-dimensional metal-halide perovskites with strong dynamic lattice disorder
Thouin, Félix; Neutzner, Stefanie; Cortecchia, Daniele; Dragomir, Vlad Alexandru; Soci, Cesare; Salim, Teddy; Lam, Yeng Ming; Leonelli, Richard; Petrozza, Annamaria; Kandada, Ajay Ram Srimath; Silva, Carlos
2018-03-01
With strongly bound and stable excitons at room temperature, single-layer, two-dimensional organic-inorganic hybrid perovskites are viable semiconductors for light-emitting quantum optoelectronics applications. In such a technological context, it is imperative to comprehensively explore all the factors—chemical, electronic, and structural—that govern strong multiexciton correlations. Here, by means of two-dimensional coherent spectroscopy, we examine excitonic many-body effects in pure, single-layer (PEA) 2PbI4 (PEA = phenylethylammonium). We determine the binding energy of biexcitons—correlated two-electron, two-hole quasiparticles—to be 44 ±5 meV at room temperature. The extraordinarily high values are similar to those reported in other strongly excitonic two-dimensional materials such as transition-metal dichalcogenides. Importantly, we show that this binding energy increases by ˜25 % upon cooling to 5 K. Our work highlights the importance of multiexciton correlations in this class of technologically promising, solution-processable materials, in spite of the strong effects of lattice fluctuations and dynamic disorder.
Marinho, Daniel A; Barbosa, Tiago M; Rouboa, Abel I; Silva, António J
2011-09-01
Nowadays the underwater gliding after the starts and the turns plays a major role in the overall swimming performance. Hence, minimizing hydrodynamic drag during the underwater phases should be a main aim during swimming. Indeed, there are several postures that swimmers can assume during the underwater gliding, although experimental results were not conclusive concerning the best body position to accomplish this aim. Therefore, the purpose of this study was to analyse the effect in hydrodynamic drag forces of using different body positions during gliding through computational fluid dynamics (CFD) methodology. For this purpose, two-dimensional models of the human body in steady flow conditions were studied. Two-dimensional virtual models had been created: (i) a prone position with the arms extended at the front of the body; (ii) a prone position with the arms placed alongside the trunk; (iii) a lateral position with the arms extended at the front and; (iv) a dorsal position with the arms extended at the front. The drag forces were computed between speeds of 1.6 m/s and 2 m/s in a two-dimensional Fluent(®) analysis. The positions with the arms extended at the front presented lower drag values than the position with the arms aside the trunk. The lateral position was the one in which the drag was lower and seems to be the one that should be adopted during the gliding after starts and turns.
Bazhenov, Alexiev M.; Heyes, David M.
1990-01-01
The thermodynamics, structure, and transport coefficients, as defined by the Green-Kubo integrals, of the one-dimensional Lennard-Jones fluid are evaluated for a wide range of state points by molecular dynamics computer simulation. These calculations are performed for the first time for thermal conductivity and the viscosity. We observe a transition from hard-rod behavior at low number density to harmonic-spring fluid behavior in the close-packed limit. The self-diffusion coefficient decays with increasing density to a finite limiting value. The thermal conductivity increases with density, tending to ∞ in the close-packed limit. The viscosity in contrast maximizes at intermediate density, tending to zero in the zero density and close-packed limits.
Quark ensembles with infinite correlation length
Molodtsov, S. V.; Zinovjev, G. M.
2014-01-01
By studying quark ensembles with infinite correlation length we formulate the quantum field theory model that, as we show, is exactly integrable and develops an instability of its standard vacuum ensemble (the Dirac sea). We argue such an instability is rooted in high ground state degeneracy (for 'realistic' space-time dimensions) featuring a fairly specific form of energy distribution, and with the cutoff parameter going to infinity this inherent energy distribution becomes infinitely narrow...
Dimensionality of heavy metal distribution in waste disposal sites using nonlinear dynamics
International Nuclear Information System (INIS)
Modis, Kostas; Komnitsas, Kostas
2008-01-01
Mapping of heavy metal contamination in mining and waste disposal sites usually relies on geostatistical approaches and linear stochastic dynamics. The present paper aims to identify, using the Grassberger-Procaccia correlation dimension (CD) algorithm, the existence of a nonlinear deterministic and chaotic dynamic behaviour in the spatial pattern of arsenic, manganese and zinc concentration in a Russian coal waste disposal site. The analysis carried out yielded embedding dimension values ranging between 7 and 8 suggesting thus from a chaotic dynamic perspective that arsenic, manganese and zinc concentration in space is a medium dimensional problem for the regionalized scale considered in this study. This alternative nonlinear dynamics approach may complement conventional geostatistical studies and may be also used for the estimation of risk and the subsequent screening and selection of a feasible remediation scheme in wider mining and waste disposal sites. Finally, the synergistic effect of this study may be further elaborated if additional factors including among others presence of hot spots, density and depth of sampling, mineralogy of wastes and sensitivity of analytical techniques are taken into account
Devos, Christophe; Ochiai, Nobuo; Sasamoto, Kikuo; Sandra, Pat; David, Frank
2012-09-14
Suspected fragrance allergens were determined in cosmetic products using a combination of full evaporation-dynamic headspace (FEDHS) with selectable one-dimensional/two-dimensional GC-MS. The full evaporation dynamic headspace approach allows the non-discriminating extraction and injection of both apolar and polar fragrance compounds, without contamination of the analytical system by high molecular weight non-volatile matrix compounds. The method can be applied to all classes of cosmetic samples, including water containing matrices such as shower gels or body creams. In combination with selectable (1)D/(2)D GC-MS, consisting of a dedicated heart-cutting GC-MS configuration using capillary flow technology (CFT) and low thermal mass GC (LTM-GC), a highly flexible and easy-to-use analytical solution is offered. Depending on the complexity of the perfume fraction, analyses can be performed in one-dimensional GC-MS mode or in heart-cutting two-dimensional GC-MS mode, without the need of hardware reconfiguration. The two-dimensional mode with independent temperature control of the first and second dimension column is especially useful to confirm the presence of detected allergen compounds when mass spectral deconvolution is not possible. Copyright © 2012 Elsevier B.V. All rights reserved.
Ground-state and dynamical properties of two-dimensional dipolar Fermi liquids
International Nuclear Information System (INIS)
Abedinpour, Saeed H.; Asgari, Reza; Tanatar, B.; Polini, Marco
2014-01-01
We study the ground-state properties of a two-dimensional spin-polarized fluid of dipolar fermions within the Euler–Lagrange Fermi-hypernetted-chain approximation. Our method is based on the solution of a scattering Schrödinger equation for the “pair amplitude” √(g(r)), where g(r) is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow–Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree–Fock limit at weak coupling. Very good agreement with recent results based on quantum Monte Carlo simulations is achieved over a wide range of coupling constants up to the liquid-to-crystal quantum phase transition. Using the fluctuation–dissipation theorem and a static approximation for the effective inter-particle interactions, we calculate the dynamical density–density response function, and furthermore demonstrate that an undamped zero-sound mode exists for any value of the interaction strength, down to infinitesimally weak couplings. -- Highlights: •We have studied the ground state properties of a strongly correlated two-dimensional fluid of dipolar fermions. •We have calculated the effective inter-particle interaction and the dynamical density–density response function. •We have shown that an undamped zero sound mode exists at any value of the interaction strength
Three-dimensional static and dynamic reactor calculations by the nodal expansion method
International Nuclear Information System (INIS)
Christensen, B.
1985-05-01
This report reviews various method for the calculation of the neutron-flux- and power distribution in an nuclear reactor. The nodal expansion method (NEM) is especially described in much detail. The nodal expansion method solves the diffusion equation. In this method the reactor core is divided into nodes, typically 10 to 20 cm in each direction, and the average flux in each node is calculated. To obtain the coupling between the nodes the local flux inside each node is expressed by use of a polynomial expansion. The expansion is one-dimensional, so inside each node such three expansions occur. To calculate the expansion coefficients it is necessary that the polynomial expansion is a solution to the one-dimensional diffusion equation. When the one-dimensional diffusion equation is established a term with the transversal leakage occur, and this term is expanded after the same polynomials. The resulting equation system with the expansion coefficients as the unknowns is solved with weigthed residual technique. The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The program and input to it are described. The program is tested on a number of examples extending from small theoretical one up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested. (author)
International Nuclear Information System (INIS)
Liu Qi; Lu Jianping; Wang Fei; Wang Li; Tian Jianming; Jin Aiguo; Zeng Hao
2003-01-01
Objective: To assess the clinical value of three-dimensional dynamic contrast-enhanced MR angiography (3D DCE-MRA) in the detection for intracranial aneurysm. Methods: 3D DCE-MRA was performed in 54 patients highly suspected with intracranial aneurysms. Then conventional digital subtraction angiography (DSA) and feasible endovascular treatment were performed simultaneously. A three-dimensional fast imaging with steady state precession (3D FISP) was used for 3D DCE-MRA(Gd-DTPA dose, 0.2 mmol per kilogram for body weight; acquisition time, 10 seconds). The source images were subtracted from mask images and transferred to computer workstation. All images were subsequently post-processed using three-dimensional reconstruction. 3D DCE-MRA images and DSA images were compared for demonstration of the aneurysm, its neck, and relationship with parent artery, and the usefulness for endovascular treatment was evaluated. Results: There were 39 cases with 45 intracranial aneurysms. The sensitivity, specificity, and accuracy of 3D DCE-MRA were 96%, 73% and 90%, respectively. Aneurysm and its neck depiction at 3D DCE-MRA was significantly better than that at DSA, especially for aneurysms adjacent to the cavernous sinus and near the PICA of vertebral artery. 3D DEC-MRA could guide neurosurgeons to the desired DSA projection, and helped them make plan for interventional or surgical treatment in advance. But the diagnosis should be very carefully made for small aneurysms located in the periphery and the arterial bifurcation. Conclusion: 3D DEC-MRA is a fast, noninvasive and efficient technique for diagnosing intracranial aneurysms. Its three dimensional information is helpful for DSA demonstration and treatment planning. Any uncertain diagnosis requires DSA confirmation
Directory of Open Access Journals (Sweden)
Moschner Carsten
2007-08-01
Full Text Available Abstract Background Decision-making is a fundamental capacity which is crucial to many higher-order psychological functions. We recorded event-related potentials (ERPs during a visual target-identification task that required go-nogo choices. Targets were identified on the basis of cross-dimensional conjunctions of particular colors and forms. Color discriminability was manipulated in three conditions to determine the effects of color distinctiveness on component processes of decision-making. Results Target identification was accompanied by the emergence of prefrontal P2a and P3b. Selection negativity (SN revealed that target-compatible features captured attention more than target-incompatible features, suggesting that intra-dimensional attentional capture was goal-contingent. No changes of cross-dimensional selection priorities were measurable when color discriminability was altered. Peak latencies of the color-related SN provided a chronometric measure of the duration of attention-related neural processing. ERPs recorded over the frontocentral scalp (N2c, P3a revealed that color-overlap distractors, more than form-overlap distractors, required additional late selection. The need for additional response selection induced by color-overlap distractors was severely reduced when color discriminability decreased. Conclusion We propose a simple model of cross-dimensional perceptual decision-making. The temporal synchrony of separate color-related and form-related choices determines whether or not distractor processing includes post-perceptual stages. ERP measures contribute to a comprehensive explanation of the temporal dynamics of component processes of perceptual decision-making.
International Nuclear Information System (INIS)
Sasaki, Ryu; Yamanaka, Itaru
1987-01-01
The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the ℎ → 0 limit (ℎ; Planck's constant divided by 2π). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie a certain class of quantum integrable systems. (orig.)
International Nuclear Information System (INIS)
Sasaki, Ryu; Yamanaka, Itaru.
1986-08-01
The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the ℎ → 0 limit (ℎ; Planck's constant divided by 2π). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie certain class of quantum integrable systems. (author)
Infinitely dilute partial molar properties of proteins from computer simulation.
Ploetz, Elizabeth A; Smith, Paul E
2014-11-13
A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.
Antikaons in infinite nuclear matter and nuclei
International Nuclear Information System (INIS)
Moeller, M.
2007-01-01
In this work we studied the properties of antikaons and hyperons in infinite cold nuclear matter. The in-medium antikaon-nucleon scattering amplitude and self-energy has been calculated within a covariant many-body framework in the first part. Nuclear saturation effects have been taken into account in terms of scalar and vector nucleon mean-fields. In the second part of the work we introduced a non-local method for the description of kaonic atoms. The many-body approach of anti KN scattering can be tested by the application to kaonic atoms. A self-consistent and covariant many-body approach has been used for the determination of the antikaon spectral function and anti KN scattering amplitudes. It considers s-, p- and d-waves and the application of an in-medium projector algebra accounts for proper mixing of partial waves in the medium. The on-shell reduction scheme is also implemented by means of the projector algebra. The Bethe-Salpeter equation has been rewritten, so that the free-space anti KN scattering can be used as the interaction kernel for the in-medium scattering equation. The latter free-space scattering is based on a realistic coupled-channel dynamics and chiral SU(3) Lagrangian. Our many-body approach is generalized for the presence of large scalar and vector nucleon mean-fields. It is supplemented by an improved renormalization scheme, that systematically avoids the occurrence of medium-induced power-divergent structures and kinematical singularities. A modified projector basis has been introduced, that allows for a convenient inclusion of nucleon mean-fields. The description of the results in terms of the 'physical' basis is done with the help of a recoupling scheme based on the projector algebra properties. (orig.)
International Nuclear Information System (INIS)
Haghbin, S.; Farahat, S.
2004-01-01
In this paper, the numerical solution of two-dimensional incompressible viscid flow by triangular unstructured grid around airfoil with dynamic ground effect and by using geometric conservation law (GCL) has been represented. In this analysis, after the mesh generation for physical model, for the purpose of adaption of meshes with physical condition, the mesh adaption method has been used. Also, for increasing the speed of results convergence, the Multigrid method has been applied to the solver of governing equations. Because of the movement of meshes in this analysis, by using a spring simulation, the generated meshes have been moved and in every time step for the purpose of controlling the quality of meshes, by considering the EquiAngle Skew coefficient (EAS) and the volume of each mesh, the meshes that had a large EAS and a volume more than and less than defined maximum and minimum value, have been removed and then regenerated. Also, because the continuity and momentum conservations law were insufficient to work with these moving grids, the geometric conservation law was combined with the other conservation laws and a general equation was obtained for the dynamic meshes. For solving this general equation, the Simple Algorithm has been used. According to the results, the dynamic ground effect causes unsteadiness and also the Lift coefficient is increased vibrationally. And with respect to the type of airfoil, the Drag coefficient can decrease or increase vibrationally. (author)
Energy Technology Data Exchange (ETDEWEB)
Butkus, Vytautas; Gelzinis, Andrius; Valkunas, Leonas [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio Ave. 9-III, 10222 Vilnius (Lithuania); Center for Physical Sciences and Technology, Savanoriu Ave. 231, 02300 Vilnius (Lithuania); Augulis, Ramūnas [Center for Physical Sciences and Technology, Savanoriu Ave. 231, 02300 Vilnius (Lithuania); Gall, Andrew; Robert, Bruno [Institut de Biologie et Technologies de Saclay, Bât 532, Commissariat à l’Energie Atomique Saclay, 91191 Gif sur Yvette (France); Büchel, Claudia [Institut für Molekulare Biowissenschaften, Universität Frankfurt, Max-von-Laue-Straße 9, Frankfurt (Germany); Zigmantas, Donatas [Department of Chemical Physics, Lund University, P.O. Box 124, 22100 Lund (Sweden); Abramavicius, Darius, E-mail: darius.abramavicius@ff.vu.lt [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio Ave. 9-III, 10222 Vilnius (Lithuania)
2015-06-07
Energy transfer processes and coherent phenomena in the fucoxanthin–chlorophyll protein complex, which is responsible for the light harvesting function in marine algae diatoms, were investigated at 77 K by using two-dimensional electronic spectroscopy. Experiments performed on femtosecond and picosecond timescales led to separation of spectral dynamics, witnessing evolutions of coherence and population states of the system in the spectral region of Q{sub y} transitions of chlorophylls a and c. Analysis of the coherence dynamics allowed us to identify chlorophyll (Chl) a and fucoxanthin intramolecular vibrations dominating over the first few picoseconds. Closer inspection of the spectral region of the Q{sub y} transition of Chl c revealed previously not identified, mutually non-interacting chlorophyll c states participating in femtosecond or picosecond energy transfer to the Chl a molecules. Consideration of separated coherent and incoherent dynamics allowed us to hypothesize the vibrations-assisted coherent energy transfer between Chl c and Chl a and the overall spatial arrangement of chlorophyll molecules.
International Nuclear Information System (INIS)
Zhao, Y.; Wilson, P.R.; Stevenson, J.D.
1995-01-01
The seismic evaluation of submerged free standing spent fuel storage racks is more complicated than most other nuclear structural systems. When subjected to three dimensional (3-D) floor seismic excitations the dynamic responses of racks in a pool are hydro dynamically coupled with each other, with the fuel assemblies water in gaps. The motion behavior of the racks is significantly different from that observed using a 3D single rack mode. Few seismic analyses using 3-D whole pool multiple rack models are available in the literature. I this paper an analysis was performed for twelve racks using potential theory for the fluid-structure interaction, and using a 3-D whole pool multi-rack finite element model developed herein. The analysis includes the potential nonlinear dynamic behavior of the impact of fuel-rack, rack-rack and rack-pool wall, the tilting or uplift and the frictional sliding of rack supports, and the impact of the rack supports to the pool floor. (author). 12 refs., 7 figs., 1 tab
Inertia-dependent dynamics of three-dimensional vesicles and red blood cells in shear flow.
Luo, Zheng Yuan; Wang, Shu Qi; He, Long; Xu, Feng; Bai, Bo Feng
2013-10-28
A three-dimensional (3D) simulation study of the effect of inertia on the dynamics of vesicles and red blood cells (RBCs) has not been reported. Here, we developed a 3D model based on the front tracking method to investigate how inertia affects the dynamics of spherical/non-spherical vesicles and biconcave-shaped RBCs with the Reynolds number ranging from 0.1 to 10. The results showed that inertia induced non-spherical vesicles transitioned from tumbling to swinging, which was not observed in previous 2D models. The critical viscosity ratio of inner/outer fluids for the tumbling–swinging transition remarkably increased with an increasing Reynolds number. The deformation of vesicles was greatly enhanced by inertia, and the frequency of tumbling and tank-treading was significantly decreased by inertia. We also found that RBCs can transit from tumbling to steady tank-treading through the swinging regime when the Reynolds number increased from 0.1 to 10. These results indicate that inertia needs to be considered at moderate Reynolds number (Re ~ 1) in the study of blood flow in the human body and the flow of deformable particle suspension in inertial microfluidic devices. The developed 3D model provided new insights into the dynamics of RBCs under shear flow, thus holding great potential to better understand blood flow behaviors under normal/disease conditions.
Energy Technology Data Exchange (ETDEWEB)
Haghbin, S.; Farahat, S. [Sistan and Baluchestan Univ., Dept. of Mechanical Engineering, Zahedan (Iran, Islamic Republic of)]. E-mail: sadegh_haghbin@yahoo.com
2004-07-01
In this paper, the numerical solution of two-dimensional incompressible viscid flow by triangular unstructured grid around airfoil with dynamic ground effect and by using geometric conservation law (GCL) has been represented. In this analysis, after the mesh generation for physical model, for the purpose of adaption of meshes with physical condition, the mesh adaption method has been used. Also, for increasing the speed of results convergence, the Multigrid method has been applied to the solver of governing equations. Because of the movement of meshes in this analysis, by using a spring simulation, the generated meshes have been moved and in every time step for the purpose of controlling the quality of meshes, by considering the EquiAngle Skew coefficient (EAS) and the volume of each mesh, the meshes that had a large EAS and a volume more than and less than defined maximum and minimum value, have been removed and then regenerated. Also, because the continuity and momentum conservations law were insufficient to work with these moving grids, the geometric conservation law was combined with the other conservation laws and a general equation was obtained for the dynamic meshes. For solving this general equation, the Simple Algorithm has been used. According to the results, the dynamic ground effect causes unsteadiness and also the Lift coefficient is increased vibrationally. And with respect to the type of airfoil, the Drag coefficient can decrease or increase vibrationally. (author)
Directory of Open Access Journals (Sweden)
SW Kang
2015-02-01
Full Text Available This article introduces an improved non-dimensional dynamic influence function method using a sub-domain method for efficiently extracting the eigenvalues and mode shapes of concave membranes with arbitrary shapes. The non-dimensional dynamic influence function method (non-dimensional dynamic influence function method, which was developed by the authors in 1999, gives highly accurate eigenvalues for membranes, plates, and acoustic cavities, compared with the finite element method. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. To overcome the inefficient procedure, this article proposes a practical approach to make the system matrix equation of the concave membrane of interest into a form of algebraic eigenvalue problem. It is shown by several case studies that the proposed method has a good convergence characteristics and yields very accurate eigenvalues, compared with an exact method and finite element method (ANSYS.
Directory of Open Access Journals (Sweden)
Sang-Wook Kang
2016-03-01
Full Text Available A new formulation for the non-dimensional dynamic influence function method, which was developed by the authors, is proposed to efficiently extract eigenvalues and mode shapes of clamped plates with arbitrary shapes. Compared with the finite element and boundary element methods, the non-dimensional dynamic influence function method yields highly accurate solutions in eigenvalue analysis problems of plates and membranes including acoustic cavities. However, the non-dimensional dynamic influence function method requires the uneconomic procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues because it produces a non-algebraic eigenvalue problem. This article describes a new approach that reduces the problem of free vibrations of clamped plates to an algebraic eigenvalue problem, the solution of which is straightforward. The validity and efficiency of the proposed method are illustrated through several numerical examples.
Infinite dimensional analysis a hitchhiker’s guide
Aliprantis, Charalambos D
1999-01-01
In the nearly five years since the publication of what we refer to as The Hitchhiker's Guide, we have been the recipients of much advice and many complaints. That, combined with the economics of the publishing industry, convinced us that the world would be a better place if we published a second edition of our book, and made it available in paperback at a more modest price. The most obvious difference between the second and the original edition is the reorganization of material that resulted in three new chapters. Chap ter 4 collects many of the purely set-theoretical results about measurable structures such as semirings and a-algebras. The material in this chapter is quite independent from notions of measure and integration, and is easily ac cessible, so we thought it should come sooner. We also divided the chapter on correspondences into two separate chapters, one dealing with continuity, the other with measurability. The material on measurable correspondences is more detailed and, we hope, better writt...
On Interconnections of Infinite-dimensional Port-Hamiltonian Systems
Pasumarthy, Ramkrishna; Schaft, Arjan J. van der
2004-01-01
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving
On interconnections of infinite-dimensional port-Hamiltonian systems
Ramkrishna Pasumarthy, R.P.; van der Schaft, Arjan
2004-01-01
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving
Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model
International Nuclear Information System (INIS)
Hao Sanru; Li Wei
1989-01-01
This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed
International Nuclear Information System (INIS)
Budinger, T.F.; DeLand, F.H.; Duggan, H.E.; Bouz, J.J.; Hoop, B. Jr.; McLaughlin, W.T.; Weber, P.M.
1975-01-01
Two-dimensional computer image-processing techniques have not proved to be of importance in diagnostic nuclear medicine primarily because the radionuclide distribution represents a three-dimensional problem. More recent developments in three-dimensional reconstruction from multiple views or multiple detectors promise to overcome the major limitations in previous work with digital computers. These techniques are now in clinical use for static imaging; however, speed limitations have prevented application to dynamic imaging. The future development of these methods will require innovations in patient positioning and multiple-view devices for either single-gamma or positron annihilation detection
Degli Esposti, M.; Giardinà, C.; Graffi, S.; Isola, S.
2001-01-01
We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is argued that there can be a large number of metastable (i.e.,
Charge solitons and their dynamical mass in one-dimensional arrays of Josephson junctions
International Nuclear Information System (INIS)
Homfeld, Jens; Protopopov, Ivan; Rachel, Stephan; Shnirman, Alexander
2011-01-01
We investigate charge transport in one-dimensional arrays of Josephson junctions. In the interesting regime of ''small charge solitons'' (polarons), ΛE J >E C >E J , where Λ is the (electrostatic) screening length, the charge dynamics are strongly influenced by the polaronic effects (i.e., by dressing of a Cooper pair by charge dipoles). In particular, the soliton's mass in this regime scales approximately as E J -2 . We employ two theoretical techniques: the many-body tight-binding approach and the mean-field approach, and the results of the two approaches agree in the regime of ''small charge solitons.'' Renormalization of the soliton's mass could be observed; for example, as enhancement of the persistent current in a ring-shaped array.
International Nuclear Information System (INIS)
Park, Jong Woon
2010-01-01
This paper provides a computational fluid dynamic (CFD) analysis method on the evaluation of debris transport under emergency recirculation mode after loss of coolant accident of a nuclear power plant. Three dimensional reactor building floor geometrical model is constructed including flow obstacles larger than 6 inches such as mechanical components and equipments and considering various inlet flow paths from the upper reactor building such as break and spray flow. In the modeling of the inlet flows from the upper floors, effect of gravitational force was also reflected. For the precision of the analysis, 3 millions of tetrahedral-shaped meshes were generated. Reference calculation showed physically reasonable results. Sensitivity studies for mesh type and turbulence model showed very similar results to the reference case. This study provides useful information on the application of CFD to the evaluation of debris transport fraction for the design of new emergency sump filters. (orig.)
Dynamics of vacancies in two-dimensional Lennard-Jones crystals
Yao, Zhenwei; Olvera de La Cruz, Monica
2015-03-01
Vacancies represent an important class of crystallographic defects, and their behaviors can be strongly coupled with relevant material properties. We report the rich dynamics of vacancies in two-dimensional Lennard-Jones crystals in several thermodynamic states. Specifically, we numerically observe significantly faster diffusion of the 2-point vacancy with two missing particles in comparison with other types of vacancies; it opens the possibility of doping 2-point vacancies into atomic materials to enhance atomic migration. In addition, the resulting dislocations in the healing of a long vacancy suggest the intimate connection between vacancies and topological defects that may provide an extra dimension in the engineering of defects in extensive crystalline materials for desired properties. We thank the financial support from the U.S. Department of Commerce, National Institute of Standards and Technology, the Office of the Director of Defense Research and Engineering (DDR&E) and the Air Force Office of Scientific Research.
Interaction and dynamics of add-atoms with 2-dimensional structures
The interaction and dynamics of add-atoms with graphene, graphene-derivate structures and, later, MoSi$_2$, two-dimensional – single and few – atomic layers will be studied with the Perturbed Angular Correlation – PAC – technique. Graphene is also envisaged as new platform for growing semiconductor nanostructure devices, such as quantum dots and as a particularly powerful catalyst. Understanding nucleation of nanostructures and clusters on graphene and related phases in wet conditions as they are used in chemical methods in research and industry require complementary studies. These systems will therefore be studied systematically using radioactive probe atoms attaching via a transfer media (e.g., water in catalysis process) or being deposited with soft-landing techniques under vacuum and UHV conditions, as put in place at the ASPIC setup at ISOLDE. The hyperfine fields obtained under different environments are expected to reveal basic information on the rich atomic and physical mechanisms associated w...
UAV formation control design with obstacle avoidance in dynamic three-dimensional environment.
Chang, Kai; Xia, Yuanqing; Huang, Kaoli
2016-01-01
This paper considers the artificial potential field method combined with rotational vectors for a general problem of multi-unmanned aerial vehicle (UAV) systems tracking a moving target in dynamic three-dimensional environment. An attractive potential field is generated between the leader and the target. It drives the leader to track the target based on the relative position of them. The other UAVs in the formation are controlled to follow the leader by the attractive control force. The repulsive force affects among the UAVs to avoid collisions and distribute the UAVs evenly on the spherical surface whose center is the leader-UAV. Specific orders or positions of the UAVs are not required. The trajectories of avoidance obstacle can be obtained through two kinds of potential field with rotation vectors. Every UAV can choose the optimal trajectory to avoid the obstacle and reconfigure the formation after passing the obstacle. Simulations study on UAV are presented to demonstrate the effectiveness of proposed method.
Energy Technology Data Exchange (ETDEWEB)
Kim, Ha Youn; Park, Sung Tae; Bae, Won Kyoung; Goo, Dong Erk [Dept. of Radiology, Soonchunhyang University Hospital, Seoul (Korea, Republic of)
2014-12-15
We studied the influence of proximal geometry on the results of computational fluid dynamics (CFD). We made five models of different proximal geometry from three dimensional angiography of 63-year-old women with intracranial aneurysm. CFD results were analyzed as peak systolic velocity (PSV) at inlet and outlet as well as flow velocity profile at proximal level of internal carotid artery (ICA) aneurysm. Modified model of cavernous one with proximal tubing showed faster PSV at outlet than that at inlet. The PSV of outlets of other models were slower than that of inlets. The flow velocity profiles at immediate proximal to ICA aneurysm showed similar patterns in all models, suggesting that proximal vessel geometries could affect CFD results.
Directory of Open Access Journals (Sweden)
Hongling Ye
2015-01-01
Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.
Molecular dynamics of shock waves in one-dimensional chains. II. Thermalization
International Nuclear Information System (INIS)
Straub, G.K.; Holian, B.L.; Petschek, R.G.
1979-01-01
The thermalization behavior behind a shock front in one-dimensional chains has been studied in a series of molecular-dynamics computer experiments. We have found that a shock wave generated in a chain initially at finite temperature has essentially the same characteristics as in a chain initially at zero temperature. We also find that the final velocity distribution function for particles behind the shock front is not the Maxwell-Boltzmann distribution for an equilibrium system of classical particles. For times long after the shock has passed, we propose a nonequilibrium velocity distribution which is based upon behavior in the harmonic and hard-rod limits and agrees with our numerical results. Temperature profiles for both harmonic and anharmonic chains are found to exhibit a long-time tail that decays inversely with time. Finally, we have run a computer experiment to generate what qualitatively resembles solitons in Toda chains by means of shock waves
A multi-dimensional dynamic linear model for monitoring slaughter pig production
DEFF Research Database (Denmark)
Jensen, Dan Børge; Cornou, Cecile; Toft, Nils
Scientists and farmers still lack an efficient way to unify the large number of different types of data series, which are increasingly being generated in relation to automatic herd monitoring. Such a unifying model should be able to account for the correlations between the various types of data......, feed-and water consumption), measured at different levels of detail (individual pig and double-pen level) and with different observational frequencies (weekly and daily), using series collected for the Danish PigIT project. The presented three-dimensional model serves as a proof of concept......, resulting in a model which could potentially yield more information than can be gained from the individual components separately. Here we present such a model for monitoring slaughter pig production, in the form of a multivariate dynamic linear model. This model unifies three types of data (live weight...
Directory of Open Access Journals (Sweden)
SERGIY KOZERENKO
2016-04-01
Full Text Available One feature of the famous Sharkovsky’s theorem is that it can be proved using digraphs of a special type (the so–called Markov graphs. The most general definition assigns a Markov graph to every continuous map from the topological graph to itself. We show that this definition is too broad, i.e. every finite digraph can be viewed as a Markov graph of some one–dimensional dynamical system on a tree. We therefore consider discrete analogues of Markov graphs for vertex maps on combinatorial trees and characterize all maps on trees whose discrete Markov graphs are of the following types: complete, complete bipartite, the disjoint union of cycles, with every arc being a loop.
(2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations
International Nuclear Information System (INIS)
Benedetti, D.; Loll, R.; Zamponi, F.
2007-01-01
We perform a nonperturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of causal dynamical triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometries. This simplifies the combinatorial problem of counting geometries just enough to enable us to calculate the transfer matrix between boundary states labeled by the area of the spatial universe, as well as the corresponding quantum Hamiltonian of the continuum theory. This is the first time in dimension larger than 2 that a Hamiltonian has been derived from such a model by mainly analytical means, and it opens the way for a better understanding of scaling and renormalization issues
Dynamics of wave packets in two-dimensional random systems with anisotropic disorder.
Samelsohn, Gregory; Gruzdev, Eugene
2008-09-01
A theoretical model is proposed to describe narrowband pulse dynamics in two-dimensional systems with arbitrary correlated disorder. In anisotropic systems with elongated cigarlike inhomogeneities, fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, the motion of the wave energy is relatively slow. Numerical simulations performed for ultra-wide-band pulses show that even at the initial stage of wave evolution, the radiation diffuses predominantly in the direction along the major axis of the correlation ellipse. Spectral analysis of the results relates the long tail of the wave observed in the transverse direction to a number of frequency domain "lucky shots" associated with the long-living resonant modes localized inside the sample.
International Nuclear Information System (INIS)
Hagel, J.; Moshammer, H.
1988-01-01
In this paper the authors study the on- momentum nonlinear equations of motion for the coupled transverse motion of a single charged particle in a storage ring. The authors seek for the maximum initial linear amplitudes in the two transverse directions x and y which lead to bounded particle motion as t tends to infinity. Although the authors restrict themselves to sextupole fields in this paper, the authors may easily extend the method to any order multipole. The aim of this work is to derive an analytic approximate expression for the dynamical aperture. The authors approach the solutions of x and y by use of a classical secular perturbation theory. Every coefficient of the perturbation series can be expressed as an analytic function of all the lower order coefficients. Although perturbation theory if it is evaluated to certain specific order leads only to an approximation in terms of bounded (trigonometric) functions the authors may derive information about the stability limit by considering the convergency radius of the general perturbation. This is done in the present paper by deriving an approximate analytic expression for the n-th order perturbation contribution of the whole series using only results up to second order. The actual calculations have been performed for the fully two dimensional case but for simplicity the authors shall explain only the one dimensional case of the pure horizontal motion
Simulations of NLC formation using a microphysical model driven by three-dimensional dynamics
Kirsch, Annekatrin; Becker, Erich; Rapp, Markus; Megner, Linda; Wilms, Henrike
2014-05-01
Noctilucent clouds (NLCs) represent an optical phenomenon occurring in the polar summer mesopause region. These clouds have been known since the late 19th century. Current physical understanding of NLCs is based on numerous observational and theoretical studies, in recent years especially observations from satellites and by lidars from ground. Theoretical studies based on numerical models that simulate NLCs with the underlying microphysical processes are uncommon. Up to date no three-dimensional numerical simulations of NLCs exist that take all relevant dynamical scales into account, i.e., from the planetary scale down to gravity waves and turbulence. Rather, modeling is usually restricted to certain flow regimes. In this study we make a more rigorous attempt and simulate NLC formation in the environment of the general circulation of the mesopause region by explicitly including gravity waves motions. For this purpose we couple the Community Aerosol and Radiation Model for Atmosphere (CARMA) to gravity-wave resolving dynamical fields simulated beforehand with the Kuehlungsborn Mechanistic Circulation Model (KMCM). In our case, the KMCM is run with a horizontal resolution of T120 which corresponds to a minimum horizontal wavelength of 350 km. This restriction causes the resolved gravity waves to be somewhat biased to larger scales. The simulated general circulation is dynamically controlled by these waves in a self-consitent fashion and provides realistic temperatures and wind-fields for July conditions. Assuming a water vapor mixing ratio profile in agreement with current observations results in reasonable supersaturations of up to 100. In a first step, CARMA is applied to a horizontal section covering the Northern hemisphere. The vertical resolution is 120 levels ranging from 72 to 101 km. In this paper we will present initial results of this coupled dynamical microphysical model focussing on the interaction of waves and turbulent diffusion with NLC-microphysics.
Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss
Kiefer-Emmanouilidis, M.; Sirker, J.
2017-12-01
We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization-group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent—in a loose sense—of Hawking radiation.
International Nuclear Information System (INIS)
Chen Xuan; Li Yulong
2011-01-01
Graphical abstract: The dynamic tensile behavior of 2D C/SiC composites was experimentally investigated by means of SHTB. Both the fracture surface and bundle fracture surfaces of composites were observed. The strain rate sensitivity of in-bundle interface was concluded as the dominant contributor to the strain rate sensitivity of the tensile strength. Highlights: → The tensile strength increases with strain rate. → The tensile failure strain remains independent of strain rate. → Macro-structural morphology reveals rough fracture surface under dynamic loading. → SEM morphology reveals integrated bundle pull-out under dynamic loading. → Strain rate sensitivity of in-bundle interface leads to that of the tensile strength. - Abstract: An investigation has been undertaken to determine the dynamic and quasi-static tensile behavior of two-dimensional carbon fiber reinforced silicon carbide matrix (2D-C/SiC) composites by means of the split Hopkinson tension bar and an electronic universal test machine respectively. The results indicate that the tensile strength of 2D C/SiC composites is increased at high strain rate. Furthermore, coated specimens show not only a 15% improvement in tensile strength but heightened strain rate sensitivity compared with uncoated ones. It is also shown that the tensile failure strain is strain rate insensitive and remains around 0.4%. Optical macrograph of failed specimens under dynamic loading revealed jagged fracture surfaces characterized by delamination and crack deviation, together with obvious fiber pull-out/splitting, in contrast with the smooth fracture surfaces under quasi-static loading. Scanning electron microscopy micrograph of fracture surface under dynamic loading clearly displayed integrated bundle pull-out which implies suppressed in-bundle debonding and enhanced in-bundle interfacial strengthening, in contrast with extensive in-bundle debonding under quasi-static loading. Thus we conclude that, with 2D C
Polynomial sequences generated by infinite Hessenberg matrices
Directory of Open Access Journals (Sweden)
Verde-Star Luis
2017-01-01
Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.
Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach
Akbarov, Surkay D
2015-01-01
This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.
Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps
International Nuclear Information System (INIS)
Méndez-Bermúdez, J.A.; Oliveira, Juliano A. de; Leonel, Edson D.
2016-01-01
The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.
Dynamics of a two-dimensional discrete-time SIS model
Directory of Open Access Journals (Sweden)
Jaime H. Barrera
2012-04-01
Full Text Available We analyze a two-dimensional discrete-time SIS model with a non-constant total population. Our goal is to determine the interaction between the total population, the susceptible class and the infective class, and the implications this may have for the disease dynamics. Utilizing a constant recruitment rate in the susceptible class, it is possible to assume the existence of an asymptotic limiting equation, which enables us to reduce the system of, two-equations into a single, dynamically equivalent equation. In this case, we are able to demonstrate the global stability of the disease-free and the endemic equilibria when the basic reproductive number (Ro is less than one and greater than one, respectively. When we consider a non-constant recruitment rate, the total population bifurcates as we vary the birth rate and the death rate. Using computer simulations, we observe different behavior among the infective class and the total population, and possibly, the occurrence of a strange attractor.
Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.
Xiao, Perry; Imhof, Robert E
2012-10-01
Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.
Dynamics of one-dimensional self-gravitating systems using Hermite-Legendre polynomials
Barnes, Eric I.; Ragan, Robert J.
2014-01-01
The current paradigm for understanding galaxy formation in the Universe depends on the existence of self-gravitating collisionless dark matter. Modelling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective non-linear dynamics of many particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyse the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase-space distribution functions f(x, v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.
Two-dimensional NMR investigations of the dynamic conformations of phospholipids and liquid crystals
Energy Technology Data Exchange (ETDEWEB)
Hong, Mei [Univ. of California, Berkeley, CA (United States). Applied Science and Technology
1996-05-01
Two-dimensional 13C, 1H, and 31P nuclear magnetic resonance (NMR) techniques are developed and used to study molecular structure and dynamics in liquid-crystalline systems, primarily phospholipids and nematic liquid crystals. NMR spectroscopy characterizes molecular conformation in terms of orientations and distances of molecular segments. In anisotropically mobile systems, this is achieved by measuring motionally-averaged nuclear dipolar couplings and chemical shift anisotropies. The short-range couplings yield useful bond order parameters, while the long-range interactions constrain the overall conformation. In this work, techniques for probing proton dipolar local fields are further developed to obtain highlyresolved dipolar couplings between protons and rare spins. By exploiting variable-angle sample spinning techniques, orientation-sensitive NMR spectra are resolved according to sitespecific isotropic chemical shifts. Moreover, the signs and magnitudes of various short-range dipolar couplings are obtained. They are used in novel theoretical analyses that provide information about segmental orientations and their distributions. Such information is obtained in a model-independent fashion or with physically reasonable assumptions. The structural investigation of phospholipids is focused on the dynam
NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications
2008-01-01
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...
Infinite possibilities: Computational structures technology
Beam, Sherilee F.
1994-12-01
Computational Fluid Dynamics (or CFD) methods are very familiar to the research community. Even the general public has had some exposure to CFD images, primarily through the news media. However, very little attention has been paid to CST--Computational Structures Technology. Yet, no important design can be completed without it. During the first half of this century, researchers only dreamed of designing and building structures on a computer. Today their dreams have become practical realities as computational methods are used in all phases of design, fabrication and testing of engineering systems. Increasingly complex structures can now be built in even shorter periods of time. Over the past four decades, computer technology has been developing, and early finite element methods have grown from small in-house programs to numerous commercial software programs. When coupled with advanced computing systems, they help engineers make dramatic leaps in designing and testing concepts. The goals of CST include: predicting how a structure will behave under actual operating conditions; designing and complementing other experiments conducted on a structure; investigating microstructural damage or chaotic, unpredictable behavior; helping material developers in improving material systems; and being a useful tool in design systems optimization and sensitivity techniques. Applying CST to a structure problem requires five steps: (1) observe the specific problem; (2) develop a computational model for numerical simulation; (3) develop and assemble software and hardware for running the codes; (4) post-process and interpret the results; and (5) use the model to analyze and design the actual structure. Researchers in both industry and academia continue to make significant contributions to advance this technology with improvements in software, collaborative computing environments and supercomputing systems. As these environments and systems evolve, computational structures technology will
Rigid-flexible coupling dynamics of three-dimensional hub-beams system
International Nuclear Information System (INIS)
Liu Jinyang; Lu Hao
2007-01-01
In the previous research of the coupling dynamics of a hub-beam system, coupling between the rotational motion of hub and the torsion deformation of beam is not taken into account since the system undergoes planar motion. Due to the small longitudinal deformation, coupling between the rotational motion of hub and the longitudinal deformation of beam is also neglected. In this paper, rigid-flexible coupling dynamics is extended to a hub-beams system with three-dimensional large overall motion. Not only coupling between the large overall motion and the bending deformation, but also coupling between the large overall motion and the torsional deformation are taken into account. In case of temperature increase, the longitudinal deformation caused by the thermal expansion is significant, such that coupling between the large overall motion and the longitudinal deformation is also investigated. Combining the characteristics of the hybrid coordinate formulation and the absolute nodal coordinate formulation, the system generalized coordinates include the relative nodal displacement and the slope of each beam element with respect to the body-fixed frame of the hub, and the variables related to the spatial large overall motion of the hub and beams. Based on precise strain-displacement relation, the geometric stiffening effect is taken into account, and the rigid-flexible coupling dynamic equations are derived using velocity variational principle. Finite element method is employed for discretization. Simulation of a hub-beams system is used to show the coupling effect between the large overall motion and the torsional deformation as well as the longitudinal deformation. Furthermore, conservation of energy in case of free motion is shown to verify the formulation
Luna, Byron Quan; Remaître, Alexandre; van Asch, Theo; Malet, Jean-Philippe; van Westen, Cees
2010-05-01
Estimating the magnitude and the intensity of rapid landslides like debris flows is fundamental to evaluate quantitatively the hazard in a specific location. Intensity varies through the travelled course of the flow and can be described by physical features such as deposited volume, velocities, height of the flow, impact forces and pressures. Dynamic run-out models are able to characterize the distribution of the material, its intensity and define the zone where the elements will experience an impact. These models can provide valuable inputs for vulnerability and risk calculations. However, most dynamic run-out models assume a constant volume during the motion of the flow, ignoring the important role of material entrained along its path. Consequently, they neglect that the increase of volume enhances the mobility of the flow and can significantly influence the size of the potential impact area. An appropriate erosion mechanism needs to be established in the analyses of debris flows that will improve the results of dynamic modeling and consequently the quantitative evaluation of risk. The objective is to present and test a simple 1D debris flow model with a material entrainment concept based on limit equilibrium considerations and the generation of excess pore water pressure through undrained loading of the in situ bed material. The debris flow propagation model is based on a one dimensional finite difference solution of a depth-averaged form of the Navier-Stokes equations of fluid motions. The flow is treated as a laminar one phase material, which behavior is controlled by a visco-plastic Coulomb-Bingham rheology. The model parameters are evaluated and the model performance is tested on a debris flow event that occurred in 2003 in the Faucon torrent (Southern French Alps).
Two-dimensional FSI simulation of closing dynamics of a tilting disc mechanical heart valve.
Govindarajan, V; Udaykumar, H S; Herbertson, L H; Deutsch, S; Manning, K B; Chandran, K B
2010-03-01
The fluid dynamics during valve closure resulting in high shear flows and large residence times of particles has been implicated in platelet activation and thrombus formation in mechanical heart valves. Our previous studies with bi-leaflet valves have shown that large shear stresses induced in the gap between the leaflet edge and the valve housing results in relatively high platelet activation levels whereas flow between the leaflets results in shed vortices not conducive to platelet damage. In this study we compare the result of closing dynamics of a tilting disc valve with that of a bi-leaflet valve. The two-dimensional fluid-structure interaction analysis of a tilting disc valve closure mechanics is performed with a fixed grid Cartesian mesh flow solver with local mesh refinement, and a Lagrangian particle dynamic analysis for computation of potential for platelet activation. Throughout the simulation the flow remains in the laminar regime and the flow through the gap width is marked by the development of a shear layer which separates from the leaflet downstream of the valve. Zones of re-circulation are observed in the gap between the leaflet edge and the valve housing on the major orifice region of the tilting disc valve and are seen to be migrating towards the minor orifice region. Jet flow is observed at the minor orifice region and a vortex is formed which sheds in the direction of fluid motion as observed in experiments using PIV measurements. The activation parameter computed for the tilting disc valve, at the time of closure was found to be 2.7 times greater than that of the bi-leaflet mechanical valve and was found to be in the vicinity of the minor orifice region mainly due to the migration of vortical structures from the major to the minor orifice region during the leaflet rebound of the closing phase.
Savin, Alexander V.; Kosevich, Yuriy A.; Cantarero, Andres
2012-08-01
We present a detailed description of semiquantum molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the effects of phonon quantum statistics are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of thermal properties and heat transport in different low-dimensional nanostructures. We describe the determination of temperature in quantum lattice systems, to which the equipartition limit is not applied. We show that one can determine the temperature of such a system from the measured power spectrum and temperature- and relaxation-rate-independent density of vibrational (phonon) states. We simulate the specific heat and heat transport in carbon nanotubes, as well as the heat transport in molecular nanoribbons with perfect (atomically smooth) and rough (porous) edges, and in nanoribbons with strongly anharmonic periodic interatomic potentials. We show that the effects of quantum statistics of phonons are essential for the carbon nanotube in the whole temperature range T<500K, in which the values of the specific heat and thermal conductivity of the nanotube are considerably less than that obtained within the description based on classical statistics of phonons. This conclusion is also applicable to other carbon-based materials and systems with high Debye temperature like graphene, graphene nanoribbons, fullerene, diamond, diamond nanowires, etc. We show that the existence of rough edges and quantum statistics of phonons change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the nanoribbon with perfect edges and classical phonon dynamics and statistics. The semiquantum molecular
Gong, Wuming; Koyano-Nakagawa, Naoko; Li, Tongbin; Garry, Daniel J
2015-03-07
Decoding the temporal control of gene expression patterns is key to the understanding of the complex mechanisms that govern developmental decisions during heart development. High-throughput methods have been employed to systematically study the dynamic and coordinated nature of cardiac differentiation at the global level with multiple dimensions. Therefore, there is a pressing need to develop a systems approach to integrate these data from individual studies and infer the dynamic regulatory networks in an unbiased fashion. We developed a two-step strategy to integrate data from (1) temporal RNA-seq, (2) temporal histone modification ChIP-seq, (3) transcription factor (TF) ChIP-seq and (4) gene perturbation experiments to reconstruct the dynamic network during heart development. First, we trained a logistic regression model to predict the probability (LR score) of any base being bound by 543 TFs with known positional weight matrices. Second, four dimensions of data were combined using a time-varying dynamic Bayesian network model to infer the dynamic networks at four developmental stages in the mouse [mouse embryonic stem cells (ESCs), mesoderm (MES), cardiac progenitors (CP) and cardiomyocytes (CM)]. Our method not only infers the time-varying networks between different stages of heart development, but it also identifies the TF binding sites associated with promoter or enhancers of downstream genes. The LR scores of experimentally verified ESCs and heart enhancers were significantly higher than random regions (p network inference model identified a region with an elevated LR score approximately -9400 bp upstream of the transcriptional start site of Nkx2-5, which overlapped with a previously reported enhancer region (-9435 to -8922 bp). TFs such as Tead1, Gata4, Msx2, and Tgif1 were predicted to bind to this region and participate in the regulation of Nkx2-5 gene expression. Our model also predicted the key regulatory networks for the ESC-MES, MES-CP and CP
Self-Assembly of Infinite Structures
Directory of Open Access Journals (Sweden)
Scott M. Summers
2009-06-01
Full Text Available We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent various notions of computation self-assemble. Several open questions are also presented and motivated.
Generated topology on infinite sets by ultrafilters
Directory of Open Access Journals (Sweden)
Alireza Bagheri Salec
2017-10-01
Full Text Available Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.
Crichton ambiguities with infinitely many partial waves
International Nuclear Information System (INIS)
Atkinson, D.; Kok, L.P.; de Roo, M.
1978-01-01
We construct families of spinless two-particle unitary cross sections that possess a nontrivial discrete phase-shift ambiguity, with in general an infinite number of nonvanishing partial waves. A numerical investigation reveals that some of the previously known finite Crichton ambiguities are merely special cases of the newly constructed examples
Crichton ambiguities with infinitely many partial waves
Atkinson, D.; Kok, L.P.; de Roo, M.
We construct families of spin less two-particle unitary cross sections that possess a nontrivial discrete phase-shift ambiguity, with in general an infinite number of nonvanishing partial waves. A numerical investigation reveals that some of the previously known finite Crichton ambiguities are
Infinite games and $sigma$-porosity
Czech Academy of Sciences Publication Activity Database
Doležal, Martin; Preiss, D.; Zelený, M.
2016-01-01
Roč. 215, č. 1 (2016), s. 441-457 ISSN 0021-2172 Institutional support: RVO:67985840 Keywords : infinite games Subject RIV: BA - General Mathematics Impact factor: 0.796, year: 2016 http://link.springer.com/article/10.1007%2Fs11856-016-1383-9
Model Checking Infinite-State Markov Chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.
2004-01-01
In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state
Gamma spectrometry of infinite 4Π geometry
International Nuclear Information System (INIS)
Nordemann, D.J.R.
1987-07-01
Owing to the weak absorption og gamma radiation by matter, gamma-ray spectrometry may be applied to samples of great volume. A very interesting case is that of the gamma-ray spectrometry applied with 4Π geometry around the detector on a sample assumed to be of infinite extension. The determination of suitable efficiencies allows this method to be quantitative. (author) [pt
A planar calculus for infinite index subfactors
Penneys, David
2011-01-01
We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.
A Planar Calculus for Infinite Index Subfactors
Penneys, David
2013-05-01
We develop an analog of Jones' planar calculus for II 1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.
Model Checking Structured Infinite Markov Chains
Remke, Anne Katharina Ingrid
2008-01-01
In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special
Saso, Tetsuro; Kim, C. I.; Kasuya, Tadao
1983-06-01
Report is given on a computer simulation of the dynamical conductivity σ(ω) of one-dimensional disordered systems with up to 106 sites by MacKinnon’s method. A comparison is made with the asymptotically exact solution valid for weak disorder by Berezinskii.
A conceptual approach to approximate tree root architecture in infinite slope models
Schmaltz, Elmar; Glade, Thomas
2016-04-01
Vegetation-related properties - particularly tree root distribution and coherent hydrologic and mechanical effects on the underlying soil mantle - are commonly not considered in infinite slope models. Indeed, from a geotechnical point of view, these effects appear to be difficult to be reproduced reliably in a physically-based modelling approach. The growth of a tree and the expansion of its root architecture are directly connected with both intrinsic properties such as species and age, and extrinsic factors like topography, availability of nutrients, climate and soil type. These parameters control four main issues of the tree root architecture: 1) Type of rooting; 2) maximum growing distance to the tree stem (radius r); 3) maximum growing depth (height h); and 4) potential deformation of the root system. Geometric solids are able to approximate the distribution of a tree root system. The objective of this paper is to investigate whether it is possible to implement root systems and the connected hydrological and mechanical attributes sufficiently in a 3-dimensional slope stability model. Hereby, a spatio-dynamic vegetation module should cope with the demands of performance, computation time and significance. However, in this presentation, we focus only on the distribution of roots. The assumption is that the horizontal root distribution around a tree stem on a 2-dimensional plane can be described by a circle with the stem located at the centroid and a distinct radius r that is dependent on age and species. We classified three main types of tree root systems and reproduced the species-age-related root distribution with three respective mathematical solids in a synthetic 3-dimensional hillslope ambience. Thus, two solids in an Euclidian space were distinguished to represent the three root systems: i) cylinders with radius r and height h, whilst the dimension of latter defines the shape of a taproot-system or a shallow-root-system respectively; ii) elliptic
International Nuclear Information System (INIS)
Ryu, Jeong-Soo; Seo, Choon-Gyo; Kim, Jae-Min; Yun, Chung-Bang
2010-01-01
This paper proposes a slightly new three-dimensional radial-shaped dynamic infinite elements fully coupled to finite elements for an analysis of soil-structure interaction system in a horizontally layered medium. We then deal with a seismic analysis technique for a three-dimensional soil-structure interactive system, based on the coupled finite-infinite method in frequency domain. The dynamic infinite elements are simulated for the unbounded domain with wave functions propagating multi-generated wave components. The accuracy of the dynamic infinite element and effectiveness of the seismic analysis technique may be demonstrated through a typical compliance analysis of square surface footing, an L-shaped mat concrete footing on layered soil medium and two kinds of practical seismic analysis tests. The practical analyses are (1) a site response analysis of the well-known Hualien site excited by all travelling wave components (primary, shear, Rayleigh waves) and (2) a generation of a floor response spectrum of a nuclear power plant. The obtained dynamic results show good agreement compared with the measured response data and numerical values of other soil-structure interaction analysis package.
Quasiclassical methods for spin-charge coupled dynamics in low-dimensional systems
Energy Technology Data Exchange (ETDEWEB)
Corini, Cosimo
2009-06-12
Spintronics is a new field of study whose broad aim is the manipulation of the spin degrees of freedom in solid state systems. One of its main goals is the realization of devices capable of exploiting, besides the charge, the carriers' - and possibly the nuclei's - spin. The presence of spin-orbit coupling in a system enables the spin and charge degrees of freedom to ''communicate'', a favorable situation if one is to realize such devices. More importantly, it offers the opportunity of doing so by relying solely on electric fields, whereas magnetic fields are otherwise required. Eminent examples of versatile systems with built-in and variously tunable spin-orbit interaction are two-dimensional electron - or hole - gases. The study of spin-charge coupled dynamics in such a context faces a large number of open questions, both of the fundamental and of the more practical type. To tackle the problem we rely on the quasiclassical formalism. This is an approximate quantum-field theoretical formulation with a solid microscopic foundation, perfectly suited for describing phenomena at the mesoscopic scale, and bearing a resemblance to standard Boltzmann theory which makes for physical transparency. Originally born to deal with transport in electron-phonon systems, we first generalize it to the case in which spin-orbit coupling is present, and then move on to apply it to specific situations and phenomena. Among these, to the description of the spin Hall effect and of voltage induced spin polarizations in two-dimensional electron gases under a variety of conditions - stationary or time-dependent, in the presence of magnetic and non-magnetic disorder, in the bulk or in confined geometries -, and to the problem of spin relaxation in narrow wires. (orig.)
Quasiclassical methods for spin-charge coupled dynamics in low-dimensional systems
International Nuclear Information System (INIS)
Corini, Cosimo
2009-01-01
Spintronics is a new field of study whose broad aim is the manipulation of the spin degrees of freedom in solid state systems. One of its main goals is the realization of devices capable of exploiting, besides the charge, the carriers' - and possibly the nuclei's - spin. The presence of spin-orbit coupling in a system enables the spin and charge degrees of freedom to ''communicate'', a favorable situation if one is to realize such devices. More importantly, it offers the opportunity of doing so by relying solely on electric fields, whereas magnetic fields are otherwise required. Eminent examples of versatile systems with built-in and variously tunable spin-orbit interaction are two-dimensional electron - or hole - gases. The study of spin-charge coupled dynamics in such a context faces a large number of open questions, both of the fundamental and of the more practical type. To tackle the problem we rely on the quasiclassical formalism. This is an approximate quantum-field theoretical formulation with a solid microscopic foundation, perfectly suited for describing phenomena at the mesoscopic scale, and bearing a resemblance to standard Boltzmann theory which makes for physical transparency. Originally born to deal with transport in electron-phonon systems, we first generalize it to the case in which spin-orbit coupling is present, and then move on to apply it to specific situations and phenomena. Among these, to the description of the spin Hall effect and of voltage induced spin polarizations in two-dimensional electron gases under a variety of conditions - stationary or time-dependent, in the presence of magnetic and non-magnetic disorder, in the bulk or in confined geometries -, and to the problem of spin relaxation in narrow wires. (orig.)
Lumped versus distributed thermoregulatory control: results from a three-dimensional dynamic model.
Werner, J; Buse, M; Foegen, A
1989-01-01
In this study we use a three-dimensional model of the human thermal system, the spatial grid of which is 0.5 ... 1.0 cm. The model is based on well-known physical heat-transfer equations, and all parameters of the passive system have definite physical values. According to the number of substantially different areas and organs, 54 spatially different values are attributed to each physical parameter. Compatibility of simulation and experiment was achieved solely on the basis of physical considerations and physiological basic data. The equations were solved using a modification of the alternating direction implicit method. On the basis of this complex description of the passive system close to reality, various lumped and distributed parameter control equations were tested for control of metabolic heat production, blood flow and sweat production. The simplest control equations delivering results on closed-loop control compatible with experimental evidence were determined. It was concluded that it is essential to take into account the spatial distribution of heat production, blood flow and sweat production, and that at least for control of shivering, distributed controller gains different from the pattern of distribution of muscle tissue are required. For sweat production this is not so obvious, so that for simulation of sweating control after homogeneous heat load a lumped parameter control may be justified. Based on these conclusions three-dimensional temperature profiles for cold and heat load and the dynamics for changes of the environmental conditions were computed. In view of the exact simulation of the passive system and the compatibility with experimentally attainable variables there is good evidence that those values extrapolated by the simulation are adequately determined. The model may be used both for further analysis of the real thermoregulatory mechanisms and for special applications in environmental and clinical health care.
Murad-Regadas, Sthela M; Regadas Filho, Francisco Sergio Pinheiro; Regadas, Francisco Sergio Pinheiro; Rodrigues, Lusmar Veras; de J R Pereira, Jacyara; da S Fernandes, Graziela Olivia; Dealcanfreitas, Iris Daiana; Mendonca Filho, Jose Jader
2014-02-01
New ultrasound techniques may complement current diagnostic tools, and combined techniques may help to overcome the limitations of individual techniques for the diagnosis of anorectal dysfunction. A high degree of agreement has been demonstrated between echodefecography (dynamic 3-dimensional anorectal ultrasonography) and conventional defecography. Our aim was to evaluate the ability of a combined approach consisting of dynamic 3-dimensional transvaginal and transrectal ultrasonography by using a 3-dimensional biplane endoprobe to assess posterior pelvic floor dysfunctions related to obstructed defecation syndrome in comparison with echodefecography. This was a prospective, observational cohort study conducted at a tertiary-care hospital. Consecutive female patients with symptoms of obstructed defecation were eligible. Each patient underwent assessment of posterior pelvic floor dysfunctions with a combination of dynamic 3-dimensional transvaginal and transrectal ultrasonography by using a biplane transducer and with echodefecography. Kappa (κ) was calculated as an index of agreement between the techniques. Diagnostic accuracy (sensitivity, specificity, and positive and negative predictive values) of the combined technique in detection of posterior dysfunctions was assessed with echodefecography as the standard for comparison. A total of 33 women were evaluated. Substantial agreement was observed regarding normal relaxation and anismus. In detecting the absence or presence of rectocele, the 2 methods agreed in all cases. Near-perfect agreement was found for rectocele grade I, grade II, and grade III. Perfect agreement was found for entero/sigmoidocele, with near-perfect agreement for rectal intussusception. Using echodefecography as the standard for comparison, we found high diagnostic accuracy of transvaginal and transrectal ultrasonography in the detection of posterior dysfunctions. This combined technique should be compared with other dynamic techniques and
Towers and ladders: Infinite parameter symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aulakh, C.S.
1984-05-01
We introduce a class of infinite dimensional algebras with a 'generalized loop structure' by considering the global symmetries of the four dimensional Lagrangian obtained by compactifying general relativity coupled to Yang-Mills in six dimensions down to M 4 xS 2 . The generalization to arbitrary dimensions is then obvious. We show by explicit construction that such algebras possess an infinite number of finite sub-algebras. Among which, for the six dimensional case, is so(1,3) realized on S 2 with vanishing Casimir invariants. This so(1,3) may be interpreted, in accord with a previous conjecture of Salam and Strathdee [Ann. Phys. 141, 316(1982)], as the 'ladder' symmetry for the Kaluza-Klein towers. (author)
Of towers and ladders: Infinite parameter symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aulakh, C.S.
1984-01-01
We introduce a class of infinite dimensional algebras with a 'generalized loop structure' by considering the global symmetries of the four-dimensional lagrangian obtained by compactifying general relativity coupled to Yang-Mills in six-dimensions down to M 4 x S 2 . The generalization to arbitrary dimensions is then obvious. We show by explicit construction that such algebras possess an infinite number of finite sub-algebras among which, for the six-dimensional case, is so (1, 3), realized on S 2 with vanishing Casimir invariants. This so (1, 3) may be interpreted, in accordance with a previous conjecture of Salam and Strathdee, as the 'ladder' symmetry for the Kaluza-Klein towers. (orig.)
3-Dimensional numerical simulations of the dynamics of the Venusian mesosphere and thermosphere
Tingle, S.; Mueller-Wodarg, I. C.
2009-12-01
We present the first results from a new 3-dimensional numerical simulation of the steady state dynamics of the Venusian mesosphere and thermosphere (60-300 km). We have adapted the dynamical core of the Titan thermosphere global circulation model (GCM) [1] to a steady state background atmosphere. Our background atmosphere is derived from a hydrostatic combination of the VTS3 [2] and Venus International Reference Atmosphere (VIRA) [3] empirical models, which are otherwise discontinuous at their 100 km interface. We use 4th order polynomials to link the VTS3 and VIRA thermal profiles and employ hydrostatic balance to derive a consistent density profile. We also present comparisons of our background atmosphere to data from the ESA Venus Express Mission. The thermal structure of the Venusian mesosphere is relatively well documented; however, direct measurements of wind speeds are limited. Venus’ slow rotation results in a negligible Coriolis force. This suggests that the zonal circulation should arise from cyclostrophic balance; where the equatorward component of the centrifugal force balances poleward meridional pressure gradients [4]. The sparseness of direct and in-situ measurements has resulted in the application of cyclostrophic balance to measured thermal profiles to derive wind speeds [5] [6] [7] [8]. However, cyclostrophic balance is only strictly valid at mid latitudes (˜ ± 30-75°) and its applicability to the Venusian mesosphere has not been conclusively demonstrated. Our simulations, by solving the full Navier-Stokes momentum equation, will enable us assess the validity of cyclostrophic balance as a description of mesospheric dynamics. This work is part of an ongoing project to develop the first GCM to encompass the atmosphere from the cloud tops into the thermosphere. When complete, this model will enable self-consistent calculations of the dynamics, energy and composition of the atmosphere. It will thus provide a framework to address many of the
Energy Technology Data Exchange (ETDEWEB)
Jo, Ju-Yeon, E-mail: ju8879@kuchem.kyoto-u.ac.jp; Ito, Hironobu, E-mail: h.ito@kuchem.kyoto-u.ac.jp; Tanimura, Yoshitaka, E-mail: tanimura@kuchem.kyoto-u.ac.jp
2016-12-20
Frequency-domain two-dimensional (2D) Raman signals, which are equivalent to coherent two-dimensional Raman scattering (COTRAS) signals, for liquid water and carbon tetrachloride were calculated using an equilibrium–nonequilibrium hybrid molecular dynamics (MD) simulation algorithm. An appropriate representation of the 2D Raman spectrum obtained from MD simulations provides an easy-to-understand depiction of structural and dynamical properties. We elucidate mechanisms governing the 2D signal profiles involving anharmonic mode–mode coupling and the nonlinearities of the polarizability for the intermolecular and intramolecular vibrational modes. The predicted signal profiles and intensities can be utilized to analyze recently developed single-beam 2D spectra, whose signals are generated from a coherently controlled pulse, allowing the single-beam measurement to be carried out more efficiently. Moreover, the MD simulation results allow us to visualize the molecular structure and dynamics by comparing the accurately calculated spectrum with experimental result.
Energy Technology Data Exchange (ETDEWEB)
Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic)
2012-06-04
In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.
International Nuclear Information System (INIS)
Sergyeyev, Artur
2012-01-01
In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.
Guide for the 2 infinities - the infinitely big and the infinitely small
International Nuclear Information System (INIS)
Armengaud, E.; Arnaud, N.; Aubourg, E.; Bassler, U.; Binetruy, P.; Bouquet, A.; Boutigny, D.; Brun, P.; Chassande-Mottin, E.; Chardin, G.; Coustenis, A.; Descotes-Genon, S.; Dole, H.; Drouart, A.; Elbaz, D.; Ferrando, Ph.; Glicenstein, J.F.; Giraud-Heraud, Y.; Halloin, H.; Kerhoas-Cavata, S.; De Kerret, H.; Klein, E.; Lachieze-Rey, M.; Lagage, P.O.; Langer, M.; Lebrun, F.; Lequeux, J.; Meheut, H.; Moniez, M.; Palanque-Delabrouille, N.; Paul, J.; Piquemal, F.; Polci, F.; Proust, D.; Richard, F.; Robert, J.L.; Rosnet, Ph.; Roudeau, P.; Royole-Degieux, P.; Sacquin, Y.; Serreau, J.; Shifrin, G.; Sida, J.L.; Smith, D.; Sordini, V.; Spiro, M.; Stolarczyk, Th.; Suomijdrvi, T.; Tagger, M.; Vangioni, E.; Vauclair, S.; Vial, J.C.; Viaud, B.; Vignaud, D.
2010-01-01
This book is to be read from both ends: one is dedicated to the path towards the infinitely big and the other to the infinitely small. Each path is made of a series of various subject entries illustrating important concepts or achievements in the quest for the understanding of the concerned infinity. For instance the part concerning the infinitely small includes entries like: quarks, Higgs bosons, radiation detection, Chooz neutrinos... while the part for the infinitely big includes: the universe, cosmic radiations, black matter, antimatter... and a series of experiments such as HESS, INTEGRAL, ANTARES, JWST, LOFAR, Planck, LSST, SOHO, Virgo, VLT, or XMM-Newton. This popularization work includes also an important glossary that explains scientific terms used in the entries. (A.C.)
Solution of the Dirichlet Problem for the Poisson's Equation in a Multidimensional Infinite Layer
Directory of Open Access Journals (Sweden)
O. D. Algazin
2015-01-01
Full Text Available The paper considers the multidimensional Poisson equation in the domain bounded by two parallel hyperplanes (in the multidimensional infinite layer. For an n-dimensional half-space method of solving boundary value problems for linear partial differential equations with constant coefficients is a Fourier transform to the variables in the boundary hyperplane. The same method can be used for an infinite layer, as is done in this paper in the case of the Dirichlet problem for the Poisson equation. For strip and infinite layer in three-dimensional space the solutions of this problem are known. And in the three-dimensional case Green's function is written as an infinite series. In this paper, the solution is obtained in the integral form and kernels of integrals are expressed in a finite form in terms of elementary functions and Bessel functions. A recurrence relation between the kernels of integrals for n-dimensional and (n + 2 -dimensional layers was obtained. In particular, is built the Green's function of the Laplace operator for the Dirichlet problem, through which the solution of the problem is recorded. Even in three-dimensional case we obtained new formula compared to the known. It is shown that the kernel of the integral representation of the solution of the Dirichlet problem for a homogeneous Poisson equation (Laplace equation is an approximate identity (δ-shaped system of functions. Therefore, if the boundary values are generalized functions of slow growth, the solution of the Dirichlet problem for the homogeneous equation (Laplace is written as a convolution of kernels with these functions.
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group
International Nuclear Information System (INIS)
Wang, S.J.
1993-04-01
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)
Statistical mechanical analysis of (1 + ∞) dimensional disordered systems
International Nuclear Information System (INIS)
Skantzos, Nikolaos Stavrou
2001-01-01
Valuable insight into the theory of disordered systems and spin-glasses has been offered by two classes of exactly solvable models: one-dimensional models and mean-field (infinite-range) ones, which, each carry their own specific techniques and restrictions. Both classes of models are now considered as 'exactly solvable' in the sense that in the thermodynamic limit the partition sum can been carried out analytically and the average over the disorder can be performed using methods which are well understood. In this thesis I study equilibrium properties of spin systems with a combination of one-dimensional short- and infinite-range interactions. I find that such systems, under either synchronous or asynchronous spin dynamics, and even in the absence of disorder, lead to phase diagrams with first-order transitions and regions with a multiple number of locally stable states. I then proceed to the study of recurrent neural network models with (1+∞)-dimensional interactions, and find that the competing short- and long-range forces lead to highly complex phase diagrams and that unlike infinite-range (Hopfield-type) models these phase diagrams depend crucially on the number of patterns stored, even away from saturation. To solve the statics of such models for the case of synchronous dynamics I first make a detour to solve the synchronous counterpart of the one-dimensional random-field Ising model, where I prove rigorously that the physics of the two random-field models (synchronous vs. sequential) becomes asymptotically the same, leading to an extensive ground state entropy and an infinite hierarchy of discontinuous transitions close to zero temperature. Finally, I propose and solve the statics of a spin model for the prediction of secondary structure in random hetero-polymers (which are considered as the natural first step to the study of real proteins). The model lies in the class of (1+∞)-dimensional disordered systems as a consequence of having steric- and hydrogen
International Nuclear Information System (INIS)
Wang, Pei; Yi, Wei; Xianlong, Gao
2015-01-01
We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems. (paper)
Wang, Pei; Yi, Wei; Xianlong, Gao
2015-01-01
We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.
Peng, NaiFu; Guan, Hui; Wu, ChuiJie
2016-04-01
In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.
Piccirillo, Bruno; Slussarenko, Sergei; Marrucci, Lorenzo; Santamato, Enrico
2015-10-19
The standard method for experimentally determining the probability distribution of an observable in quantum mechanics is the measurement of the observable spectrum. However, for infinite-dimensional degrees of freedom, this approach would require ideally infinite or, more realistically, a very large number of measurements. Here we consider an alternative method which can yield the mean and variance of an observable of an infinite-dimensional system by measuring only a two-dimensional pointer weakly coupled with the system. In our demonstrative implementation, we determine both the mean and the variance of the orbital angular momentum of a light beam without acquiring the entire spectrum, but measuring the Stokes parameters of the optical polarization (acting as pointer), after the beam has suffered a suitable spin-orbit weak interaction. This example can provide a paradigm for a new class of useful weak quantum measurements.
One dimensional FexCo1-x nanowires; ferromagnetic resonance and magnetization dynamics
Directory of Open Access Journals (Sweden)
Shehreen Aslam
2017-05-01
Full Text Available Soft magnetic nanowires (NWs are widely used for microwave and mm-wave components. The investigation of magnetization damping behavior of NWs have attracted great interest due to large influence of loss to the device, like integrated microwave device, magnetic sensors, and magnetic random access memory. With increasing operational frequency and degree of integration, the requirements to characterize 1-dimensional NWs become increasingly high. The purpose of this work is to study the magnetization dynamics in FexCo1-x NWs. A series of FexCo1-x (x=0, 0.25, 0.5, 0.75, 1 NWs were grown by controlled electro-deposition. By adjusting FexCo1-x concentration (x=0 to 1, the saturation magnetization, increased more than 20%. Ferromagnetic resonance (FMR both in field and frequency sweep mode are employed to characterize the NWs in flip-chip geometry. It is observed that FMR field (Hr increases with increase in applied frequency. At a fixed frequency, Fe NWs resonate at a lower field than the Co substituted NWs. FMR field linewidth (ΔH as well as frequency width (Δf are largest for Co NWs and decreased for Fe NWs. Whereas ΔH and Δf decreased further for FexCo1-x nanowires with increasing x.
Three-Dimensional Model Retrieval Using Dynamic Multi-Descriptor Fusion
Institute of Scientific and Technical Information of China (English)
Jau-Ling Shi; Chang-Hsing Lee; Yao-Wen Hou; Po-Ting Yeh
2017-01-01
In this paper, we propose a dynamic multi-descriptor fusion (DMDF) approach to improving the retrieval accuracy of 3-dimensional (3D) model retrieval systems. First, an independent retrieval list is generated by using each individual descriptor. Second, we propose an automatic relevant/irrelevant models selection (ARMS) approach to selecting the relevant and irrelevant 3D models automatically without any user interaction. A weighted distance, in which the weight associated with each individual descriptor is learnt by using the selected relevant and irrelevant models, is used to measure the similarity between two 3D models. Furthermore, a descriptor-dependent adaptive query point movement (AQPM) approach is employed to update every feature vector. This set of new feature vectors is used to index 3D models in the next search process. Four 3D model databases are used to compare the retrieval accuracy of our proposed DMDF approach with several descriptors as well as some well-known information fusion methods. Experimental results have shown that our proposed DMDF approach provides a promising retrieval result and always yields the best retrieval accuracy.
Kato, Koichi; Nakayoshi, Tomoki; Fukuyoshi, Shuichi; Kurimoto, Eiji; Oda, Akifumi
2017-10-12
Although various higher-order protein structure prediction methods have been developed, almost all of them were developed based on the three-dimensional (3D) structure information of known proteins. Here we predicted the short protein structures by molecular dynamics (MD) simulations in which only Newton's equations of motion were used and 3D structural information of known proteins was not required. To evaluate the ability of MD simulationto predict protein structures, we calculated seven short test protein (10-46 residues) in the denatured state and compared their predicted and experimental structures. The predicted structure for Trp-cage (20 residues) was close to the experimental structure by 200-ns MD simulation. For proteins shorter or longer than Trp-cage, root-mean square deviation values were larger than those for Trp-cage. However, secondary structures could be reproduced by MD simulations for proteins with 10-34 residues. Simulations by replica exchange MD were performed, but the results were similar to those from normal MD simulations. These results suggest that normal MD simulations can roughly predict short protein structures and 200-ns simulations are frequently sufficient for estimating the secondary structures of protein (approximately 20 residues). Structural prediction method using only fundamental physical laws are useful for investigating non-natural proteins, such as primitive proteins and artificial proteins for peptide-based drug delivery systems.
International Nuclear Information System (INIS)
Abadi, Mohammad Tahaye
2015-01-01
A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.
Coordinated three-dimensional motion of the head and torso by dynamic neural networks.
Kim, J; Hemami, H
1998-01-01
The problem of trajectory tracking control of a three dimensional (3D) model of the human upper torso and head is considered. The torso and the head are modeled as two rigid bodies connected at one point, and the Newton-Euler method is used to derive the nonlinear differential equations that govern the motion of the system. The two-link system is driven by six pairs of muscle like actuators that possess physiologically inspired alpha like and gamma like inputs, and spindle like and Golgi tendon organ like outputs. These outputs are utilized as reflex feedback for stability and stiffness control, in a long loop feedback for the purpose of estimating the state of the system (somesthesis), and as part of the input to the controller. Ideal delays of different duration are included in the feedforward and feedback paths of the system to emulate such delays encountered in physiological systems. Dynamical neural networks are trained to learn effective control of the desired maneuvers of the system. The feasibility of the controller is demonstrated by computer simulation of the successful execution of the desired maneuvers. This work demonstrates the capabilities of neural circuits in controlling highly nonlinear systems with multidelays in their feedforward and feedback paths. The ultimate long range goal of this research is toward understanding the working of the central nervous system in controlling movement. It is an interdisciplinary effort relying on mechanics, biomechanics, neuroscience, system theory, physiology and anatomy, and its short range relevance to rehabilitation must be noted.
Duncan, Comer; Jones, Jim
1993-01-01
A key ingredient in the simulation of self-gravitating astrophysical fluid dynamical systems is the gravitational potential and its gradient. This paper focuses on the development of a mixed method multigrid solver of the Poisson equation formulated so that both the potential and the Cartesian components of its gradient are self-consistently and accurately generated. The method achieves this goal by formulating the problem as a system of four equations for the gravitational potential and the three Cartesian components of the gradient and solves them using a distributed relaxation technique combined with conventional full multigrid V-cycles. The method is described, some tests are presented, and the accuracy of the method is assessed. We also describe how the method has been incorporated into our three-dimensional hydrodynamics code and give an example of an application to the collision of two stars. We end with some remarks about the future developments of the method and some of the applications in which it will be used in astrophysics.
Two-dimensional simulation of the thermal stress effect on static and dynamic VDMOS characteristics
International Nuclear Information System (INIS)
Alwan, M.; Beydoun, B.; Ketata, K.; Zoaeter, M.
2005-01-01
Using a two-dimensional simulator, the effect of the thermal stress on static and dynamic vertical double-diffusion metal oxide semiconductor (VDMOS) characteristics have been investigated. The use of the device under certain thermal stress conditions can produce modifications of its physical and electrical properties. Based on physics and 2D simulations, this paper proposes an analysis of this stress effect observed on the electrical characteristics of the device. Parameters responsible of these modifications are determined. Approximate expressions of the ionization coefficients and breakdown voltage in terms of temperature are proposed. Non-punch-through junction theory is used to express the breakdown voltage and the space charge extension with respect to the impurity concentration and the temperature. The capacitances of the device have been also studied. The effect of the stress on C-V characteristics is observed and analyzed. We notice that the drain-gate, drain-source and gate-source capacitances are shifted due to the degradation of device physical properties versus thermal stress
Energy Technology Data Exchange (ETDEWEB)
Abadi, Mohammad Tahaye [Aerospace Research Institute, Tehran (Iran, Islamic Republic of)
2015-10-15
A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.
Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics
International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2009-01-01
Scaling symmetries of the planar, one-dimensional gas dynamic equations with adiabatic index γ are used to obtain Lagrangian and Eulerian conservation laws associated with the symmetries. The known Eulerian symmetry operators for the scaling symmetries are converted to the Lagrangian form, in which the Eulerian spatial position of the fluid element is given in terms of the Lagrangian fluid labels. Conditions for a linear combination of the three scaling symmetries to be a divergence or variational symmetry of the action are established. The corresponding Lagrangian and Eulerian form of the conservation laws are determined by application of Noether's theorem. A nonlocal conservation law associated with the scaling symmetries is obtained by applying a nonlocal symmetry operator to the scaling symmetry-conserved vector. An action principle incorporating known conservation laws using Lagrangian constraints is developed. Noether's theorem for the constrained action principle gives the same formulas for the conserved vector as the classical Noether theorem, except that the Lie symmetry vector field now includes the effects of nonlocal potentials. Noether's theorem for the constrained action principle is used to obtain nonlocal conservation laws. The scaling symmetry conservation laws only apply for special forms of the entropy of the gas.
A novel procedure to assess anismus using three-dimensional dynamic anal ultrasonography.
Murad-Regadas, S M; Regadas, F S P; Rodrigues, L V; Souza, M H L P; Lima, D M R; Silva, F R S; Filho, F S P R
2007-02-01
This study aimed to determine the value of three-dimensional (3D) dynamic endosonography in the assessment of anismus. Sixty-one women submitted to anorectal manometry were enrolled including 40 healthy women and 21 patients with anismus diagnosed by manometry. Patients were submitted to 3D endosonography. Images were acquired at rest and during straining and analysed in axial and midline longitudinal planes. Sphincter integrity was quantified. The angle between the internal edge of the puborectalis with a vertical line according to the anal canal axis was calculated at rest and during straining. The angle increased in 39 of the 40 normal individuals and decreased in all patients with anismus during straining compared with the angle at rest (88.36 degrees ) and straining (98.65 degrees ) in normal individuals. In the anismus group, the angle decreased at rest (90.91 degrees ) and straining (84.89 degrees ). The difference between angle sizes in normal and anismus patients during straining was statistically significant (P anismus confirming the anorectal manometric results.
Lin, Hui; Gao, Jian; Mei, Qing; He, Yunbo; Liu, Junxiu; Wang, Xingjin
2016-04-04
It is a challenge for any optical method to measure objects with a large range of reflectivity variation across the surface. Image saturation results in incorrect intensities in captured fringe pattern images, leading to phase and measurement errors. This paper presents a new adaptive digital fringe projection technique which avoids image saturation and has a high signal to noise ratio (SNR) in the three-dimensional (3-D) shape measurement of objects that has a large range of reflectivity variation across the surface. Compared to previous high dynamic range 3-D scan methods using many exposures and fringe pattern projections, which consumes a lot of time, the proposed technique uses only two preliminary steps of fringe pattern projection and image capture to generate the adapted fringe patterns, by adaptively adjusting the pixel-wise intensity of the projected fringe patterns based on the saturated pixels in the captured images of the surface being measured. For the bright regions due to high surface reflectivity and high illumination by the ambient light and surfaces interreflections, the projected intensity is reduced just to be low enough to avoid image saturation. Simultaneously, the maximum intensity of 255 is used for those dark regions with low surface reflectivity to maintain high SNR. Our experiments demonstrate that the proposed technique can achieve higher 3-D measurement accuracy across a surface with a large range of reflectivity variation.
International Nuclear Information System (INIS)
Hadek, J.
1999-01-01
The paper gives a brief survey of the fifth three-dimensional dynamic Atomic Energy Research benchmark calculation results received with the code DYN3D/ATHLET at NRI Rez. This benchmark was defined at the seventh Atomic Energy Research Symposium (Hoernitz near Zittau, 1997). Its initiating event is a symmetrical break of the main steam header at the end of the first fuel cycle and hot shutdown conditions with one stuck out control rod group. The calculations were performed with the externally coupled codes ATHLET Mod.1.1 Cycle C and DYN3DH1.1/M3. The standard WWER-440/213 input deck of ATHLET code was adopted for benchmark purposes and for coupling with the code DYN3D. The first part of paper contains a brief characteristics of NPP input deck and reactor core model. The second part shows the time dependencies of important global and local parameters. In comparison with the results published at the eighth Atomic Energy Research Symposium (Bystrice nad Pernstejnem, 1998), the results published in this paper are based on improved ATHLET descriptions of control and safety systems. (Author)
Dynamics of laser ablative shock waves from one dimensional periodic structured surfaces
Paturi, Prem Kiran; Chelikani, Leela; Pinnoju, Venkateshwarlu; Acrhem Team
2015-06-01
Spatio-temporal evolution of Laser ablative shock waves (LASWs) from one dimensional periodic structured surfaces (1D-PSS) of Aluminum is studied using time resolved defocused shadowgraphy technique. LASWs are generated by focusing 7 ns pulses from second harmonic of Nd:YAG (532 nm, 10 Hz) laser on to 1D-PSS with sinusoidal and triangular modulations of varying periodicity. An expanded He-Ne laser (632.8 nm) is used as probe beam for shadowgraphy. Evolution of ablative shock front (SF) with 1.5 ns temporal resolution is used to measure position of the SF, its nature, density and pressure behind the SF. The effect of surface modulation on the LASW and contact front dynamics was compared to those from a flat surface (FS) of Aluminum. SWs from FS and PSS obeyed Taylor's solution for spherical and planar nature, respectively. The velocity of SF from 1D PSS had a twofold increase compared to the FS. This was further enhanced for structures whose periodicity is of the order of excitation wavelength. Variation of SF properties with varying periodicity over a range of 3.3 μm to 0.55 μm has the potential to tailor shockwaves of required parameters. The work is supported by Defence Research and Developement Organization, India through Grants-in-Aid Program. The periodic surfaces were procured with financial support from BRFST project No. NFP-MAT-A12-04.
A three-dimensional computer code for the nonlinear dynamic response of an HTGR core
International Nuclear Information System (INIS)
Subudhi, M.; Lasker, L.; Koplik, B.; Curreri, J.; Goradia, H.
1979-01-01
A three-dimensional dynamic code has been developed to determine the nonlinear response of an HTGR core. The HTGR core consists of several thousands of hexagonal core blocks. These are arranged in layers stacked together. Each layer contains many core blocks surrounded on their outer periphery by reflector blocks. The entire assembly is contained within a prestressed concrete reactor vessel. Gaps exist between adjacent blocks in any horizontal plane. Each core block in a given layer is connected to the blocks directly above and below it via three dowell pins. The present analytical study is directed towards an investigation of the nonlinear response of the reactor core blocks in the event of a seismic occurrence. The computer code is developed for a specific mathematical model which represents a vertical arrangement of layers of blocks. This comprises a 'block module' of core elements which would be obtained by cutting a cylindrical portion consisting of seven fuel blocks per layer. It is anticipated that a number of such modules properly arranged could represent the entire core. Hence, the predicted response of this module would exhibit the response characteristics of the core. (orig.)
International Nuclear Information System (INIS)
Zhang, Jianxin; Zhang, Zhenjun; Tong, Peiqing
2013-01-01
We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth
Three-dimensional computer code for the nonlinear dynamic response of an HTGR core
International Nuclear Information System (INIS)
Subudhi, M.; Lasker, L.; Koplik, B.; Curreri, J.; Goradia, H.
1979-01-01
A three-dimensional dynamic code has been developed to determine the nonlinear response of an HTGR core. The HTGR core consists of several thousands of hexagonal core blocks. These are arranged inlayers stacked together. Each layer contains many core blocks surrounded on their outer periphery by reflector blocks. The entire assembly is contained within a prestressed concrete reactor vessel. Gaps exist between adjacent blocks in any horizontal plane. Each core block in a given layer is connected to the blocks directly above and below it via three dowell pins. The present analystical study is directed towards an invesstigation of the nonlinear response of the reactor core blocks in the event of a seismic occurrence. The computer code is developed for a specific mathemtical model which represents a vertical arrangement of layers of blocks. This comprises a block module of core elements which would be obtained by cutting a cylindrical portion consisting of seven fuel blocks per layer. It is anticipated that a number of such modules properly arranged could represent the entire core. Hence, the predicted response of this module would exhibit the response characteristics of the core
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jianxin; Zhang, Zhenjun [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Tong, Peiqing, E-mail: pqtong@njnu.edu.cn [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023 (China)
2013-07-15
We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth.
Kwon, Hyeok-Chan; Yang, Wooseok; Lee, Daehee; Ahn, Jihoon; Lee, Eunsong; Ma, Sunihl; Kim, Kyungmi; Yun, Seong-Cheol; Moon, Jooho
2018-05-22
Organometal halide perovskite materials have become an exciting research topic as manifested by intense development of thin film solar cells. Although high-performance solar-cell-based planar and mesoscopic configurations have been reported, one-dimensional (1-D) nanostructured perovskite solar cells are rarely investigated despite their expected promising optoelectrical properties, such as enhanced charge transport/extraction. Herein, we have analyzed the 1-D nanostructure effects of organometal halide perovskite (CH 3 NH 3 PbI 3- x Cl x ) on recombination and charge carrier dynamics by utilizing a nanoporous anodized alumina oxide scaffold to fabricate a vertically aligned 1-D nanopillared array with controllable diameters. It was observed that the 1-D perovskite exhibits faster charge transport/extraction characteristics, lower defect density, and lower bulk resistance than the planar counterpart. As the aspect ratio increases in the 1-D structures, in addition, the charge transport/extraction rate is enhanced and the resistance further decreases. However, when the aspect ratio reaches 6.67 (diameter ∼30 nm), the recombination rate is aggravated due to high interface-to-volume ratio-induced defect generation. To obtain the full benefits of 1-D perovskite nanostructuring, our study provides a design rule to choose the appropriate aspect ratio of 1-D perovskite structures for improved photovoltaic and other optoelectrical applications.
DEFF Research Database (Denmark)
Mouritsen, Ole G.; Praestgaard, Eigil
1988-01-01
obeys dynamical scaling and the shape of the dynamical scaling function pertaining to the structure factor is found to depend on P. Specifically, this function is described by a Porod-law behavior, q-ω, where ω increases with the wall softness. The kinetic exponent, which describes how the linear domain...... infinite to zero temperature as well as to nonzero temperatures below the ordering transition. The continuous nature of the spin variables causes the domain walls to be ‘‘soft’’ and characterized by a finite thickness. The steady-state thickness of the walls can be varied by a model parameter, P. At zero...... size varies with time, R(t)∼tn, is for both models at zero temperature determined to be n≃0.25, independent of P. At finite temperatures, the growth kinetics is found to cross over to the Lifshitz-Allen-Cahn law characterized by n≃0.50. The results support the idea of two separate zero...
Bing, Xue; Yicai, Ji
2018-06-01
In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.
Yamashita, Koichi; Morokuma, Keiji; Le Quéré, Frederic; Leforestier, Claude
1992-04-01
New ab initio potential energy surfaces (PESs) of the ground and B ( 1B 2) states of ozone have been calculated with the CASSCF-SECI/DZP method to describe the three-dimensional photodissociation process. The dissociation energy of the ground state and the vertical barrier height of the B PES are obtained to be 0.88 and 1.34 eV, respectively, in better agreement with the experimental values than the previous calculation. The photodissociation autocorrelation function, calculated on the new B PES, based on exact three-dimensional quantum dynamics, reproduces well the main recurrence feature extracted from the experimental spectra.
International Nuclear Information System (INIS)
Yang Xiao-Gang; Wang Qi; Forest, M. Gregory
2014-01-01
We systematically explore near equilibrium, flow-driven, and flow-activity coupled dynamics of polar active liquid crystals using a continuum model. Firstly, we re-derive the hydrodynamic model to ensure the thermodynamic laws are obeyed and elastic stresses and forces are consistently accounted. We then carry out a linear stability analysis about constant steady states to study near equilibrium dynamics around the steady states, revealing long-wave instability inherent in this model system and how active parameters in the model affect the instability. We then study model predictions for one-dimensional (1D) spatial—temporal structures of active liquid crystals in a channel subject to physical boundary conditions. We discuss the model prediction in two selected regimes, one is the viscous stress dominated regime, also known as the flow-driven regime, while the other is the full regime, in which all active mechanisms are included. In the viscous stress dominated regime, the polarity vector is driven by the prescribed flow field. Dynamics depend sensitively on the physical boundary condition and the type of the driven flow field. Bulk-dominated temporal periodic states and spatially homogeneous states are possible under weak anchoring conditions while spatially inhomogeneous states exist under strong anchoring conditions. In the full model, flow-orientation interaction generates a host of planar as well as out-of-plane spatial—temporal structures related to the spontaneous flows due to the molecular self-propelled motion. These results provide contact with the recent literature on active nematic suspensions. In addition, symmetry breaking patterns emerge as the additional active viscous stress due to the polarity vector is included in the force balance. The inertia effect is found to limit the long-time survival of spatial structures to those with small wave numbers, i.e., an asymptotic coarsening to long wave structures. A rich set of mechanisms for generating
Representations of the infinite symmetric group
Borodin, Alexei
2016-01-01
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.
Quark ensembles with the infinite correlation length
Zinov'ev, G. M.; Molodtsov, S. V.
2015-01-01
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.
Quark ensembles with the infinite correlation length
International Nuclear Information System (INIS)
Zinov’ev, G. M.; Molodtsov, S. V.
2015-01-01
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble
Quark ensembles with the infinite correlation length
Energy Technology Data Exchange (ETDEWEB)
Zinov’ev, G. M. [National Academy of Sciences of Ukraine, Bogoliubov Institute for Theoretical Physics (Ukraine); Molodtsov, S. V., E-mail: molodtsov@itep.ru [Joint Institute for Nuclear Research (Russian Federation)
2015-01-15
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.
Directory of Open Access Journals (Sweden)
M.R. Mofakhami
2008-01-01
Full Text Available In this paper sound transmission through the multilayered viscoelastic air filled cylinders subjected to the incident acoustic wave is studied using the technique of separation of variables on the basis of linear three dimensional theory of elasticity. The effect of interior acoustic medium on the mode maps (frequency vs geometry and noise reduction is investigated. The effects of internal absorption and external moving medium on noise reduction are also evaluated. The dynamic viscoelastic properties of the structure are rigorously taken into account with a power law technique that models the viscoelastic damping of the cylinder. A parametric study is also performed for the two layered infinite cylinders to obtain the effect of viscoelastic layer characteristics such as thickness, material type and frequency dependency of viscoelastic properties on the noise reduction. It is shown that using constant and frequency dependent viscoelastic material with high loss factor leads to the uniform noise reduction in the frequency domain. It is also shown that the noise reduction obtained for constant viscoelastic material property is subjected to some errors in the low frequency range with respect to those obtained for the frequency dependent viscoelastic material.
Multidimensional pattern formation has an infinite number of constants of motion
International Nuclear Information System (INIS)
Mineev-Weinstein, M.B.
1993-01-01
Extending our previous work on two-dimensional growth for the Laplace equation [M. B. Mineev, Physica D 43, 288 (1990)] we study here multidimensional growth for arbitrary elliptic equations, describing inhomogeneous and anisotropic pattern-formation processes. We find that these nonlinear processes are governed by an infinite number of conservation laws. Moreover, in many cases all 2 dynamics of the interface can be reduced to the linear time dependence of only one ''moment'' M 0 , which corresponds to the changing volume, while all higher moments M l are constant in time. These moments have a purely geometrical nature, and thus carry information about the moving shape. These conserved quantities [Eqs. (7) and (8) of this article] are interpreted as coefficients of the multipole expansion of the Newtonian potential created by the mass uniformly occupying the domain enclosing the moving interface. Thus the question of how to recover the moving shape using these conserved quantities is reduced to the classical inverse potential problem of reconstructing the shape of a body from its exterior gravitational potential. Our results also suggest the possibility of controlling a moving interface by appropriately varying the location and strength of sources and sinks
Suemitsu, Yoshikazu; Nara, Shigetoshi
2004-09-01
Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.
Algorithms for Calculating Alternating Infinite Series
International Nuclear Information System (INIS)
Garcia, Hector Luna; Garcia, Luz Maria
2015-01-01
This paper are presented novel algorithms for exact limits of a broad class of infinite alternating series. Many of these series are found in physics and other branches of science and their exact values found for us are in complete agreement with the values obtained by other authors. Finally, these simple methods are very powerful in calculating the limits of many series as shown by the examples
Infinite Responsibility: An expression of Saintliness
Conceição Soares
2009-01-01
In this paper I will focus my attention in the distinctions embedded in standard moral philosophy, especially in the philosophy of Kant between, on the one hand, duty and supererogation on the other hand, with the aim to contrast them with the Levinas’s perspective, namely his notion of infinite responsibility. My account of Levinas’s philosophy will show that it challenges – breaking down – deeply entrenched distinctions in the dominant strands of moral philosophy, within which the theory of...
Infinite degeneracy of states in quantum gravity
International Nuclear Information System (INIS)
Hackett, Jonathan; Wan Yidun
2011-01-01
The setting of Braided Ribbon Networks is used to present a general result in spin-networks embedded in manifolds: the existence of an infinite number of species of conserved quantities. Restricted to three-valent networks the number of such conserved quantities in a given network is shown to be determined by the number of nodes in the network. The implication of these conserved quantities is discussed in the context of Loop Quantum Gravity.
Comments related to infinite wedge representations
Grieve, Nathan
2016-01-01
We study the infinite wedge representation and show how it is related to the universal extension of $g[t,t^{-1}]$ the loop algebra of a complex semi-simple Lie algebra $g$. We also give an elementary proof of the boson-fermion correspondence. Our approach to proving this result is based on a combinatorial construction with partitions combined with an application of the Murnaghan-Nakayama rule.
Finiteness properties of congruence classes of infinite matrices
Eggermont, R.H.
2014-01-01
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
On infinite walls in deformation quantization
International Nuclear Information System (INIS)
Kryukov, S.; Walton, M.A.
2005-01-01
We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In deformation quantization, considered as an autonomous formulation of quantum mechanics, the Wigner function of stationary states must be found by solving the so-called *-genvalue ('stargenvalue') equation for the Hamiltonian. For the cases considered here, this pseudo-differential equation is difficult to solve directly, without an ad hoc modification of the potential. Here we treat the infinite wall as the limit of a solvable exponential potential. Before the limit is taken, the corresponding *-genvalue equation involves the Wigner function at momenta translated by imaginary amounts. We show that it can be converted to a partial differential equation, however, with a well-defined limit. We demonstrate that the Wigner functions calculated from the standard Schroedinger wave functions satisfy the resulting new equation. Finally, we show how our results may be adapted to allow for the presence of another, non-singular part in the potential
Pure infiniteness and ideal structure of C*-algebras associated to Fell bundles
DEFF Research Database (Denmark)
Kwasniewski, Bartosz; Szymanski, Wojciech
2017-01-01
are introduced and investigated by themselves and in relation to the partial dynamical system dual to B. Several criteria of pure infiniteness of C^*_r(B) are given. It is shown that they generalize and unify corresponding results obtained in the context of crossed products, by the following duos: Laca...
Infinitely connected subgraphs in graphs of uncountable chromatic number
DEFF Research Database (Denmark)
Thomassen, Carsten
2016-01-01
Erdős and Hajnal conjectured in 1966 that every graph of uncountable chromatic number contains a subgraph of infinite connectivity. We prove that every graph of uncountable chromatic number has a subgraph which has uncountable chromatic number and infinite edge-connectivity. We also prove that......, if each orientation of a graph G has a vertex of infinite outdegree, then G contains an uncountable subgraph of infinite edge-connectivity....
Supersolids: Solids Having Finite Volume and Infinite Surfaces.
Love, William P.
1989-01-01
Supersolids furnish an ideal introduction to the calculus topic of infinite series, and are useful for combining that topic with integration. Five examples of supersolids are presented, four requiring only a few basic properties of infinite series and one requiring a number of integration principles as well as infinite series. (MNS)
Dynamical decoupling of unbounded Hamiltonians
Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin
2018-03-01
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
Chen, Yung-Chuan; Tu, Yuan-Kun; Zhuang, Jun-Yan; Tsai, Yi-Jung; Yen, Cheng-Yo; Hsiao, Chih-Kun
2017-11-01
A three-dimensional dynamic elastoplastic finite element model was constructed and experimentally validated and was used to investigate the parameters which influence bone temperature during drilling, including the drill speed, feeding force, drill bit diameter, and bone density. Results showed the proposed three-dimensional dynamic elastoplastic finite element model can effectively simulate the temperature elevation during bone drilling. The bone temperature rise decreased with an increase in feeding force and drill speed, however, increased with the diameter of drill bit or bone density. The temperature distribution is significantly affected by the drilling duration; a lower drilling speed reduced the exposure duration, decreases the region of the thermally affected zone. The constructed model could be applied for analyzing the influence parameters during bone drilling to reduce the risk of thermal necrosis. It may provide important information for the design of drill bits and surgical drilling powers.
Yonamine, Yusuke; Cervantes-Salguero, Keitel; Minami, Kosuke; Kawamata, Ibuki; Nakanishi, Waka; Hill, Jonathan P; Murata, Satoshi; Ariga, Katsuhiko
2016-05-14
In this study, a Langmuir-Blodgett (LB) system has been utilized for the regulation of polymerization of a DNA origami structure at the air-water interface as a two-dimensionally confined medium, which enables dynamic condensation of DNA origami units through variation of the film area at the macroscopic level (ca. 10-100 cm(2)). DNA origami sheets were conjugated with a cationic lipid (dioctadecyldimethylammonium bromide, 2C18N(+)) by electrostatic interaction and the corresponding LB-film was prepared. By applying dynamic pressure variation through compression-expansion processes, the lipid-modified DNA origami sheets underwent anisotropic polymerization forming a one-dimensionally assembled belt-shaped structure of a high aspect ratio although the thickness of the polymerized DNA origami was maintained at the unimolecular level. This approach opens up a new field of mechanical induction of the self-assembly of DNA origami structures.
DEFF Research Database (Denmark)
Kumari Ramachandran, Gireesh Kumar Vasanta; Bredmose, Henrik; Sørensen, Jens Nørkær
2014-01-01
, which is a consequence of the wave-induced rotor dynamics. Loads and coupled responses are predicted for a set of load cases with different wave headings. Further, an advanced aero-elastic code, Flex5, is extended for the TLP wind turbine configuration and the response comparison with the simpler model......A dynamic model for a tension-leg platform (TLP) floating offshore wind turbine is proposed. The model includes three-dimensional wind and wave loads and the associated structural response. The total system is formulated using 17 degrees of freedom (DOF), 6 for the platform motions and 11...... for the wind turbine. Three-dimensional hydrodynamic loads have been formulated using a frequency-and direction-dependent spectrum. While wave loads are computed from the wave kinematics using Morison's equation, the aerodynamic loads are modeled by means of unsteady blade-element-momentum (BEM) theory...
Chen, Lian-Wang; Lu, Yuan-Zhong; Liu, Jie; Guo, Ruo-Mei
2001-09-01
Using three dimensional (3D) viscoelastic finite element method (FEM) we study the dynamic evolution pattern of the coseismic change of Coulomb failure stress and postseismic change, on time scale of hundreds years, of rheological effect induced by the M S=7.2 Xingtai earthquake on March 22, 1966. Then, we simulate the coseismic disturbance in stress field in North China and dynamic change rate on one-year scale caused by the Xingtai earthquake and Tangshan earthquake during 15 years from 1966 to 1980. Finally, we discuss the triggering of a strong earthquake to another future strong earthquake.
Li, Bing; Li, Yongkun; Zhang, Xuemei
2016-01-01
In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).
Three Dimensional Dynamic Model Based Wind Field Reconstruction from Lidar Data
International Nuclear Information System (INIS)
Raach, Steffen; Schlipf, David; Haizmann, Florian; Cheng, Po Wen
2014-01-01
Using the inflowing horizontal and vertical wind shears for individual pitch controller is a promising method if blade bending measurements are not available. Due to the limited information provided by a lidar system the reconstruction of shears in real-time is a challenging task especially for the horizontal shear in the presence of changing wind direction. The internal model principle has shown to be a promising approach to estimate the shears and directions in 10 minutes averages with real measurement data. The static model based wind vector field reconstruction is extended in this work taking into account a dynamic reconstruction model based on Taylor's Frozen Turbulence Hypothesis. The presented method provides time series over several seconds of the wind speed, shears and direction, which can be directly used in advanced optimal preview control. Therefore, this work is an important step towards the application of preview individual blade pitch control under realistic wind conditions. The method is tested using a turbulent wind field and a detailed lidar simulator. For the simulation, the turbulent wind field structure is flowing towards the lidar system and is continuously misaligned with respect to the horizontal axis of the wind turbine. Taylor's Frozen Turbulence Hypothesis is taken into account to model the wind evolution. For the reconstruction, the structure is discretized into several stages where each stage is reduced to an effective wind speed, superposed with a linear horizontal and vertical wind shear. Previous lidar measurements are shifted using again Taylor's Hypothesis. The wind field reconstruction problem is then formulated as a nonlinear optimization problem, which minimizes the residual between the assumed wind model and the lidar measurements to obtain the misalignment angle and the effective wind speed and the wind shears for each stage. This method shows good results in reconstructing the wind characteristics of a three
Validation of dynamic MLC-controller log files using a two-dimensional diode array
International Nuclear Information System (INIS)
Li, Jonathan G.; Dempsey, James F.; Ding Li; Liu, Chihray; Palta, Jatinder R.
2003-01-01
Intensity-modulated radiation therapy (IMRT) delivered with multi-leaf collimator (MLC) in the step-and-shoot mode uses multiple static MLC segments to achieve intensity modulation. For typical IMRT treatment plans, significant numbers of segments are delivered with monitor units (MUs) of much less than 10. Verification of the ability of the linear accelerator (linac) to deliver small MU segments accurately is an important step in the IMRT commissioning and quality assurance (QA) process. Recent studies have reported large discrepancies between the intended and delivered segment MUs. These discrepancies could potentially cause large errors in the delivered patient dose. We have undertaken a systematic study to evaluate the accuracy of the dynamic MLC log files, which are created automatically by our commercial MLC workstation after each delivery, in recording the fractional MU delivered in the step-and-shoot mode. Two linac models were evaluated with simple-geometry leaf sequences and delivered with different total MUs and different nominal dose rates. A commercial two-dimensional diode array was used for the measurement. Large discrepancies between the intended and delivered segment MUs were found. The discrepancies were larger for small MU segments at higher dose rate, with some small MU segments completely undelivered. The recorded fractional MUs in the log files were found to agree with what was delivered within the limits of our experimental uncertainty. Our results indicate that it is important to verify the delivery accuracy of small MU segments that could potentially occur in a patient treatment and that the log files are useful in checking the integrity of the linac delivery once validated. Thus validated log files can be used as a QA tool for general IMRT delivery and patient-specific plan verification
The evaluation of three-dimensional dynamic contrast enhanced MR angiography in portal hypertension
International Nuclear Information System (INIS)
Wu Zhuo; Liang Biling; Liu Qingyu; Zhong Jinglian; Ye Ruixin; Ling Yunbiao; Ou Qingjia
2006-01-01
Objective: To evaluate the techniques of three-dimensional dynamic contrast enhanced MR angiography (3D DCE MRA)with normative timing of sequences, enhancive 3D slab thickness and subtraction in portosystemic collaterals. Methods: Before April 2003, 12 patients were performed with 75-90 mm of 3D slab thickness and 3-5 repeated sequences estimated by breath, after April 2003, 18 patients were performed with 150-180 mm of 3D slab thickness and 5 normative repeated sequences respectively at 0, 20, 40, 60 and 90 s. After subtracting selective arterial phase images from subsequent portal venous phase images, two radiologists assessed visualization of portal collaterals independently with a four - point scale for ranking of image quality in maximum intensity projection (MIP) images with and without subtraction. Results: Average scores for image quality in visualization of the portal vein with subtraction were significantly depressed compared with the scores without subtraction (2.53±0.49 versus 2.74±0.31, P<0.05). However, subtraction three dimension-maximum intensity projection (3D-MIP) gave superior visualization of portal collaterals compared with non-subtraction 3D-MIP(2.58±0.30 versus 1.63±0.50). A statistically significant difference (P<0.01) was found between the two groups of esophageal varices. Most of portosystemic shunts demonstrated in the same time as the portal vein at about 20s, but some of collaterals demonstrated in delay time. Conclusion: Subtraction 3D-MIP demonstrates portosystemic collaterals more clearly than non-subtraction; normative timing of sequences ensure against omitting varices displayed late, 3 D slab thickness provides details about paraumbilical vein and retroperitoneal collaterals. (authors)
Directory of Open Access Journals (Sweden)
Shankhadeep Das
2016-01-01
Full Text Available Sedimentation is one of the most popular wastewater treatment processes, and is used to separate solid particles from carrier fluid in settling tanks known as clarifiers. The clarifier, as the last major facility in wastewater treatment plants (WWTPs, can limit or define the performance of the overall WWTP. This paper presents a novel three-dimensional unsteady computational fluid dynamics (CFD model to improve the efficiency of an industrial clarifier that had been experiencing underperformance and reduction in wastewater handling capacity. We propose a numerical technique to address the transient process of removing sludge from the floor of clarifiers by using rotating rakes. The CFD model was first applied to analyzing the ramifications of the current clarifier geometry on performance. The results show that the root causes for underperformance are related to the unconventional top side feed design of the clarifier, which leads to significant asymmetry in the flow distribution. The CFD model was next used to investigate various design modifications with the goal of improving the clarifier performance. A few geometry modification ideas such as an inward baffle, dissipating inlets, and a submerged skirt were found to create a more uniform flow distribution in the clarifier, significantly reducing the backflow into the feedwell and the velocity of the flow exiting the feedwell, which helps the solid particles to settle in the clarifier. These three designs were found to reduce the effluent total suspended solids (TSS by more than 80% and thus significantly improve clarifier performance. It is believed that the CFD model developed in this study can become a computationally efficient tool for investigating the performance of industrial clarifiers with complex geometries and rotating rakes.
Allaire, S E; Yates, S R; Ernst, F F; Gan, J
2002-01-01
There is an important need to develop instrumentation that allows better understanding of atmospheric emission of toxic volatile compounds associated with soil management. For this purpose, chemical movement and distribution in the soil profile should be simultaneously monitored with its volatilization. A two-dimensional rectangular soil column was constructed and a dynamic sequential volatilization flux chamber was attached to the top of the column. The flux chamber was connected through a manifold valve to a gas chromatograph (GC) for real-time concentration measurement. Gas distribution in the soil profile was sampled with gas-tight syringes at selected times and analyzed with a GC. A pressure transducer was connected to a scanivalve to automatically measure the pressure distribution in the gas phase of the soil profile. The system application was demonstrated by packing the column with a sandy loam in a symmetrical bed-furrow system. A 5-h furrow irrigation was started 24 h after the injection of a soil fumigant, propargyl bromide (3-bromo-1-propyne; 3BP). The experience showed the importance of measuring lateral volatilization variability, pressure distribution in the gas phase, chemical distribution between the different phases (liquid, gas, and sorbed), and the effect of irrigation on the volatilization. Gas movement, volatilization, water infiltration, and distribution of degradation product (Br-) were symmetric around the bed within 10%. The system saves labor cost and time. This versatile system can be modified and used to compare management practices, estimate concentration-time indexes for pest control, study chemical movement, degradation, and emissions, and test mathematical models.
Studying Operation Rules of Cascade Reservoirs Based on Multi-Dimensional Dynamics Programming
Directory of Open Access Journals (Sweden)
Zhiqiang Jiang
2017-12-01
Full Text Available Although many optimization models and methods are applied to the optimization of reservoir operation at present, the optimal operation decision that is made through these models and methods is just a retrospective review. Due to the limitation of hydrological prediction accuracy, it is practical and feasible to obtain the suboptimal or satisfactory solution by the established operation rules in the actual reservoir operation, especially for the mid- and long-term operation. In order to obtain the optimized sample data with global optimality; and make the extracted operation rules more reasonable and reliable, this paper presents the multi-dimensional dynamic programming model of the optimal joint operation of cascade reservoirs and provides the corresponding recursive equation and the specific solving steps. Taking Li Xianjiang cascade reservoirs as a case study, seven uncertain problems in the whole operation period of the cascade reservoirs are summarized after a detailed analysis to the obtained optimal sample data, and two sub-models are put forward to solve these uncertain problems. Finally, by dividing the whole operation period into four characteristic sections, this paper extracts the operation rules of each reservoir for each section respectively. When compared the simulation results of the extracted operation rules with the conventional joint operation method; the result indicates that the power generation of the obtained rules has a certain degree of improvement both in inspection years and typical years (i.e., wet year; normal year and dry year. So, the rationality and effectiveness of the extracted operation rules are verified by the comparative analysis.
Anderson, B. H.; Putt, C. W.; Giamati, C. C.
1981-01-01
Color coding techniques used in the processing of remote sensing imagery were adapted and applied to the fluid dynamics problems associated with turbofan mixer nozzles. The computer generated color graphics were found to be useful in reconstructing the measured flow field from low resolution experimental data to give more physical meaning to this information and in scanning and interpreting the large volume of computer generated data from the three dimensional viscous computer code used in the analysis.
Wei, Xiaoyan; Kumar, Mohit; Schuttelaars, Henk M.
2017-01-01
A semianalytical three-dimensional model is set up to dynamically calculate the coupled water motion and salinity for idealized well-mixed estuaries and prognostically investigate the influence of each physical mechanism on the residual salt transport. As a study case, a schematized estuary with an exponentially converging width and a channel–shoal structure is considered. The temporal correlation between horizontal tidal velocities and tidal salinities is the dominant process for the landwar...
International Nuclear Information System (INIS)
Nagai, Haruyasu; Yamazawa, Hiromi
1994-11-01
A three-dimensional atmospheric dynamic model (PHYSIC) was improved and its performance was examined using the meteorological data observed at a coastal area with a complex terrain. To introduce synoptic meteorological conditions into the model, the initial and boundary conditions were improved. By this improvement, the model can predict the temporal change of wind field for more than 24 hours. Moreover, the model successfully simulates the land and sea breeze observed at Shimokita area in the summer of 1992. (author)
Energy Technology Data Exchange (ETDEWEB)
Ren, Qing-Bao [Department of Physics, Lishui University, Lishui 323000 (China); Luo, Meng-Bo, E-mail: Luomengbo@zju.edu.cn [Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2013-10-30
We study the dynamics of a two-dimensional vortex system in a strong square pinning array at the second matching field. Two kinds of depinning behaviors, a continuous depinning transition at weak pinning and a discontinuous one at strong pinning, are found. We show that the two different kinds of vortex depinning transitions can be identified in transport as a function of the pinning strength and temperature. Moreover, interstitial vortex state can be probed from the transport properties of vortices.
Bound eigenstate dynamics under a sudden shift of the well's wall
Granot, Er'El; Marchewka, Avi
2010-03-01
We investigate the dynamics of the eigenstate of an infinite well under an abrupt shift of the well’s wall. It is shown that when the shift is small compared to the initial well’s dimensions, the short-time behavior changes from the well-known t3/2 behavior to t1/2. It is also shown that the complete dynamical picture converges to a universal function, which has fractal structure with dimensionality D=1.25.
Bound eigenstate dynamics under a sudden shift of the well's wall
International Nuclear Information System (INIS)
Granot, Er'el; Marchewka, Avi
2010-01-01
We investigate the dynamics of the eigenstate of an infinite well under an abrupt shift of the well's wall. It is shown that when the shift is small compared to the initial well's dimensions, the short-time behavior changes from the well-known t 3/2 behavior to t 1/2 . It is also shown that the complete dynamical picture converges to a universal function, which has fractal structure with dimensionality D=1.25.
Liu, Tianhui; Chen, Jun; Zhang, Zhaojun; Shen, Xiangjian; Fu, Bina; Zhang, Dong H.
2018-04-01
We constructed a nine-dimensional (9D) potential energy surface (PES) for the dissociative chemisorption of H2O on a rigid Ni(100) surface using the neural network method based on roughly 110 000 energies obtained from extensive density functional theory (DFT) calculations. The resulting PES is accurate and smooth, based on the small fitting errors and the good agreement between the fitted PES and the direct DFT calculations. Time dependent wave packet calculations also showed that the PES is very well converged with respect to the fitting procedure. The dissociation probabilities of H2O initially in the ground rovibrational state from 9D quantum dynamics calculations are quite different from the site-specific results from the seven-dimensional (7D) calculations, indicating the importance of full-dimensional quantum dynamics to quantitatively characterize this gas-surface reaction. It is found that the validity of the site-averaging approximation with exact potential holds well, where the site-averaging dissociation probability over 15 fixed impact sites obtained from 7D quantum dynamics calculations can accurately approximate the 9D dissociation probability for H2O in the ground rovibrational state.
Theoretical Research Progress in High-Velocity/Hypervelocity Impact on Semi-Infinite Targets
Directory of Open Access Journals (Sweden)
Yunhou Sun
2015-01-01
Full Text Available With the hypervelocity kinetic weapon and hypersonic cruise missiles research projects being carried out, the damage mechanism for high-velocity/hypervelocity projectile impact on semi-infinite targets has become the research keystone in impact dynamics. Theoretical research progress in high-velocity/hypervelocity impact on semi-infinite targets was reviewed in this paper. The evaluation methods for critical velocity of high-velocity and hypervelocity impact were summarized. The crater shape, crater scaling laws and empirical formulae, and simplified analysis models of crater parameters for spherical projectiles impact on semi-infinite targets were reviewed, so were the long rod penetration state differentiation, penetration depth calculation models for the semifluid, and deformed long rod projectiles. Finally, some research proposals were given for further study.
International Nuclear Information System (INIS)
Honeck, H.C.
1984-01-01
1 - Description of problem or function: HAMMER performs infinite lattice, one-dimensional cell multigroup calculations, followed (optionally) by one-dimensional, few-group, multi-region reactor calculations with neutron balance edits. 2 - Method of solution: Infinite lattice parameters are calculated by means of multigroup transport theory, composite reactor parameters by few-group diffusion theory. 3 - Restrictions on the complexity of the problem: - Cell calculations - maxima of: 30 thermal groups; 54 epithermal groups; 20 space points; 20 regions; 18 isotopes; 10 mixtures; 3 thermal up-scattering mixtures; 200 resonances per group; no overlap or interference; single level only. - Reactor calculations - maxima of : 40 regions; 40 mixtures; 250 space points; 4 groups
BMS3 invariant fluid dynamics at null infinity
Penna, Robert F.
2018-02-01
We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \