Global structure of exact scalar hairy dynamical black holes

Energy Technology Data Exchange (ETDEWEB)

Fan, Zhong-Ying [Center for High Energy Physics, Peking University,No. 5 Yiheyuan Rd, Beijing, 100871 P.R. (China); Chen, Bin [Center for High Energy Physics, Peking University,No. 5 Yiheyuan Rd, Beijing, 100871 P.R. (China); Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University, No. 5 Yiheyuan Rd, Beijing, 100871 P.R. (China); Collaborative Innovation Center of Quantum Matter,No. 5 Yiheyuan Rd, Beijing, 100871 P.R. (China); Lü, H. [Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University,Beijing, 100875 P.R. (China)

2016-05-30

We study the global structure of some exact scalar hairy dynamical black holes which were constructed in Einstein gravity either minimally or non-minimally coupled to a scalar field. We find that both the apparent horizon and the local event horizon (measured in luminosity coordinate) monotonically increase with the advanced time as well as the Vaidya mass. At late advanced times, the apparent horizon approaches the event horizon and gradually becomes future outer. Correspondingly, the space-time arrives at stationary black hole states with the relaxation time inversely proportional to the 1/(n−1) power of the final black hole mass, where n is the space-time dimension. These results strongly support the solutions describing the formation of black holes with scalar hair. We also obtain new charged dynamical solutions in the non-minimal theory by introducing an Maxwell field which is non-minimally coupled to the scalar. The presence of the electric charge strongly modifies the dynamical evolution of the space-time.

Entanglement dynamics following a sudden quench: An exact solution

Science.gov (United States)

Ghosh, Supriyo; Gupta, Kumar S.; Srivastava, Shashi C. L.

2017-12-01

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N. The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.

Exact stationary state for an asymmetric exclusion process with fully parallel dynamics

NARCIS (Netherlands)

Gier, J.C.|info:eu-repo/dai/nl/170218430; Nienhuis, B.

The exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product ansatz. We give a simple derivation for the deterministic case by a physical interpretation of the dimension of the matrices. We prove the stationarity via a cancellation

Numerically exact dynamics of the interacting many-body Schroedinger equation for Bose-Einstein condensates. Comparison to Bose-Hubbard and Gross-Pitaevskii theory

Energy Technology Data Exchange (ETDEWEB)

Sakmann, Kaspar

2010-07-21

In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schroedinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a bosonic Josephson junction is investigated by solving the time-dependent many-body Schroedinger equation numerically exactly. These are the first exact results in literature in this context. It is shown that the standard approximations of the field, Gross-Pitaevskii theory and the Bose-Hubbard model fail at weak interaction strength and within their range of expected validity. For stronger interactions the dynamics becomes strongly correlated and a new equilibration phenomenon is discovered. By comparison with exact results it is shown that a symmetry of the Bose- Hubbard model between attractive and repulsive interactions must be considered an artefact of the model. A conceptual innovation of this thesis are time-dependent Wannier functions. Equations of motion for time-dependent Wannier functions are derived from the variational principle. By comparison with exact results it is shown that lattice models can be greatly improved at little computational cost by letting the Wannier functions of a lattice model become time-dependent. (orig.)

Time-dependent reduced density matrix functional theory applied to laser-driven, correlated two-electron dynamics

Energy Technology Data Exchange (ETDEWEB)

Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.

The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix

International Nuclear Information System (INIS)

Kim, Jeong Soo; Kim, Moon Kyum

2012-01-01

In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.

Exact thermodynamic principles for dynamic order existence and evolution in chaos

International Nuclear Information System (INIS)

Mahulikar, Shripad P.; Herwig, Heinz

2009-01-01

The negentropy proposed first by Schroedinger is re-examined, and its conceptual and mathematical definitions are introduced. This re-definition of negentropy integrates Schroedinger's intention of its introduction, and the subsequent diverse notions in literature. This negentropy is further corroborated by its ability to state the two exact thermodynamic principles: negentropy principle for dynamic order existence and principle of maximum negentropy production (PMNEP) for dynamic order evolution. These principles are the counterparts of the existing entropy principle and the law of maximum entropy production, respectively. The PMNEP encompasses the basic concepts in the evolution postulates by Darwin and de Vries. Perspectives of dynamic order evolution in literature point to the validity of PMNEP as the law of evolution. These two additional principles now enable unified explanation of order creation, existence, evolution, and destruction; using thermodynamics.

Exactly soluble dynamics of (p,q) string near macroscopic fundamental strings

International Nuclear Information System (INIS)

Bak, Dongsu; Rey, Soojong; Yee, Houng

2004-01-01

We study dynamics of type-IIB bound-state of a Dirichlet string and n fundamental strings in the background of N fundamental strings. Because of supergravity potential, the bound-state string is pulled to the background fundamental strings, whose motion is described by open string rolling radion field. The string coupling can be made controllably weak and, in the limit 1 2 st n 2 st N, the bound-state energy involved is small compared to the string scale. We thus propose rolling dynamics of open string radion in this system as an exactly solvable analog for rolling dynamics of open string tachyon in decaying D-brane. The dynamics bears a novel feature that the worldsheet electric field increases monotonically to the critical value as the bound-state string falls into the background string. Close to the background string, D string constituent inside the bound-state string decouples from fundamental string constituents. (author)

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

International Nuclear Information System (INIS)

Fu Jingli; Jimenez, Salvador; Tang Yifa; Vazquez, Luis

2008-01-01

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Fu Jingli [Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)], E-mail: sqfujingli@163.com; Jimenez, Salvador [Departamento de Matematica Aplicada TTII, E.T.S.I. Telecomunicacion, Universidad Politecnica de Madrid, 28040 Madrid (Spain); Tang Yifa [State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Vazquez, Luis [Departamento de Matematica Aplicada Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de Astrobiologia (CSIC-INTA), Torrejon de Ardoz, 28850 Madrid (Spain)

2008-03-03

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.

Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities

International Nuclear Information System (INIS)

Hirata, So; Ivanov, Stanislav; Bartlett, Rodney J.; Grabowski, Ireneusz

2005-01-01

Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP

Exact folded-band chaotic oscillator.

Science.gov (United States)

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS).

Science.gov (United States)

Hartmann, Richard; Strunz, Walter T

2017-12-12

We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular, we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and nonzero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the nonlinear variant of HOPS. In order to include nonzero-temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero-temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.

Quasi-exact solvability

International Nuclear Information System (INIS)

Ushveridze, A.G.

1992-01-01

This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite

Exact decoherence dynamics of a single-mode optical field

International Nuclear Information System (INIS)

An, J.-H.; Yeo Ye; Oh, C.H.

2009-01-01

We apply the influence-functional method of Feynman and Vernon to the study of a single-mode optical field that interacts with an environment at zero temperature. Using the coherent-state formalism of the path integral, we derive a generalized master equation for the single-mode optical field. Our analysis explicitly shows how non-Markovian effects manifest in the exact decoherence dynamics for different environmental correlation time scales. Remarkably, when these are equal to or greater than the time scale for significant change in the system, the interplay between the backaction-induced coherent oscillation and the dissipative effect of the environment causes the non-Markovian effect to have a significant impact not only on the short-time behavior but also on the long-time steady-state behavior of the system.

Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.

Science.gov (United States)

Liu, Xinzijian; Liu, Jian

2018-03-14

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

Long-term stable time integration scheme for dynamic analysis of planar geometrically exact Timoshenko beams

Science.gov (United States)

Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed

2017-05-01

In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.

Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics

DEFF Research Database (Denmark)

Nørrelykke, Simon F; Flyvbjerg, Henrik

2011-01-01

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...

Exact solution of the Schroedinger equation with the spin-boson Hamiltonian

International Nuclear Information System (INIS)

Gardas, Bartlomiej

2011-01-01

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (environment). An exact solution of the Schroedinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.

Exact milestoning

International Nuclear Information System (INIS)

Bello-Rivas, Juan M.; Elber, Ron

2015-01-01

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied

Dynamic of exact perturbations in Bianchi IX type cosmological models

International Nuclear Information System (INIS)

Mello Neto, J.R.T. de.

1985-01-01

The dynamic of Bianchi IX type cosmological models is studied, after reducing Einstein equations to Hamiltonian system. Using the Melnikov method, the existence of chaos in the dynamic of these models is proved, and some numerical experiments are carried out. (M.C.K.) [pt

Large scale exact quantum dynamics calculations: Ten thousand quantum states of acetonitrile

Science.gov (United States)

Halverson, Thomas; Poirier, Bill

2015-03-01

'Exact' quantum dynamics (EQD) calculations of the vibrational spectrum of acetonitrile (CH3CN) are performed, using two different methods: (1) phase-space-truncated momentum-symmetrized Gaussian basis and (2) correlated truncated harmonic oscillator basis. In both cases, a simple classical phase space picture is used to optimize the selection of individual basis functions-leading to drastic reductions in basis size, in comparison with existing methods. Massive parallelization is also employed. Together, these tools-implemented into a single, easy-to-use computer code-enable a calculation of tens of thousands of vibrational states of CH3CN to an accuracy of 0.001-10 cm-1.

Universality in exact quantum state population dynamics and control

International Nuclear Information System (INIS)

Wu, Lian-Ao; Segal, Dvira; Brumer, Paul; Egusquiza, Inigo L.

2010-01-01

We consider an exact population transition, defined as the probability of finding a state at a final time that is exactly equal to the probability of another state at the initial time. We prove that, given a Hamiltonian, there always exists a complete set of orthogonal states that can be employed as time-zero states for which this exact population transition occurs. The result is general: It holds for arbitrary systems, arbitrary pairs of initial and final states, and for any time interval. The proposition is illustrated with several analytic models. In particular, we demonstrate that in some cases, by tuning the control parameters, a complete transition might occur, where a target state, vacant at t=0, is fully populated at time τ.

Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach

International Nuclear Information System (INIS)

Tanaka, Midori; Tanimura, Yoshitaka

2010-01-01

Multiple displaced oscillators coupled to an Ohmic heat bath are used to describe electron transfer (ET) in a dissipative environment. By performing a canonical transformation, the model is reduced to a multilevel system coupled to a heat bath with the Brownian spectral distribution. A reduced hierarchy equations of motion approach is introduced for numerically rigorous simulation of the dynamics of the three-level system with various oscillator configurations, for different nonadiabatic coupling strengths and damping rates, and at different temperatures. The time evolution of the reduced density matrix elements illustrates the interplay of coherences between the electronic and vibrational states. The ET reaction rates, defined as a flux-flux correlation function, are calculated using the linear response of the system to an external perturbation as a function of activation energy. The results exhibit an asymmetric inverted parabolic profile in a small activation regime due to the presence of the intermediate state between the reactant and product states and a slowly decaying profile in a large activation energy regime, which arises from the quantum coherent transitions.

EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon–Mann–Whitney Test

Directory of Open Access Journals (Sweden)

Alexander Marx

2016-02-01

Full Text Available In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney (WMW test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD. We found that approximated P values were generally higher than the exact solution provided by EDISON-WMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.

Exact EGB models for spherical static perfect fluids

Energy Technology Data Exchange (ETDEWEB)

Hansraj, Sudan; Chilambwe, Brian; Maharaj, Sunil D. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Private Bag 54001, Durban (South Africa)

2015-06-15

We obtain a new exact solution to the field equations for a 5-dimensional spherically symmetric static distribution in the Einstein-Gauss-Bonnet modified theory of gravity. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissibility. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound-speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss-Bonnet and the Einstein case reveal that the pressure is unaffected, while the energy density increases under the influence of the Gauss-Bonnet term. (orig.)

Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures

International Nuclear Information System (INIS)

Xing Liudong; Shrestha, Akhilesh; Dai Yuanshun

2011-01-01

Many real-life fault-tolerant systems are subjected to sequence-dependent failure behavior, in which the order in which the fault events occur is important to the system reliability. Such systems can be modeled by dynamic fault trees (DFT) with priority-AND (pAND) gates. Existing approaches for the reliability analysis of systems subjected to sequence-dependent failures are typically state-space-based, simulation-based or inclusion-exclusion-based methods. Those methods either suffer from the state-space explosion problem or require long computation time especially when results with high degree of accuracy are desired. In this paper, an analytical method based on sequential binary decision diagrams is proposed. The proposed approach can analyze the exact reliability of non-repairable dynamic systems subjected to the sequence-dependent failure behavior. Also, the proposed approach is combinatorial and is applicable for analyzing systems with any arbitrary component time-to-failure distributions. The application and advantages of the proposed approach are illustrated through analysis of several examples. - Highlights: → We analyze the sequence-dependent failure behavior using combinatorial models. → The method has no limitation on the type of time-to-failure distributions. → The method is analytical and based on sequential binary decision diagrams (SBDD). → The method is computationally more efficient than existing methods.

Exact solution for the quench dynamics of a nested integrable system

Science.gov (United States)

Mestyán, Márton; Bertini, Bruno; Piroli, Lorenzo; Calabrese, Pasquale

2017-08-01

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

Machine Learning-based discovery of closures for reduced models of dynamical systems

Science.gov (United States)

Pan, Shaowu; Duraisamy, Karthik

2017-11-01

Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

New approach to study mobility in the vicinity of dynamical arrest; exact application to a kinetically constrained model

Science.gov (United States)

DeGregorio, P.; Lawlor, A.; Dawson, K. A.

2006-04-01

We introduce a new method to describe systems in the vicinity of dynamical arrest. This involves a map that transforms mobile systems at one length scale to mobile systems at a longer length. This map is capable of capturing the singular behavior accrued across very large length scales, and provides a direct route to the dynamical correlation length and other related quantities. The ideas are immediately applicable in two spatial dimensions, and have been applied to a modified Kob-Andersen type model. For such systems the map may be derived in an exact form, and readily solved numerically. We obtain the asymptotic behavior across the whole physical domain of interest in dynamical arrest.

Prepotential approach to exact and quasi-exact solvabilities

International Nuclear Information System (INIS)

Ho, C.-L.

2008-01-01

Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations

Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

Science.gov (United States)

Scopa, Stefano; Unterberger, Jéremie; Karevski, Dragi

2018-05-01

We study the unitary dynamics of a 1D gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency . Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

Free Vibration Analysis for Shells of Revolution Using an Exact Dynamic Stiffness Method

Directory of Open Access Journals (Sweden)

Xudong Chen

2016-01-01

Full Text Available An exact generalised formulation for the free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is introduced. Starting from the basic shell theories, the vibration governing equations are obtained in the Hamilton form, from which dynamic stiffness is computed using the ordinary differential equations solver COLSYS. Natural frequencies and modes are determined by employing the Wittrick-Williams (W-W algorithm in conjunction with the recursive Newton’s method, thus expanding the applications of the abovementioned techniques from one-dimensional skeletal structures to two-dimensional shells of revolution. A solution for solving the number of clamped-end frequencies J0 in the W-W algorithm is presented for both uniform and nonuniform shell segment members. Based on these theories, a FORTRAN program is written. Numerical examples on circular cylindrical shells, hyperboloidal cooling tower shells, and spherical shells are given, and error analysis is performed. The convergence of the proposed method on J0 is verified, and comparisons with frequencies from existing literature show that the dynamic stiffness method is robust, reliable, and accurate.

QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems part I: spin chains

Directory of Open Access Journals (Sweden)

Phillip Weinberg, Marin Bukov

2017-02-01

Full Text Available We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i Standard exact diagonalisation of XXZ chain (ii adiabatic ramping of parameters in the many-body localised XXZ model, (iii heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Science.gov (United States)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Exact results for the Kuramoto model with a bimodal frequency distribution

DEFF Research Database (Denmark)

Martens, Erik Andreas; Barreto, E.; Strogatz, S. H.

2009-01-01

weighted Lorentzians. Using an ansatz recently discov- ered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence......, where all the oscillators are desynchronized; partial synchrony, where a macro- scopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented...

On exactly soluble model in quantum electrodynamics

International Nuclear Information System (INIS)

Bogolubov, N.N.; Shumovsky, A.S.; Fam Le Kien

1984-01-01

Equations of motion describing the dynamics of three-level atom of ladder type interacting with two modes of quantized radiation field are solved exactly. Evolution of level population and photon rumbers under different unitial conditions is irvestigated

Entanglement, decoherence and thermal relaxation in exactly solvable models

International Nuclear Information System (INIS)

Lychkovskiy, Oleg

2011-01-01

Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evolution. The duration of the regular stage is proportional to the number of spins in the chain. We observe a 'quiet and cold period' in the end of the regular stage, which breaks up abruptly at some threshold time.

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

Exact gravitational quasinormal frequencies of topological black holes

International Nuclear Information System (INIS)

Birmingham, Danny; Mokhtari, Susan

2006-01-01

We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

Science.gov (United States)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

RG-Whitham dynamics and complex Hamiltonian systems

Directory of Open Access Journals (Sweden)

A. Gorsky

2015-06-01

Full Text Available Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG-like Whitham behavior. We show that at the Argyres–Douglas (AD point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

Science.gov (United States)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Optimising stochastic trajectories in exact quantum jump approaches of interacting systems

International Nuclear Information System (INIS)

Lacroix, D.

2004-11-01

The standard methods used to substitute the quantum dynamics of two interacting systems by a quantum jump approach based on the Stochastic Schroedinger Equation (SSE) are described. It turns out that for a given situation, there exists an infinite number of SSE reformulation. This fact is used to propose general strategies to optimise the stochastic paths in order to reduce the statistical fluctuations. In this procedure, called the 'adaptative noise method', a specific SSE is obtained for which the noise depends explicitly on both the initial state and on the properties of the interaction Hamiltonian. It is also shown that this method can be further improved by the introduction of a mean-field dynamics. The different optimisation procedures are illustrated quantitatively in the case of interacting spins. A significant reduction of the statistical fluctuations is obtained. Consequently, a much smaller number of trajectories is needed to accurately reproduce the exact dynamics as compared to the standard SSE method. (author)

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

Exact approaches for scaffolding

OpenAIRE

Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe

2015-01-01

This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...

Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics

OpenAIRE

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

2017-01-01

We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponenti...

Bursting and critical layer frequencies in minimal turbulent dynamics and connections to exact coherent states

Science.gov (United States)

Park, Jae Sung; Shekar, Ashwin; Graham, Michael D.

2018-01-01

The dynamics of the turbulent near-wall region is known to be dominated by coherent structures. These near-wall coherent structures are observed to burst in a very intermittent fashion, exporting turbulent kinetic energy to the rest of the flow. In addition, they are closely related to invariant solutions known as exact coherent states (ECS), some of which display nonlinear critical layer dynamics (motions that are highly localized around the surface on which the streamwise velocity matches the wave speed of ECS). The present work aims to investigate temporal coherence in minimal channel flow relevant to turbulent bursting and critical layer dynamics and its connection to the instability of ECS. It is seen that the minimal channel turbulence displays frequencies very close to those displayed by an ECS family recently identified in the channel flow geometry. The frequencies of these ECS are determined by critical layer structures and thus might be described as "critical layer frequencies." While the bursting frequency is predominant near the wall, the ECS frequencies (critical layer frequencies) become predominant over the bursting frequency at larger distances from the wall, and increasingly so as Reynolds number increases. Turbulent bursts are classified into strong and relatively weak classes with respect to an intermittent approach to a lower branch ECS. This temporally intermittent approach is closely related to an intermittent low drag event, called hibernating turbulence, found in minimal and large domains. The relationship between the strong burst and the instability of the lower branch ECS is further discussed in state space. The state-space dynamics of strong bursts is very similar to that of the unstable manifolds of the lower branch ECS. In particular, strong bursting processes are always preceded by hibernation events. This precursor dynamics to strong turbulence may aid in development of more effective control schemes by a way of anticipating dynamics

Generalized reduced fluid model with finite ion-gyroradius effects

International Nuclear Information System (INIS)

Hsu, C.T.; Hazeltine, R.D.; Morrison, P.J.

1985-04-01

Reduced fluid models have become important tools for studying the nonlinear dynamics of plasma in a large aspect-ratio tokamak. A self-consistent nonlinear reduced fluid model, with finite ion-gyroradius effects is presented. The model is distinctive in allowing for arbitrary beta and in satisfying an exact, relatively simple energy conservation law

Classes of exact Einstein Maxwell solutions

Science.gov (United States)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Configuring Airspace Sectors with Approximate Dynamic Programming

Science.gov (United States)

Bloem, Michael; Gupta, Pramod

2010-01-01

In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

Exact many-body dynamics with stochastic one-body density matrix evolution

International Nuclear Information System (INIS)

Lacroix, D.

2004-05-01

In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)

G-Consistent Subsets and Reduced Dynamical Quantum Maps

Science.gov (United States)

Ceballos, Russell R.

A quantum system which evolves in time while interacting with an external environ- ment is said to be an open quantum system (OQS), and the influence of the environment on the unperturbed unitary evolution of the system generally leads to non-unitary dynamics. This kind of open system dynamical evolution has been typically modeled by a Standard Prescription (SP) which assumes that the state of the OQS is initially uncorrelated with the environment state. It is here shown that when a minimal set of physically motivated assumptions are adopted, not only does there exist constraints on the reduced dynamics of an OQS such that this SP does not always accurately describe the possible initial cor- relations existing between the OQS and environment, but such initial correlations, and even entanglement, can be witnessed when observing a particular class of reduced state transformations termed purity extractions are observed. Furthermore, as part of a more fundamental investigation to better understand the minimal set of assumptions required to formulate well defined reduced dynamical quantum maps, it is demonstrated that there exists a one-to-one correspondence between the set of initial reduced states and the set of admissible initial system-environment composite states when G-consistency is enforced. Given the discussions surrounding the requirement of complete positivity and the reliance on the SP, the results presented here may well be found valuable for determining the ba- sic properties of reduced dynamical maps, and when restrictions on the OQS dynamics naturally emerge.

Exact solutions in dynamics of alternation open spin chains s = 1/2 with XY-Hamiltonian and its application to the problems of many-quantum dynamics and quantum information theory

International Nuclear Information System (INIS)

Kuznetsova, E.I.; Fel'dman, Eh.B.

2006-01-01

Paper deals with a method of exact diagonalization of XY-Hamiltonian of s=1/2 alternated open chain of spins based on the Jordan-Wigner transform and analysis of dynamics of spinless fermions. One studied the many-quantum spin dynamics of alternated chains under high temperatures and calculated the intensities of many-quantum coherencies. One attacked the problem dealing with transfer of a quantum state from one end of the alternated chain to the opposite end. It is shown that perfect transfer of cubits may take place in alternated chains with larger number of spins in contrast to homogeneous chains [ru

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian

2014-08-17

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

Separation Transformation and New Exact Solutions of the (N + 1)-dimensional Dispersive Double sine-Gordon Equation

International Nuclear Information System (INIS)

Tian Ye; Chen Jing; Zhang Zhifei

2012-01-01

In this paper, the separation transformation approach is extended to the (N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the (N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N > 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

Holonomy-reduced dynamics of triatomic molecules

International Nuclear Information System (INIS)

Ciftci, Uenver; Waalkens, Holger

2011-01-01

Whereas it is easy to reduce the translational symmetry of a molecular system using, e.g., Jacobi coordinates, the situation is much more involved for rotational symmetry. In this paper, we address the latter problem using holonomy reduction. We suggest that the configuration space may be considered as the reduced holonomy bundle with a connection induced by the mechanical connection. Using the fact that for the special case of the three-body problem the holonomy group is SO(2) (as opposed to SO(3) like in systems with more than three bodies), we obtain a holonomy-reduced configuration space of topology R + 3 xS 1 . The dynamics then takes place on the cotangent bundle over the holonomy-reduced configuration space. On this phase space, there is an S 1 symmetry action coming from the conserved reduced angular momentum which can be reduced using the standard symplectic reduction method. Using a theorem by Arnold it follows that the resulting symmetry-reduced phase space is again a natural mechanical phase space, i.e. a cotangent bundle. This is different from what is obtained from the usual approach where symplectic reduction is used from the outset. This difference is discussed in some detail, and a connection between the reduced dynamics of a triatomic molecule and the motion of a charged particle in a magnetic field is established.

Holonomy-reduced dynamics of triatomic molecules

Energy Technology Data Exchange (ETDEWEB)

Ciftci, Uenver [Department of Mathematics, Namik Kemal University, 59030 Tekirdag (Turkey); Waalkens, Holger, E-mail: uciftci@nku.edu.tr, E-mail: h.waalkens@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, PO Box 407, 9700 AK Groningen (Netherlands)

2011-04-22

Whereas it is easy to reduce the translational symmetry of a molecular system using, e.g., Jacobi coordinates, the situation is much more involved for rotational symmetry. In this paper, we address the latter problem using holonomy reduction. We suggest that the configuration space may be considered as the reduced holonomy bundle with a connection induced by the mechanical connection. Using the fact that for the special case of the three-body problem the holonomy group is SO(2) (as opposed to SO(3) like in systems with more than three bodies), we obtain a holonomy-reduced configuration space of topology R{sub +}{sup 3}xS{sup 1}. The dynamics then takes place on the cotangent bundle over the holonomy-reduced configuration space. On this phase space, there is an S{sup 1} symmetry action coming from the conserved reduced angular momentum which can be reduced using the standard symplectic reduction method. Using a theorem by Arnold it follows that the resulting symmetry-reduced phase space is again a natural mechanical phase space, i.e. a cotangent bundle. This is different from what is obtained from the usual approach where symplectic reduction is used from the outset. This difference is discussed in some detail, and a connection between the reduced dynamics of a triatomic molecule and the motion of a charged particle in a magnetic field is established.

ExactPack Documentation

Energy Technology Data Exchange (ETDEWEB)

Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory

2016-05-09

For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.

Exact Lattice Supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Catterall, Simon; Kaplan, David B.; Unsal, Mithat

2009-03-31

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.

Towards a string formulation of vortex dynamics

International Nuclear Information System (INIS)

Elsebeth Schroeder; Ola Toernkvist

1998-01-01

We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom

Finding optimal exact reducts

KAUST Repository

AbouEisha, Hassan M.

2014-01-01

The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.

Exact models for isotropic matter

Science.gov (United States)

Thirukkanesh, S.; Maharaj, S. D.

2006-04-01

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

Exact Boundary Controllability of Electromagnetic Fields in a General Region

International Nuclear Information System (INIS)

Eller, M. M.; Masters, J. E.

2002-01-01

We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain

Exact model reduction of combinatorial reaction networks

Directory of Open Access Journals (Sweden)

Fey Dirk

2008-08-01

Full Text Available Abstract Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

Science.gov (United States)

Chen, Yusui; You, J. Q.; Yu, Ting

2014-11-01

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

Quantum decay model with exact explicit analytical solution

Science.gov (United States)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Exact solutions in the dynamics of alternating open chains of spins s = 1/2 with the XY Hamiltonian and their application to problems of multiple-quantum dynamics and quantum information theory

International Nuclear Information System (INIS)

Kuznetsova, E. I.; Fel'dman, E. B.

2006-01-01

A method for exactly diagonalizing the XY Hamiltonian of an alternating open chain of spins s = 1/2 has been proposed on the basis of the Jordan-Wigner transformation and analysis of the dynamics of spinless fermions. The multiple-quantum spin dynamics of alternating open chains at high temperatures has been analyzed and the intensities of multiple-quantum coherences have been calculated. The problem of the transfer of a quantum state from one end of the alternating chain to the other is studied. It has been shown that the ideal transfer of qubits is possible in alternating chains with a larger number of spins than that in homogeneous chains

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

Science.gov (United States)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Bifurcations of Exact Traveling Wave Solutions for (2+1)-Dimensional HNLS Equation

International Nuclear Information System (INIS)

Xu Yuanfen

2012-01-01

For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. (general)

Two-dimensional nonlinear string-type equations and their exact integration

International Nuclear Information System (INIS)

Leznov, A.N.; Saveliev, M.V.

1982-01-01

On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions

Novel correlations in two dimensions: Some exact solutions

International Nuclear Information System (INIS)

Murthy, M.V.; Bhaduri, R.K.; Sen, D.

1996-01-01

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. copyright 1996 The American Physical Society

Exact complexity: The spectral decomposition of intrinsic computation

International Nuclear Information System (INIS)

Crutchfield, James P.; Ellison, Christopher J.; Riechers, Paul M.

2016-01-01

We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's ϵ-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography. - Highlights: • We provide exact, closed-form expressions for a hidden stationary process' intrinsic computation. • These include information measures such as the excess entropy, transient information, and synchronization information and the entropy-rate finite-length approximations. • The method uses an epsilon-machine's mixed-state presentation. • The spectral decomposition of the mixed-state presentation relies on the recent development of meromorphic functional calculus for nondiagonalizable operators.

The Probabilistic Convolution Tree: Efficient Exact Bayesian Inference for Faster LC-MS/MS Protein Inference

Science.gov (United States)

Serang, Oliver

2014-01-01

Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to and the space to where is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions. PMID:24626234

Power-law tails and non-Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory

Science.gov (United States)

Chakraborty, Ahana; Sensarma, Rajdeep

2018-03-01

The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.

Exact Optimum Design of Segmented Thermoelectric Generators

Directory of Open Access Journals (Sweden)

M. Zare

2016-01-01

Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

Science.gov (United States)

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Two-dimensional exactly and completely integrable dynamic systems (Monopoles, instantons, dual models, relativistic strings, Lund-Regge model, generalized Toda lattice, etc)

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

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

Science.gov (United States)

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Dynamic and reduced-dynamic precise orbit determination of satellites in low earth orbits

International Nuclear Information System (INIS)

Swatschina, P.

2009-01-01

The precise positioning of satellites in Low Earth Orbits (LEO) has become a key technology for advanced space missions. Dedicated satellite missions, such as CHAMP, GRACE and GOCE, that aim to map the Earths gravity field and its variation over time with unprecedented accuracy, initiated the demand for highly precise orbit solutions of LEO satellites. Furthermore, a wide range of additional science opportunities opens up with the capability to generate accurate LEO orbits. For all considered satellite missions, the primary measurement system for navigation is a spaceborne GPS receiver. The goal of this thesis is to establish and implement methods for Precise Orbit Determination (POD) of LEO satellites using GPS. Striving for highest precision using yet efficient orbit generation strategies, the attained orbit solutions are aimed to be competitive with the most advanced solutions of other institutions. Dynamic and reduced-dynamic orbit models provide the basic concepts of this work. These orbit models are subsequently adjusted to the highly accurate GPS measurements. The GPS measurements are introduced at the zero difference level in the ionosphere free linear combination. Appropriate procedures for GPS data screening and editing are established to detect erroneous data and to employ measurements of good quality only. For the dynamic orbit model a sophisticated force model, especially designed for LEO satellites, has been developed. In order to overcome the limitations that are induced by the deficiencies of the purely dynamical model, two different types of empirical parameters are introduced into the force model. These reduced-dynamic orbit models allow for the generation of much longer orbital arcs while preserving the spacecraft dynamics to the most possible extent. The two methods for reduced-dynamic orbit modeling are instantaneous velocity changes (pulses) or piecewise constant accelerations. For both techniques highly efficient modeling algorithms are

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

Endotoxemia reduces cerebral perfusion but enhances dynamic cerebrovascular autoregulation at reduced arterial carbon dioxide tension*

DEFF Research Database (Denmark)

Brassard, Patrice; Kim, Yu-Sok; van Lieshout, Johannes

2012-01-01

OBJECTIVE:: The administration of endotoxin to healthy humans reduces cerebral blood flow but its influence on dynamic cerebral autoregulation remains unknown. We considered that a reduction in arterial carbon dioxide tension would attenuate cerebral perfusion and improve dynamic cerebral autoreg...

System and method for reducing combustion dynamics in a combustor

Science.gov (United States)

Uhm, Jong Ho; Ziminsky, Willy Steve; Johnson, Thomas Edward; Srinivasan, Shiva; York, William David

2016-11-29

A system for reducing combustion dynamics in a combustor includes an end cap that extends radially across the combustor and includes an upstream surface axially separated from a downstream surface. A combustion chamber is downstream of the end cap, and tubes extend from the upstream surface through the downstream surface. Each tube provides fluid communication through the end cap to the combustion chamber. The system further includes means for reducing combustion dynamics in the combustor. A method for reducing combustion dynamics in a combustor includes flowing a working fluid through tubes that extend axially through an end cap that extends radially across the combustor and obstructing at least a portion of the working fluid flowing through a first set of the tubes.

Output Tracking for Systems with Non-Hyperbolic and Near Non-Hyperbolic Internal Dynamics: Helicopter Hover Control

Science.gov (United States)

Devasia, Santosh

1996-01-01

A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics is presented. This approach integrates stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics is used (1) to remove non-hyperbolicity which an obstruction to applying stable inversion techniques and (2) to reduce large pre-actuation time needed to apply stable inversion for near non-hyperbolic cases. The method is applied to an example helicopter hover control problem with near non-hyperbolic internal dynamic for illustrating the trade-off between exact tracking and reduction of pre-actuation time.

Exact solutions and critical chaos in dilaton gravity with a boundary

Energy Technology Data Exchange (ETDEWEB)

Fitkevich, Maxim [Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary Prospect 7a, Moscow 117312 (Russian Federation); Moscow Institute of Physics and Technology,Institutskii per. 9, Dolgoprudny 141700, Moscow Region (Russian Federation); Levkov, Dmitry [Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary Prospect 7a, Moscow 117312 (Russian Federation); Zenkevich, Yegor [Dipartimento di Fisica, Università di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); INFN, sezione di Milano-Bicocca,I-20126 Milano (Italy); National Research Nuclear University MEPhI,Moscow 115409 (Russian Federation)

2017-04-19

We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2, ℝ) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflection of matter waves off the boundary at low energies and formation of black holes at energies above critical. They can be related to the eigenstates of the auxiliary integrable system, the Gaudin spin chain. We argue that despite being exactly solvable, the model in the critical regime, i.e. at the verge of black hole formation, displays dynamical instabilities specific to chaotic systems. We believe that this model will be useful for studying black holes and gravitational scattering.

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

Dynamic Simulation of Water Networks to Control and Reduce Physical Unaccounted-for Water

Directory of Open Access Journals (Sweden)

Nima Zorriasateyn

2005-09-01

Full Text Available A significant percentage of unaccounted-for water consists of leakage in water distribution networks in Iran. To detect leakage area with less costs and time spending and then identify the exact  place of it with special instruments, would be economical and a better water resource management. In this research, a real case has been selected and examined with dynamic simulation using MIKE NET. The method that has been carried out in this research based on maximizing the correlation coefficient and minimizing the sum of error squares between pressure measured inputs (observed data and calculated pressure (by model. According to the results, dynamic simulation of municipal water distribution system can be used as a guide to determine the place and the amount of leakage.Thereby the area of  large leakage can be simulated with appropriate accuracy through measured pressure. Therefor from management aspect, dynamic simulation can be used to decrease time consumption and to save costs for detecting leakage.

Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

Science.gov (United States)

Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.

2017-12-01

We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

Designing and Simulation of a Two-Axis Solar Tracking System by Exact Relations of Solar Angles

Directory of Open Access Journals (Sweden)

Faezeh Esmaili Ranjbar

2013-01-01

Full Text Available In this study, a system has been designed and simulated to track sunlight, which identifies sun location based on the exact relations of solar angles and without any optical sensor. In fact the relations which have been used in this study are far more accurate compared to similar cases, because of using the "equation of time" and reducing the tracking time of every 15 minutes. In this system, an economical micro-controller has been used to generate the necessary orders to control system and two stepper motors for powering solar array. By adding a real-time clock IC (RTC to angle differentiation circuit, dynamic plane has improved.

Exact results for Wilson loops in arbitrary representations

Energy Technology Data Exchange (ETDEWEB)

Fiol, Bartomeu; Torrents, Genís [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain)

2014-01-08

We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of N=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.

Exact and Heuristic Algorithms for Runway Scheduling

Science.gov (United States)

Malik, Waqar A.; Jung, Yoon C.

2016-01-01

This paper explores the Single Runway Scheduling (SRS) problem with arrivals, departures, and crossing aircraft on the airport surface. Constraints for wake vortex separations, departure area navigation separations and departure time window restrictions are explicitly considered. The main objective of this research is to develop exact and heuristic based algorithms that can be used in real-time decision support tools for Air Traffic Control Tower (ATCT) controllers. The paper provides a multi-objective dynamic programming (DP) based algorithm that finds the exact solution to the SRS problem, but may prove unusable for application in real-time environment due to large computation times for moderate sized problems. We next propose a second algorithm that uses heuristics to restrict the search space for the DP based algorithm. A third algorithm based on a combination of insertion and local search (ILS) heuristics is then presented. Simulation conducted for the east side of Dallas/Fort Worth International Airport allows comparison of the three proposed algorithms and indicates that the ILS algorithm performs favorably in its ability to find efficient solutions and its computation times.

An exact solution in Einstein-Cartan

International Nuclear Information System (INIS)

Roque, W.L.

1982-01-01

The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt

Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

Directory of Open Access Journals (Sweden)

Jacopo De Nardis, Miłosz Panfil

2016-12-01

Full Text Available We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.

Exact master equations for the non-Markovian decay of a qubit

International Nuclear Information System (INIS)

Vacchini, Bassano; Breuer, Heinz-Peter

2010-01-01

Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.

Exact Solutions to a Combined sinh-cosh-Gordon Equation

International Nuclear Information System (INIS)

Wei Long

2010-01-01

Based on a transformed Painleve property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. (general)

Exact explicit travelling wave solutions for (n + 1)-dimensional Klein-Gordon-Zakharov equations

International Nuclear Information System (INIS)

Li Jibin

2007-01-01

Using the methods of dynamical systems for the (n + 1)-dimensional KGS nonlinear wave equations, five classes of exact explicit parametric representations of the bounded travelling solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are given

Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results

International Nuclear Information System (INIS)

Baumann, Florian; Henkel, Malte; Pleimling, Michel; Richert, Jean

2005-01-01

Ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair-contact process. The two-time correlation function and the two-time response function are explicitly found. In the ageing regime, the dynamical scaling of these is analysed and exact results for the ageing exponents and the scaling functions are derived. For the critical bosonic pair-contact process, the autocorrelation and autoresponse exponents agree but the ageing exponents a and b are shown to be distinct

Exact solutions to chaotic and stochastic systems

Science.gov (United States)

González, J. A.; Reyes, L. I.; Guerrero, L. E.

2001-03-01

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng

2015-02-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng; Chung, Weiho; Han, Yunghsiangsam; Al-Naffouri, Tareq Y.

2015-01-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

Three faces of node importance in network epidemiology: Exact results for small graphs

Science.gov (United States)

Holme, Petter

2017-12-01

We investigate three aspects of the importance of nodes with respect to susceptible-infectious-removed (SIR) disease dynamics: influence maximization (the expected outbreak size given a set of seed nodes), the effect of vaccination (how much deleting nodes would reduce the expected outbreak size), and sentinel surveillance (how early an outbreak could be detected with sensors at a set of nodes). We calculate the exact expressions of these quantities, as functions of the SIR parameters, for all connected graphs of three to seven nodes. We obtain the smallest graphs where the optimal node sets are not overlapping. We find that (i) node separation is more important than centrality for more than one active node, (ii) vaccination and influence maximization are the most different aspects of importance, and (iii) the three aspects are more similar when the infection rate is low.

Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations

International Nuclear Information System (INIS)

Rowlands, G; Infeld, E; Skorupski, A A

2013-01-01

We find a class of exact solutions to the Lighthill–Whitham–Richards–Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg–de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end. (paper)

BWR stability using a reducing dynamical model

International Nuclear Information System (INIS)

Ballestrin Bolea, J. M.; Blazquez Martinez, J. B.

1990-01-01

BWR stability can be treated with reduced order dynamical models. When the parameters of the model came from dynamical models. When the parameters of the model came from experimental data, the predictions are accurate. In this work an alternative derivation for the void fraction equation is made, but remarking the physical structure of the parameters. As the poles of power/reactivity transfer function are related with the parameters, the measurement of the poles by other techniques such as noise analysis will lead to the parameters, but the system of equations is non-linear. Simple parametric calculation of decay ratio are performed, showing why BWRs become unstable when they are operated at low flow and high power. (Author)

Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle

International Nuclear Information System (INIS)

Salazar, Domingos S P; Lira, Sérgio A

2016-01-01

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions. (paper)

Exact cosmological solutions for MOG

International Nuclear Information System (INIS)

Roshan, Mahmood

2015-01-01

We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

Science.gov (United States)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

Quasi-exact solutions of nonlinear differential equations

OpenAIRE

Kudryashov, Nikolay A.; Kochanov, Mark B.

2014-01-01

The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.

Does really Born-Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

International Nuclear Information System (INIS)

Kuznetsov, Alexander M.; Medvedev, Igor G.

2006-01-01

Effects of deviation from the Born-Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus-Hush-Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied

Exact wavefunctions for a time-dependent Coulomb potential

International Nuclear Information System (INIS)

Menouar, S; Maamache, M; Saadi, Y; Choi, J R

2008-01-01

The one-dimensional Schroedinger equation associated with a time-dependent Coulomb potential is studied. The invariant operator method (Lewis and Riesenfeld) and unitary transformation approach are employed to derive quantum solutions of the system. We obtain an ordinary second-order differential equation whose analytical exact solution has been unknown. It is confirmed that the form of this equation is similar to the radial Schroedinger equation for the hydrogen atom in a (arbitrary) strong magnetic field. The qualitative properties for the eigenstates spectrum are described separately for the different values of the parameter ω 0 appearing in the x 2 term, x being the position, i.e., ω 0 > 0, ω 0 0 = 0. For the ω 0 = 0 case, the eigenvalue equation of invariant operator reduces to a solvable form and, consequently, we have provided exact eigenstates of the time-dependent Hamiltonian system

Exact scattering solutions in an energy sudden (ES) representation

International Nuclear Information System (INIS)

Chang, B.; Eno, L.; Rabitz, H.

1983-01-01

In this paper, we lay down the theoretical foundations for computing exact scattering wave functions in a reference frame which moves in unison with the system internal coordinates. In this frame the (internal) coordinates appear to be fixed and its adoption leads very naturally (in zeroth order) to the energy sudden (ES) approximation [and the related infinite order sudden (IOS) method]. For this reason we call the new representation for describing the exact dynamics of a many channel scattering problem, the ES representation. Exact scattering solutions are derived in both time dependent and time independent frameworks for the representation and many interesting results in these frames are established. It is shown, e.g., that in a time dependent frame the usual Schroedinger propagator factorizes into internal Hamiltonian, ES, and energy correcting propagators. We also show that in a time independent frame the full Green's functions can be similarly factorized. Another important feature of the new representation is that it forms a firm foundation for seeking corrections to the ES approximation. Thus, for example, the singularity which arises in conventional perturbative expansions of the full Green's functions (with the ES Green's function as the zeroth order solution) is avoided in the ES representation. Finally, a number of both time independent and time dependent ES correction schemes are suggested

Analysis on Dynamic Transmission Accuracy for RV Reducer

Directory of Open Access Journals (Sweden)

Zhang Fengshou

2017-01-01

Full Text Available By taking rotate vector (RV reducer as the research object, the factors affecting the transmission accuracy are studied, including the machining errors of the main parts, assembly errors, clearance, micro-displacement, gear mesh stiffness and damping, bearing stiffness. Based on Newton second law, the transmission error mathematical model of RV reducer is set up. Then, the RV reducer transmission error curve is achieved by solving the mathematical model using the Runge-Kutta methods under the combined action of various error factors. Through the analysis of RV reducer transmission test, it can be found that there are similar variation trend and frequency components compared the theoretical research and experimental result. The presented method is useful to the research on dynamic transmission accuracy of RV reducer, and also applies to research the transmission accuracy of other cycloid drive systems.

A computationally exact method of Dawson's model for hole dynamics of one-dimensional plasma

International Nuclear Information System (INIS)

Kitahara, Kazuo; Tanno, Kohki; Takada, Toshio; Hatori, Tadatsugu; Urata, Kazuhiro; Irie, Haruyuki; Nambu, Mitsuhiro; Saeki, Kohichi.

1990-01-01

We show a simple but computationally exact solution of the one-dimensional plasma model, so-called 'Dawson's model'. Using this solution, we can describe the evolution of the plasma and find the relative stabilization of a big hole after the instability of two streams. (author)

The exact solutions of the Schroedinger equation with the Morse potential via Laplace transforms

International Nuclear Information System (INIS)

Chen Gang

2004-01-01

In this Letter, we reduce the second-order differential equation about the one-dimensional Schroedinger equation with the Morse potential reduced to the first-order differential equation in terms of Laplace transforms and then obtain the exact bound state solutions

Truncated Wigner dynamics and conservation laws

Science.gov (United States)

Drummond, Peter D.; Opanchuk, Bogdan

2017-10-01

Ultracold Bose gases can be used to experimentally test many-body theory predictions. Here we point out that both exact conservation laws and dynamical invariants exist in the topical case of the one-dimensional Bose gas, and these provide an important validation of methods. We show that the first four quantum conservation laws are exactly conserved in the approximate truncated Wigner approach to many-body quantum dynamics. Center-of-mass position variance is also exactly calculable. This is nearly exact in the truncated Wigner approximation, apart from small terms that vanish as N-3 /2 as N →∞ with fixed momentum cutoff. Examples of this are calculated in experimentally relevant, mesoscopic cases.

Shadowing in dynamical systems

CERN Document Server

Pilyugin, Sergei Yu

1999-01-01

This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.

Exact partition functions for gauge theories on Rλ3

Directory of Open Access Journals (Sweden)

Jean-Christophe Wallet

2016-11-01

Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

A conditionally exactly solvable generalization of the inverse square root potential

Energy Technology Data Exchange (ETDEWEB)

Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, Ashtarak 0203 (Armenia); Armenian State Pedagogical University, Yerevan 0010 (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)

2016-11-25

We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. - Highlights: • We present a conditionally exactly solvable singular potential for 1D Schrödinger equation. • Each of the two fundamental solutions is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. • The exact equation for the energy spectrum is written using two Hermite functions that do not reduce to polynomials.

Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique

International Nuclear Information System (INIS)

Destainville, N

2003-01-01

We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium

Steering the dynamics within reduced space through quantum learning control

International Nuclear Information System (INIS)

Kim, Young Sik

2003-01-01

In quantum dynamics of many-body systems, to identify the Hamiltonian becomes more difficult very rapidly as the number of degrees of freedom increases. In order to simplify the dynamics and to deduce dynamically relevant Hamiltonian information, it is desirable to control the dynamics to lie within a reduced space. With a judicious choice for the cost functional, the closed loop optimal control experiments can be manipulated efficiently to steer the dynamics to lie within a subspace of the system eigenstates without requiring any prior detailed knowledge about the system Hamiltonian. The procedure is simulated for optimally controlled population transfer experiments in the system of two degrees of freedom. To show the feasibility of steering the dynamics to lie in a specified subspace, the learning algorithms guiding the dynamics are presented along with frequency filtering. The results demonstrate that the optimal control fields derive the system to the desired target state through the desired subspace

Exact error estimation for solutions of nuclide chain equations

International Nuclear Information System (INIS)

Tachihara, Hidekazu; Sekimoto, Hiroshi

1999-01-01

The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated. The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one. (author)

Exact soliton-like solutions of the radial Gross–Pitaevskii equation

International Nuclear Information System (INIS)

Toikka, L A; Hietarinta, J; Suominen, K-A

2012-01-01

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e. radial) Gross–Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlevé transcendent. In each case the potential can be chosen to be time independent. (paper)

Exact piecewise flat gravitational waves

NARCIS (Netherlands)

van de Meent, M.

2011-01-01

We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to

Exact solitary waves of the Fisher equation

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

Study on dynamic characteristics of reduced analytical model for PWR reactor internal structures

International Nuclear Information System (INIS)

Yoo, Bong; Lee, Jae Han; Kim, Jong Bum; Koo, Kyeong Hoe

1993-01-01

The objective of this study is to establish the procedure of the reduced analytical modeling technique for the PWR reactor internal(RI) structures and to carry out the sensitivity study of the dynamic characteristics of the structures by varying the structural parameters such as the stiffness, the mass and the damping. Modeling techniques for the PWR reactor internal structures and computer programs used for the dynamic analysis of the reactor internal structures are briefly investigated. Among the many components of RI structures, the dynamic characteristics for CSB was performed. The sensitivity analysis of the dynamic characteristics for the reduced analytical model considering the variations of the stiffnesses for the lower and upper flanges of the CSB and for the RV Snubber were performed to improve the dynamic characteristics of the RI structures against the external loadings given. In order to enhance the structural design margin of the RI components, the nonlinear time history analyses were attempted for the RI reduced models to compare the structural responses between the reference model and the modified one. (Author)

Quasi-Exact Coulomb Dynamics of n Charges n-1 of Which Are Equal

Directory of Open Access Journals (Sweden)

Wolodymyr Skrypnik

2017-01-01

Full Text Available For n≥3 point charges n-1 of which are negative and equal quasi-exact periodic solutions of their Coulomb equation of motion are found. These solutions describe a motion of the negative charges around a coordinate axis in such a way that their coordinates coincide with vertices of a regular polygon in planes perpendicular to the axis along which the positive charge moves. The Weinstein and center Lyapunov theorems are utilized.

Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories

Energy Technology Data Exchange (ETDEWEB)

Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)

2017-11-15

In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O(N) λφ{sup 4} scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz-invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding β-function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit. (orig.)

CONDITIONS FOR EXACT CAVALIERI ESTIMATION

Directory of Open Access Journals (Sweden)

Mónica Tinajero-Bravo

2014-03-01

Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.

Geometrically exact nonlinear analysis of pre-twisted composite rotor blades

Directory of Open Access Journals (Sweden)

Li'na SHANG

2018-02-01

Full Text Available Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape, generally anisotropic material behavior and large deflections has been presented based on Hodges’ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton’s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade. Keywords: Geometrically exact, Nonlinear, Pre-twisted composite blade, Transverse shear deformation, Variational asymptotic, Warping

Exact solutions for rotating charged dust

International Nuclear Information System (INIS)

Islam, J.N.

1984-01-01

Earlier work by the author on rotating charged dust is summarized. An incomplete class of exact solutions for differentially rotating charged dust in Newton-Maxwell theory for the equal mass and charge case that was found earlier is completed. A new global exact solution for cylindrically symmetric differentially rotating charged dust in Newton-Maxwell theory is presented. Lastly, a new exact solution for cylindrically symmetric rigidly rotating charged dust in general relativity is given. (author)

Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique

Energy Technology Data Exchange (ETDEWEB)

Destainville, N [Laboratoire de Physique Theorique - IRSAMC, CNRS/Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04 (France)

2003-04-04

We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.

Exact scattering and diffraction of antiplane shear waves by a vertical edge crack

Science.gov (United States)

Tsaur, Deng-How

2010-06-01

Scattering and diffraction problems of a vertical edge crack connected to the surface of a half space are considered for antiplane shear wave incidence. The method of separation of variables is adopted to derive an exact series solution. The total displacement field is expressed as infinite series containing products of radial and angular Mathieu functions with unknown coefficients. An exact analytical determination of unknown coefficients is carried out by insuring the vanishing of normal stresses on crack faces. Frequency-domain results are given for extremely near, near, and far fields, whereas time-domain ones are for horizontal surface and subsurface motions. Comparisons with published data for the dynamic stress intensity factor show good agreement. The exact analytical nature of proposed solutions can be applied very conveniently and rapidly to high-frequency steady-state cases, enhancing the computation efficiency in transient cases when performing the fast Fourier transform. A sampled set of time slices for underground wave propagation benefits the interpretation of scattering and diffraction phenomena induced by a vertical edge crack.

On melting dynamics and the glass transition. II. Glassy dynamics as a melting process.

Science.gov (United States)

Krzakala, Florent; Zdeborová, Lenka

2011-01-21

There are deep analogies between the melting dynamics in systems with a first-order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first-order transition--namely p-spin models on the so-called Nishimori line--it can be shown that the melting dynamics can be exactly mapped to the equilibrium dynamics. In this mapping the dynamical--or mode-coupling--glass transition corresponds to the spinodal point, while the Kauzmann transition corresponds to the first-order phase transition itself. Both in mean field and finite dimensional models this mapping provides an exact realization of the random first-order theory scenario for the glass transition. The corresponding glassy phenomenology can then be understood in the framework of a standard first-order phase transition.

Discrete dynamics versus analytic dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2014-01-01

For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....

Reduced density matrix functional theory via a wave function based approach

Energy Technology Data Exchange (ETDEWEB)

Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)

2016-07-01

We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

Science.gov (United States)

Cadilhe, A.; Voter, Arthur F.

2018-02-01

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. Here, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. Finally, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R.K.

2012-01-01

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein—Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions

Exact and Heuristic Algorithms for Routing AGV on Path with Precedence Constraints

Directory of Open Access Journals (Sweden)

Liang Xu

2016-01-01

Full Text Available A new problem arises when an automated guided vehicle (AGV is dispatched to visit a set of customers, which are usually located along a fixed wire transmitting signal to navigate the AGV. An optimal visiting sequence is desired with the objective of minimizing the total travelling distance (or time. When precedence constraints are restricted on customers, the problem is referred to as traveling salesman problem on path with precedence constraints (TSPP-PC. Whether or not it is NP-complete has no answer in the literature. In this paper, we design dynamic programming for the TSPP-PC, which is the first polynomial-time exact algorithm when the number of precedence constraints is a constant. For the problem with number of precedence constraints, part of the input can be arbitrarily large, so we provide an efficient heuristic based on the exact algorithm.

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

E2-quasi-exact solvability for non-Hermitian models

International Nuclear Information System (INIS)

Fring, Andreas

2015-01-01

We propose the notion of E 2 -quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the complex Mathieu Hamiltonian in a double scaling limit, which enables us to compute the exceptional points in the energy spectrum of the latter as a limiting process of the zeros for some algebraic equations. The coefficient functions in the quasi-exact eigenfunctions are univariate polynomials in the energy obeying a three-term recurrence relation. The latter property guarantees the existence of a linear functional such that the polynomials become orthogonal. The polynomials are shown to factorize for all levels above the quantization condition leading to vanishing norms rendering them to be weakly orthogonal. In two concrete examples we compute the explicit expressions for the Stieltjes measure. (paper)

E2-quasi-exact solvability for non-Hermitian models

Science.gov (United States)

Fring, Andreas

2015-04-01

We propose the notion of E2-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the complex Mathieu Hamiltonian in a double scaling limit, which enables us to compute the exceptional points in the energy spectrum of the latter as a limiting process of the zeros for some algebraic equations. The coefficient functions in the quasi-exact eigenfunctions are univariate polynomials in the energy obeying a three-term recurrence relation. The latter property guarantees the existence of a linear functional such that the polynomials become orthogonal. The polynomials are shown to factorize for all levels above the quantization condition leading to vanishing norms rendering them to be weakly orthogonal. In two concrete examples we compute the explicit expressions for the Stieltjes measure.

The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

DEFF Research Database (Denmark)

Iskhakov, Fedor; Rust, John; Schjerning, Bertel

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs in equili......We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs...... in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition...... leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique...

Approximate and exact hybrid algorithms for private nearest-neighbor queries with database protection

KAUST Repository

Ghinita, Gabriel; Kalnis, Panos; Kantarcioǧlu, Murâ t; Bertino, Elisa

2010-01-01

Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O({pipe}D{pipe}) in the worst case). PIR, on the other hand, reduces this bound to O(√{pipe}D{pipe}), but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead. © 2010

Approximate and exact hybrid algorithms for private nearest-neighbor queries with database protection

KAUST Repository

Ghinita, Gabriel

2010-12-15

Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O({pipe}D{pipe}) in the worst case). PIR, on the other hand, reduces this bound to O(√{pipe}D{pipe}), but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead. © 2010

Exact lattice supersymmetry: The two-dimensional N=2 Wess-Zumino model

International Nuclear Information System (INIS)

Catterall, Simon; Karamov, Sergey

2002-01-01

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving exactly a single supersymmetric invariance at finite lattice spacing a. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to O(ga 2 ) where g is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the mass gaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing

Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

Directory of Open Access Journals (Sweden)

Boris V. Kapitonov

2010-02-01

Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

Dynamics and bistability in a reduced model of the lac operon

Science.gov (United States)

Yildirim, Necmettin; Santillán, Moisés; Horike, Daisuke; Mackey, Michael C.

2004-06-01

It is known that the lac operon regulatory pathway is capable of showing bistable behavior. This is an important complex feature, arising from the nonlinearity of the involved mechanisms, which is essential to understand the dynamic behavior of this molecular regulatory system. To find which of the mechanisms involved in the regulation of the lac operon is the origin of bistability, we take a previously published model which accounts for the dynamics of mRNA, lactose, allolactose, permease and β-galactosidase involvement and simplify it by ignoring permease dynamics (assuming a constant permease concentration). To test the behavior of the reduced model, three existing sets of data on β-galactosidase levels as a function of time are simulated and we obtain a reasonable agreement between the data and the model predictions. The steady states of the reduced model were numerically and analytically analyzed and it was shown that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.

Dynamic combinatorial chemistry

NARCIS (Netherlands)

Otto, Sijbren; Furlan, Ricardo L.E.; Sanders, Jeremy K.M.

2002-01-01

A combinatorial library that responds to its target by increasing the concentration of strong binders at the expense of weak binders sounds ideal. Dynamic combinatorial chemistry has the potential to achieve exactly this. In this review, we will highlight the unique features that distinguish dynamic

On exact solutions of scattering problems

International Nuclear Information System (INIS)

Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.

1982-01-01

Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived

Reducing Visual Discomfort with HMDs Using Dynamic Depth of Field.

Science.gov (United States)

Carnegie, Kieran; Rhee, Taehyun

2015-01-01

Although head-mounted displays (HMDs) are ideal devices for personal viewing of immersive stereoscopic content, exposure to VR applications on them results in significant discomfort for the majority of people, with symptoms including eye fatigue, headaches, nausea, and sweating. A conflict between accommodation and vergence depth cues on stereoscopic displays is a significant cause of visual discomfort. This article describes the results of an evaluation used to judge the effectiveness of dynamic depth-of-field (DoF) blur in an effort to reduce discomfort caused by exposure to stereoscopic content on HMDs. Using a commercial game engine implementation, study participants report a reduction of visual discomfort on a simulator sickness questionnaire when DoF blurring is enabled. The study participants reported a decrease in symptom severity caused by HMD exposure, indicating that dynamic DoF can effectively reduce visual discomfort.

Exact and Direct Modeling Technique for Rotor-Bearing Systems with Arbitrary Selected Degrees-of-Freedom

Directory of Open Access Journals (Sweden)

Shilin Chen

1994-01-01

Full Text Available An exact and direct modeling technique is proposed for modeling of rotor-bearing systems with arbitrary selected degrees-of-freedom. This technique is based on the combination of the transfer and dynamic stiffness matrices. The technique differs from the usual combination methods in that the global dynamic stiffness matrix for the system or the subsystem is obtained directly by rearranging the corresponding global transfer matrix. Therefore, the dimension of the global dynamic stiffness matrix is independent of the number of the elements or the substructures. In order to show the simplicity and efficiency of the method, two numerical examples are given.

Effectiveness of multi tuned liquid dampers with slat screens for reducing dynamic responses of structures

Science.gov (United States)

Nguyen, T. P.; Pham, D. T.; Ngo, K. T.

2018-04-01

Reducing vibration in structures under lateral load always attracts many researchers in during pastime, hence the mainly purpose of paper analyzes effectiveness of multiple-tuned liquid dampers for reducing dynamic responses of structures under ground acceleration of earthquakes. In this study, the multi-tuned liquid damper with slat screens (M-TLDWSS) is considered in detail for analyzing dynamic response of multi-degrees of freedom structure due to earthquake, which is more different previous studies. Then, the general equation of motion of the structure and M-TLDWSS under ground acceleration of earthquake is established based on dynamic balance of principle and solved by numerical method in the time domain. The effects of characteristic parameters of M-TLDWSS on dynamic response of the structure are investigated. The results obtained in this study demonstrate that the M-TLDWSS has significantly effectiveness for reducing dynamic response of the structure.

Cesarean section and the manipulation of exact delivery time.

Science.gov (United States)

Fabbri, Daniele; Monfardini, Chiara; Castaldini, Ilaria; Protonotari, Adalgisa

2016-07-01

Physicians are often alleged responsible for the manipulation of delivery timing. We investigate this issue in a setting that negates the influence of financial incentives on physician's behavior. Working on a sample of women admitted at the onset of labor in a big public hospital in Italy we estimate a model for the exact time of delivery as driven by individual Indication to Cesarean Section (ICS) and covariates. We find that ICS does not affect the day of delivery but leads to a circadian rhythm in the likelihood of delivery. The pattern is consistent with the postponement of high ICS deliveries in the late night\\early morning shift. Our evidence hardly supports the manipulation of timing of births as driven by medical staff's "demand for leisure". Physicians seem to manipulate the exact timing of delivery to reduce exposure to risk factors extant during off-peak periods. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

The exact effects of radiation and joule heating on magnetohydrodynamic Marangoni convection over a flat surface

Directory of Open Access Journals (Sweden)

Khaled S.M.

2018-01-01

Full Text Available In this paper, we re-investigate the problem describing effects of radiation, Joule heating, and viscous dissipation on magnetohydrodynamic Marangoni convection boundary layer over a flat surface with suction/injection. The analytical solution obtained for the reduced system of non-linear-coupled differential equations governing the problem. Laplace transform successfully implemented to get the exact expression for the temperature profile. Furthermore, comparing the current exact results with approximate numerical results obtained using Runge-Kutta-Fehlberg method is introduced. These comparisons declare that the published numerical results agree with the current exact results. In addition, the effects of various parameters on the temperature profile are discussed graphically.

Time measurement - technical importance of most exact clocks

International Nuclear Information System (INIS)

Goebel, E.O.; Riehle, F.

2004-01-01

The exactness of the best atomic clocks currently shows a temporal variation of 1 second in 30 million years. This means that we have reached the point of the most exact frequency and time measurement ever. In the past, there was a trend towards increasing the exactness in an increasingly fast sequence. Will this trend continue? And who will profit from it? This article is meant to give answers to these questions. This is done by presenting first the level reached currently with the best atomic clocks and describing the research activities running worldwide with the aim of achieving even more exact clocks. In the second part, we present examples of various areas of technical subjects and research in which the most exact clocks are being applied presently and even more exact ones will be needed in the future [de

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

Institute of Scientific and Technical Information of China (English)

WANG; Shunjin; ZHANG; Hua

2006-01-01

The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

Compiled data set of exact NOE distance limits, residual dipolar couplings and scalar couplings for the protein GB3

Directory of Open Access Journals (Sweden)

Beat Vögeli

2015-12-01

Full Text Available We compiled an NMR data set consisting of exact nuclear Overhauser enhancement (eNOE distance limits, residual dipolar couplings (RDCs and scalar (J couplings for GB3, which forms one of the largest and most diverse data set for structural characterization of a protein to date. All data have small experimental errors, which are carefully estimated. We use the data in the research article Vogeli et al., 2015, Complementarity and congruence between exact NOEs and traditional NMR probes for spatial decoding of protein dynamics, J. Struct. Biol., 191, 3, 306–317, doi:10.1016/j.jsb.2015.07.008 [1] for cross-validation in multiple-state structural ensemble calculation. We advocate this set to be an ideal test case for molecular dynamics simulations and structure calculations.

System and method for reducing combustion dynamics in a combustor

Science.gov (United States)

Uhm, Jong Ho; Johnson, Thomas Edward; Zuo, Baifang; York, William David

2013-08-20

A system for reducing combustion dynamics in a combustor includes an end cap having an upstream surface axially separated from a downstream surface, and tube bundles extend through the end cap. A diluent supply in fluid communication with the end cap provides diluent flow to the end cap. Diluent distributors circumferentially arranged inside at least one tube bundle extend downstream from the downstream surface and provide fluid communication for the diluent flow through the end cap. A method for reducing combustion dynamics in a combustor includes flowing fuel through tube bundles that extend axially through an end cap, flowing a diluent through diluent distributors into a combustion chamber, wherein the diluent distributors are circumferentially arranged inside at least one tube bundle and each diluent distributor extends downstream from the end cap, and forming a diluent barrier in the combustion chamber between at least one pair of adjacent tube bundles.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Science.gov (United States)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo

International Nuclear Information System (INIS)

Overy, Catherine; Blunt, N. S.; Shepherd, James J.; Booth, George H.; Cleland, Deidre; Alavi, Ali

2014-01-01

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems

A quasi-exactly solvable Lipkin-Meshkov-Glick model

International Nuclear Information System (INIS)

Pan Feng; Lin Jijie; Xue Xiaogang; Draayer, J P

2010-01-01

We prove that a special Lipkin-Meshkov-Glick model is quasi-exactly solvable with solutions that can be expressed in the SU(2) coherent state form. Ground-state properties of the model are studied analytically. We also show that the model reduces to the standard two-site Bose-Hubbard model in the large-N limit for finite U/t or large (N - 1)|U|/t cases with finite N, which proves that in these cases the ground state of the standard two-site Bose-Hubbard model is an SU(2) coherent state.

Exact solution of the generalized time-dependent Jaynes-Cummings Hamiltonian

International Nuclear Information System (INIS)

Gruver, J.L.; Aliaga, J.; Cerdeira, H.A.; Proto, A.N.

1993-04-01

A time-dependent generalization of the Jaynes-Cummings Hamiltonian is studied using the maximum entropy formalism. The approach, related to a semi-Lie algebra, allows to find three different sets of physical relevant operators which describe the dynamics of the system for any temporal dependence. It is shown how the initial conditions of the operators are determined via the maximum entropy principle density operator, where the inclusion of the temperature turns the description of the problem into a thermodynamical one. The generalized time-independent Jaynes-Cummings Hamiltonian is exactly solved as a particular example. (author). 14 refs

New exact solutions of the mBBM equation

International Nuclear Information System (INIS)

Zhang Zhe; Li Desheng

2013-01-01

The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

An Exact Solvable Model of Rocket Dynamics in Atmosphere

Science.gov (United States)

Rodrigues, H.; Pinho, M. O.; Portes, D., Jr.; Santiago, A.

2009-01-01

In basic physics courses at undergraduate level, the dynamics of self-propelled bodies is presented as an example of momentum conservation law applied to systems with time-varying mass. However, is often studied the simple situation of free motion or the motion under the action of a constant gravitational field. In this work, we investigate the…

Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

Science.gov (United States)

Saengow, C.; Giacomin, A. J.

2017-12-01

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2017-11-01

Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines

The Hall module of an exact category with duality

OpenAIRE

Young, Matthew B.

2012-01-01

We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced sigma-analogue of the quantum Kac-Moody algebra attached to the quiver. For finite type quivers, we explicitly determin...

Exact exchange-correlation potential and approximate exchange potential in terms of density matrices

International Nuclear Information System (INIS)

Holas, A.; March, N.H.

1995-01-01

An exact expression in terms of density matrices (DM) is derived for δF[n]/δn(r), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohn-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchange-correlation potential v xc (r) is obtained which is analogous in character to that for δF[n]/δn(r), but involving, besides the interacting-system DMs, also the noninteracitng DMs. Equating the former DMs to the latter ones, we reduce the result for the exact v xc (r) to that for an approximate exchange-only potential v x (r). This leads naturally to the Harbola-Sahni exchange-only potential

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

Exact, almost and delayed fault detection

DEFF Research Database (Denmark)

Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.

1999-01-01

Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

BWR stability using a reduced dynamical model

International Nuclear Information System (INIS)

Ballestrin Bolea, J.M.; Blazquez, J.B.

1990-01-01

BWR stability can be treated with reduced order dynamical models. When the parameters of the model came from experimental data, the predictions are accurate. In this work an alternative derivation for the void fraction equation is made, but remarking the physical struct-ure of the parameters. As the poles of power/reactivity transfer function are related with the parameters, the measurement of the poles by other techniques such as noise analysis will lead to the parameters, but the system of equations in non-linear. Simple parametric calculat-ion of decay ratio are performed, showing why BWRs become unstable when they are operated at low flow and high power. (Author). 7 refs

Cosmological dynamics with non-minimally coupled scalar field and a constant potential function

International Nuclear Information System (INIS)

Hrycyna, Orest; Szydłowski, Marek

2015-01-01

Dynamical systems methods are used to investigate global behaviour of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of the dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory

Cosmological dynamics with non-minimally coupled scalar field and a constant potential function

Energy Technology Data Exchange (ETDEWEB)

Hrycyna, Orest [Theoretical Physics Division, National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Szydłowski, Marek, E-mail: orest.hrycyna@ncbj.gov.pl, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Kraków (Poland)

2015-11-01

Dynamical systems methods are used to investigate global behaviour of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of the dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory.

MapReduce particle filtering with exact resampling and deterministic runtime

Science.gov (United States)

Thiyagalingam, Jeyarajan; Kekempanos, Lykourgos; Maskell, Simon

2017-12-01

Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as the number of particles increases, it is natural to consider as many particles as possible. MapReduce is a generic programming model that makes it possible to scale a wide variety of algorithms to Big data. However, despite the application of particle filters across many domains, little attention has been devoted to implementing particle filters using MapReduce. In this paper, we describe an implementation of a particle filter using MapReduce. We focus on a component that what would otherwise be a bottleneck to parallel execution, the resampling component. We devise a new implementation of this component, which requires no approximations, has O( N) spatial complexity and deterministic O((log N)2) time complexity. Results demonstrate the utility of this new component and culminate in consideration of a particle filter with 224 particles being distributed across 512 processor cores.

Perturbation of an exact strong gravity solution

International Nuclear Information System (INIS)

Baran, S.A.

1982-10-01

Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)

Exact Controllability of a Piezoelectric Body. Theory and Numerical Simulation

International Nuclear Information System (INIS)

Miara, Bernadette; Muench, Arnaud

2009-01-01

We study the exact controllability of a three-dimensional body made of a material whose constitutive law introduces an elasticity-electricity coupling. We show that a coupled elastic-electric control acting on the whole boundary of the body drives the system to rest after time large enough. Two-dimensional numerical experiments suggest that controllability can still be achieved by relaxing this restrictive condition using either both controls on a reduced support or elastic control alone

Dynamical image-charge effect in molecular tunnel junctions

DEFF Research Database (Denmark)

Jin, Chengjun; Thygesen, Kristian Sommer

2014-01-01

the finite IC formation time affects charge transport through a molecule suspended between two electrodes. For a single-level model, an analytical treatment shows that the conductance is suppressed by a factor Z(2), where Z is the quasiparticle renormalization factor, compared to the static IC approximation...... that the dynamical corrections can reduce the conductance by more than a factor of two when compared to static GW or density functional theory where the molecular energy levels have been shifted to match the exact quasiparticle levels....

Exact moduli space metrics for hyperbolic vortex polygons

International Nuclear Information System (INIS)

Krusch, S.; Speight, J. M.

2010-01-01

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Σ n,m , are spaces of C n -invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of Σ n,m are investigated, and it is found that Σ n,n-1 is isometric to the hyperbolic plane of curvature -(3πn) -1 . The geodesic flow on Σ n,m and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.

On symmetries and exact solutions of the Einstein–Maxwell field equations via the symmetry approach

International Nuclear Information System (INIS)

Kaur, Lakhveer; Gupta, R K

2013-01-01

Using the Lie symmetry approach, we have examined herein the system of partial differential equations corresponding to the Einstein–Maxwell equations for a static axially symmetric spacetime. The method used reduces the system of partial differential equations to a system of ordinary differential equations according to the Lie symmetry admitted. In particular, we found the relevant system of ordinary differential equations is all optimal subgroups. The system of ordinary differential equations is further solved in general to obtain exact solutions. Several new physically important families of exact solutions are derived. (paper)

High protein flexibility and reduced hydration water dynamics are key pressure adaptive strategies in prokaryotes

KAUST Repository

Martinez, N.

2016-09-06

Water and protein dynamics on a nanometer scale were measured by quasi-elastic neutron scattering in the piezophile archaeon Thermococcus barophilus and the closely related pressure-sensitive Thermococcus kodakarensis, at 0.1 and 40 MPa. We show that cells of the pressure sensitive organism exhibit higher intrinsic stability. Both the hydration water dynamics and the fast protein and lipid dynamics are reduced under pressure. In contrast, the proteome of T. barophilus is more pressure sensitive than that of T. kodakarensis. The diffusion coefficient of hydration water is reduced, while the fast protein and lipid dynamics are slightly enhanced with increasing pressure. These findings show that the coupling between hydration water and cellular constituents might not be simply a master-slave relationship. We propose that the high flexibility of the T. barophilus proteome associated with reduced hydration water may be the keys to the molecular adaptation of the cells to high hydrostatic pressure.

High protein flexibility and reduced hydration water dynamics are key pressure adaptive strategies in prokaryotes

KAUST Repository

Martinez, N.; Michoud, Gregoire; Cario, A.; Ollivier, J.; Franzetti, B.; Jebbar, M.; Oger, P.; Peters, J.

2016-01-01

Water and protein dynamics on a nanometer scale were measured by quasi-elastic neutron scattering in the piezophile archaeon Thermococcus barophilus and the closely related pressure-sensitive Thermococcus kodakarensis, at 0.1 and 40 MPa. We show that cells of the pressure sensitive organism exhibit higher intrinsic stability. Both the hydration water dynamics and the fast protein and lipid dynamics are reduced under pressure. In contrast, the proteome of T. barophilus is more pressure sensitive than that of T. kodakarensis. The diffusion coefficient of hydration water is reduced, while the fast protein and lipid dynamics are slightly enhanced with increasing pressure. These findings show that the coupling between hydration water and cellular constituents might not be simply a master-slave relationship. We propose that the high flexibility of the T. barophilus proteome associated with reduced hydration water may be the keys to the molecular adaptation of the cells to high hydrostatic pressure.

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

Science.gov (United States)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Exact optics - III. Schwarzschild's spectrograph camera revised

Science.gov (United States)

Willstrop, R. V.

2004-03-01

Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.

Exact evaluation of entropic quantities in a solvable two-particle model

International Nuclear Information System (INIS)

Glasser, M.L.; Nagy, I.

2013-01-01

It has long been known that the von Neumann entropy S N and the Jozsa–Robb–Wootters subentropy Q JRW [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin's natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.

Exact evaluation of entropic quantities in a solvable two-particle model

Energy Technology Data Exchange (ETDEWEB)

Glasser, M.L., E-mail: laryg@clarkson.edu [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States); Donostia International Physics Center, P. Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Nagy, I. [Donostia International Physics Center, P. Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest (Hungary)

2013-11-08

It has long been known that the von Neumann entropy S{sub N} and the Jozsa–Robb–Wootters subentropy Q{sub JRW} [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin's natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.

On reduction and exact solutions of nonlinear many-dimensional Schroedinger equations

International Nuclear Information System (INIS)

Barannik, A.F.; Marchenko, V.A.; Fushchich, V.I.

1991-01-01

With the help of the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra AO(n) the rank n and n-1 maximal subalgebras of the extended isochronous Galileo algebra, the rank n maximal subalgebras of the generalized extended classical Galileo algebra AG(a,n) the extended special Galileo algebra AG(2,n) and the extended whole Galileo algebra AG(3,n) are described. By using the rank n subalgebras, ansatze reducing the many dimensional Schroedinger equations to ordinary differential equations is found. With the help of the reduced equation solutions exact solutions of the Schroedinger equation are considered

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

Directory of Open Access Journals (Sweden)

Roman Cherniha

2018-04-01

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

Relativistic plasma dielectric tensor evaluation based on the exact plasma dispersion functions concept

International Nuclear Information System (INIS)

Castejon, F.; Pavlov, S. S.

2006-01-01

The fully relativistic plasma dielectric tensor for any wave and plasma parameter is estimated on the basis of the exact plasma dispersion functions concept. The inclusion of this concept allows one to write the tensor in a closed and compact form and to reduce the tensor evaluation to the calculation of those functions. The main analytical properties of these functions are studied and two methods are given for their evaluation. The comparison between the exact dielectric tensor with the weakly relativistic approximation, widely used presently in plasma waves calculations, is given as well as the range of plasma temperature, harmonic number, and propagation angle in which the weakly relativistic approximation is valid

Exact and approximate multiple diffraction calculations

International Nuclear Information System (INIS)

Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

1976-08-01

A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point

International Nuclear Information System (INIS)

Lenci, Marco

2016-01-01

Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0, 1], with countably many surjective branches and a strongly neutral fixed point in 0.

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

Science.gov (United States)

Park, DaeKil

2018-06-01

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.

Reduced order dynamic model for polysaccharides molecule attached to an atomic force microscope

International Nuclear Information System (INIS)

Tang Deman; Li Aiqin; Attar, Peter; Dowell, Earl H.

2004-01-01

A dynamic analysis and numerical simulation has been conducted of a polysaccharides molecular structure (a ten (10) single-α-D-glucose molecule chain) connected to a moving atomic force microscope (AFM). Sinusoidal base excitation of the AFM cantilevered beam is considered. First a linearized perturbation model is constructed for the complex polysaccharides molecular structure. Then reduced order (dynamic) models based upon a proper orthogonal decomposition (POD) technique are constructed using global modes for both the linearized perturbation model and for the full nonlinear model. The agreement between the original and reduced order models (ROM/POD) is very good even when only a few global modes are included in the ROM for either the linear case or for the nonlinear case. The computational advantage of the reduced order model is clear from the results presented

Explore or Exploit? A Generic Model and an Exactly Solvable Case

Science.gov (United States)

Gueudré, Thomas; Dobrinevski, Alexander; Bouchaud, Jean-Philippe

2014-02-01

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.

Explore or exploit? A generic model and an exactly solvable case.

Science.gov (United States)

Gueudré, Thomas; Dobrinevski, Alexander; Bouchaud, Jean-Philippe

2014-02-07

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.

Exact distributions of two-sample rank statistics and block rank statistics using computer algebra

NARCIS (Netherlands)

Wiel, van de M.A.

1998-01-01

We derive generating functions for various rank statistics and we use computer algebra to compute the exact null distribution of these statistics. We present various techniques for reducing time and memory space used by the computations. We use the results to write Mathematica notebooks for

An Exact Solution of The Neutron Slowing Down Equation

Energy Technology Data Exchange (ETDEWEB)

Stefanovic, D [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1970-07-01

The slowing down equation for an infinite homogeneous monoatomic medium is solved exactly. The cross sections depend on neutron energy. The solution is given in analytical form within each of the lethargy intervals. This analytical form is the sum of probabilities which are given by the Green functions. The calculated collision density is compared with the one obtained by Bednarz and also with an approximate Wigner formula for the case of a resonance not wider than one collision interval. For the special case of hydrogen, the present solution reduces to Bethe's solution. (author)

A theory of electron baths: One-electron system dynamics

International Nuclear Information System (INIS)

McDowell, H.K.

1992-01-01

The second-quantized, many-electron, atomic, and molecular Hamiltonian is partitioned both by the identity or labeling of the spin orbitals and by the dynamics of the spin orbitals into a system coupled to a bath. The electron bath is treated by a molecular time scale generalized Langevin equation approach designed to include one-electron dynamics in the system dynamics. The bath is formulated as an equivalent chain of spin orbitals through the introduction of equivalent-chain annihilation and creation operators. Both the dynamics and the quantum grand canonical statistical properties of the electron bath are examined. Two versions for the statistical properties of the bath are pursued. Using a weak bath assumption, a bath statistical average is defined which allows one to achieve a reduced dynamics description of the electron system which is coupled to the electron bath. In a strong bath assumption effective Hamiltonians are obtained which reproduce the dynamics of the bath and which lead to the same results as found in the weak bath assumption. The effective (but exact) Hamiltonian is found to be a one-electron Hamiltonian. A reduced dynamics equation of motion for the system population matrix is derived and found to agree with a previous version. This equation of motion is useful for studying electron transfer in the system when coupled to an electron bath

Quasistationary model of high-current relativistic electron beam. 1. Exact solution of Poisson equations

International Nuclear Information System (INIS)

Brenner, S.E.; Gandyl', E.M.; Podkopaev, A.P.

1995-01-01

The dynamics of high-current relativistic electron beam moving trough the cylindrical drift space has been modelled by the large particles, the shape of which allows to solve the Poisson equations exactly, and in such a way to avoid the linearization being usually used in those problems. The expressions for the components of own electric field of electron beam passing through the cylindrical drift space have been obtained. (author). 11 refs., 1 fig

Sum rules for four-spinon dynamic structure factor in XXX model

International Nuclear Information System (INIS)

Si Lakhal, B.; Abada, A.

2005-01-01

In the context of the antiferromagnetic spin 12 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor S 4 by calculating a number of sum rules the total dynamic structure factor S is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of S 4 is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor S 2 is between 70% and 75%. The calculations are numerical and Monte Carlo based. Good statistics are obtained

Lessons on electronic decoherence in molecules from exact modeling

Science.gov (United States)

Hu, Wenxiang; Gu, Bing; Franco, Ignacio

2018-04-01

Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.

Exact solutions of (3 + 1-dimensional generalized KP equation arising in physics

Directory of Open Access Journals (Sweden)

Syed Tauseef Mohyud-Din

Full Text Available In this work, we have obtained some exact solutions to (3 + 1-dimensional generalized KP Equation. The improved tanϕ(ξ2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanϕ(ξ2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3 + 1-dimensional generalized KP equation

Exact solutions for a system of nonlinear plasma fluid equations

International Nuclear Information System (INIS)

Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

1991-04-01

A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

Dynamics of atom-field entanglement for Tavis-Cummings models

Science.gov (United States)

Bashkirov, Eugene K.

2018-04-01

An exact solution of the problem of two-atom one- and two-mode Jaynes-Cummings model with intensity- dependent coupling is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for both models is shown. Conditions and times of disentanglement are derived.

Efficient computing procedures and impossibility to solve the problem of exact prediction of events in the quantum world

International Nuclear Information System (INIS)

Namiot, V.A.; Chernavskii, D.S.

2003-01-01

It is well known, that in the classical mechanics the dynamic chaos is possible. When it takes place, the exact prediction of events in the future appears impossible. But in the quantum theory the dynamic chaos (connected with perturbations of the initial conditions) formally is absent. Nevertheless, as it is shown in this Letter, in case of the quantum theory there are other reasons related directly to so-called paradoxes of formal logic which do not allow one to predict the future precisely

Exact classical scaling formalism for nonreactive processes

International Nuclear Information System (INIS)

DePristo, A.E.

1981-01-01

A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively

Dynamic ductile fracture of a central crack

Science.gov (United States)

Tsai, Y. M.

1976-01-01

A central crack, symmetrically growing at a constant speed in a two dimensional ductile material subject to uniform tension at infinity, is investigated using the integral transform methods. The crack is assumed to be the Dugdale crack, and the finite stress condition at the crack tip is satisfied during the propagation of the crack. Exact expressions of solution are obtained for the finite stress condition at the crack tip, the crack shape, the crack opening displacement, and the energy release rate. All those expressions are written as the product of explicit dimensional quantities and a nondimensional dynamic correction function. The expressions reduce to the associated static results when the crack speed tends to zero, and the nondimensional dynamic correction functions were calculated for various values of the parameter involved.

Exact solutions in three-dimensional gravity

CERN Document Server

Garcia-Diaz, Alberto A

2017-01-01

A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

Data-assisted reduced-order modeling of extreme events in complex dynamical systems.

Science.gov (United States)

Wan, Zhong Yi; Vlachas, Pantelis; Koumoutsakos, Petros; Sapsis, Themistoklis

2018-01-01

The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM) regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more significant in

Data-assisted reduced-order modeling of extreme events in complex dynamical systems.

Directory of Open Access Journals (Sweden)

Zhong Yi Wan

Full Text Available The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more

Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

International Nuclear Information System (INIS)

Singh, L.P.; Ram, S.D.; Singh, D.B.

2011-01-01

Highlights: → An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. → The density ahead of the shock is taken as a power of the position from the origin of the shock wave. → For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. → The solution obtained for the planer, and cylindrically symmetric flow is new one. → The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.

Finding optimal exact reducts

KAUST Repository

AbouEisha, Hassan M.

2014-01-01

The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts

Quasi-exactly solvable relativistic soft-core Coulomb models

Energy Technology Data Exchange (ETDEWEB)

Agboola, Davids, E-mail: davagboola@gmail.com; Zhang, Yao-Zhong, E-mail: yzz@maths.uq.edu.au

2012-09-15

By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.

Quaternionic formulation of the exact parity model

Energy Technology Data Exchange (ETDEWEB)

Brumby, S.P.; Foot, R.; Volkas, R.R.

1996-02-28

The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.

Quaternionic formulation of the exact parity model

International Nuclear Information System (INIS)

Brumby, S.P.; Foot, R.; Volkas, R.R.

1996-01-01

The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs

An exact conformal symmetry Ansatz on Kaluza-Klein reduced TMG

Science.gov (United States)

Moutsopoulos, George; Ritter, Patricia

2011-11-01

Using a Kaluza-Klein dimensional reduction, and further imposing a conformal Killing symmetry on the reduced metric generated by the dilaton, we show an Ansatz that yields many of the known stationary axisymmetric solutions to TMG.

Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters

Energy Technology Data Exchange (ETDEWEB)

Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Purba, Victor [University of Minnesota; Jafarpour, Saber [University of California Santa-Barbara; Bullo, Francesco [University of California Santa-Barbara; Dhople, Sairaj V. [University of Minnesota

2017-08-21

Next-generation power networks will contain large numbers of grid-connected inverters satisfying a significant fraction of system load. Since each inverter model has a relatively large number of dynamic states, it is impractical to analyze complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model with lumped parameters for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. We show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as any individual inverter in the system. Numerical simulations validate the reduced-order model.

Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

Science.gov (United States)

Goto, Shin-itiro; Umeno, Ken

2018-03-01

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.

Renormalization group for centrosymmetric gauge transformations of the dynamic motion for a Markov-ordered polymer chain

International Nuclear Information System (INIS)

Mikhailov, I.D.; Zhuravskii, L.V.

1987-01-01

A method is proposed for calculating the vibrational-state density averaged over all configurations for a polymer chain with Markov disorder. The method is based on using a group of centrally symmetric gauge transformations that reduce the dynamic matrix for along polymer chain to renormalized dynamic matrices for short fragments. The short-range order is incorporated exactly in the averaging procedure, while the long-range order is incorporated in the self-consistent field approximation. Results are given for a simple skeletal model for a polymer containing tacticity deviations of Markov type

Dynamics of Financial System: A System Dynamics Approach

OpenAIRE

Girish K. Nair; Lewlyn Lester Raj Rodrigues

2013-01-01

There are several ratios which define the financial health of an organization but the importance of Net cash flow, Gross income, Net income, Pending bills, Receivable bills, Debt, and Book value can never be undermined as they give the exact picture of the financial condition. While there are several approaches to study the dynamics of these variables, system dynamics based modelling and simulation is one of the modern techniques. The paper explores this method to simulate the before mentione...

The exact wavefunction factorization of a vibronic coupling system

International Nuclear Information System (INIS)

Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.

2014-01-01

We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation

Dissociation between exact and approximate addition in developmental dyslexia.

Science.gov (United States)

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

Exact and Heuristic Solutions to Minimize Total Waiting Time in the Blood Products Distribution Problem

Directory of Open Access Journals (Sweden)

Amir Salehipour

2012-01-01

Full Text Available This paper presents a novel application of operations research to support decision making in blood distribution management. The rapid and dynamic increasing demand, criticality of the product, storage, handling, and distribution requirements, and the different geographical locations of hospitals and medical centers have made blood distribution a complex and important problem. In this study, a real blood distribution problem containing 24 hospitals was tackled by the authors, and an exact approach was presented. The objective of the problem is to distribute blood and its products among hospitals and medical centers such that the total waiting time of those requiring the product is minimized. Following the exact solution, a hybrid heuristic algorithm is proposed. Computational experiments showed the optimal solutions could be obtained for medium size instances, while for larger instances the proposed hybrid heuristic is very competitive.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

Science.gov (United States)

Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

2018-02-01

In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

General exact harmonic analysis of in-plane timoshenko beam structures

Directory of Open Access Journals (Sweden)

C. A. N. Dias

Full Text Available The exact solution for the problem of damped, steady state response, of in-plane Timoshenko frames subjected to harmonically time varying external forces is here described. The solution is obtained by using the classical dynamic stiffness matrix (DSM, which is non-linear and transcendental in respect to the excitation frequency, and by performing the harmonic analysis using the Laplace transform. As an original contribution, the partial differential coupled governing equations, combining displacements and forces, are directly subjected to Laplace transforms, leading to the member DSM and to the equivalent load vector formulations. Additionally, the members may have rigid bodies attached at any of their ends where, optionally, internal forces can be released. The member matrices are then used to establish the global matrices that represent the dynamic equilibrium of the overall framed structure, preserving close similarity to the finite element method. Several application examples prove the certainty of the proposed method by comparing the model results with the ones available in the literature or with finite element analyses.

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

A Class of Quasi-exact Solutions of Rabi Hamiltonian

International Nuclear Information System (INIS)

Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.

2007-01-01

A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.

Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

International Nuclear Information System (INIS)

Holm, D.D.

1976-07-01

The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented

Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

Energy Technology Data Exchange (ETDEWEB)

Holm, D.D.

1976-07-01

The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.

Dynamical system of scalar field from 2-dimension to 3-D and its cosmological implications

Energy Technology Data Exchange (ETDEWEB)

Fang, Wei [Shanghai Normal University, Department of Physics, Shanghai (China); The Shanghai Key Lab for Astrophysics, Shanghai (China); Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Tu, Hong [Shanghai Normal University, Department of Physics, Shanghai (China); The Shanghai Key Lab for Astrophysics, Shanghai (China); Huang, Jiasheng [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Shu, Chenggang [The Shanghai Key Lab for Astrophysics, Shanghai (China)

2016-09-15

We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, K-essence, and general non-canonical scalar field models, change the dynamical variables from variables (x, y, λ) to observable related variables (w{sub φ}, Ω{sub φ}, λ), and show the intimate relationships between those scalar fields that the three-dimensional system of K-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and K-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in (w{sub φ}, Ω{sub φ}, λ) instead of variables (x, y, λ) and to investigate the dynamical system in three dimensions instead of two dimensions. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter. (orig.)

Extremal black holes as exact string solutions

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution

Quasi exact solution of the Rabi Hamiltonian

CERN Document Server

Koç, R; Tuetuencueler, H

2002-01-01

A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.

Criteria for exact qudit universality

International Nuclear Information System (INIS)

Brennen, Gavin K.; O'Leary, Dianne P.; Bullock, Stephen S.

2005-01-01

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H jk x =(ℎ/2π)Ω(vertical bar k> jk y =(ℎ/2π)Ω(i vertical bar k> jk x,y are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=(ℎ/2π)Ω vertical bar d-1,d-1> 87 Rb and construct an optimal gate sequence using Raman laser pulses

Exact theory of freeze-out

Science.gov (United States)

Cannoni, Mirco

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.

Quasitraces on exact C*-algebras are traces

DEFF Research Database (Denmark)

Haagerup, Uffe

2014-01-01

It is shown that all 2-quasitraces on a unital exact C ∗   -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗   -algebra has a tracial state, and (2) if an AW ∗   -factor of type II 1   is generated (as an AW ∗   -algebra) by an exact C ∗   -subalgebra, then i......, then it is a von Neumann II 1   -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0  for every simple non-commutative torus of any dimension...

Exact solutions for MHD flow of couple stress fluid with heat transfer

Directory of Open Access Journals (Sweden)

Najeeb Alam Khan

2016-01-01

Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.

New exact solutions of the Dirac equation. 11

International Nuclear Information System (INIS)

Bagrov, V.G.; Noskov, M.D.

1984-01-01

Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

Exact solitary waves of the Korteveg - de Vries - Burgers equation

OpenAIRE

Kudryashov, N. A.

2004-01-01

New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

INDEFINITE COPOSITIVE MATRICES WITH EXACTLY ONE POSITIVE EIGENVALUE OR EXACTLY ONE NEGATIVE EIGENVALUE

NARCIS (Netherlands)

Jargalsaikhan, Bolor

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out

Stability of molecular dynamics simulations of classical systems

DEFF Research Database (Denmark)

Toxværd, Søren

2012-01-01

The existence of a shadow Hamiltonian for discrete classical dynamics, obtained by an asymptotic expansion for a discrete symplectic algorithm, is employed to determine the limit of stability for molecular dynamics (MD) simulations with respect to the time-increment h of the discrete dynamics....... The investigation is based on the stability of the shadow energy, obtained by including the first term in the asymptotic expansion, and on the exact solution of discrete dynamics for a single harmonic mode. The exact solution of discrete dynamics for a harmonic potential with frequency ω gives a criterion...... for the limit of stability h ⩽ 2/ω. Simulations of the Lennard-Jones system and the viscous Kob-Andersen system show that one can use the limit of stability of the shadow energy or the stability criterion for a harmonic mode on the spectrum of instantaneous frequencies to determine the limit of stability of MD...

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

Science.gov (United States)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

Analytic progress on exact lattice chiral symmetry

International Nuclear Information System (INIS)

Kikukawa, Y.

2002-01-01

Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)

Classification problem for exactly integrable embeddings of two-dimensional manifolds and coefficients of the third fundametal forms

International Nuclear Information System (INIS)

Saveliev, M.V.

1983-01-01

A method is proposed for classification of exactly and completely integrable embeddings of two dimensional manifoilds into Riemann or non-Riemann enveloping space, which are based on the algebraic approach to the integration of nonlinear dynamical systems.Here the grading conditions and spectral structure of the Lax-pair operators taking the values in a graded Lie algebra that pick out the integrable class of nonlinear systems are formulated 1n terms of a structure of the 3-d fundamental form tensors. Corresponding to every embedding of three-dimensional subalgebra sb(2) into a simple finite-dimensional (infinite-dimensional of finite growth) Lie algebra L is a definite class of exactly (completely) integrable embeddings of two dimensional manifold into the corresponding enveloping space supplied with the structure of L

Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics

CERN Document Server

2016-01-01

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...

Exactly solvable birth and death processes

International Nuclear Information System (INIS)

Sasaki, Ryu

2009-01-01

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.

Non-Markovian reduced dynamics of ultrafast charge transfer at an oligothiophene–fullerene heterojunction

Energy Technology Data Exchange (ETDEWEB)

Hughes, Keith H., E-mail: keith.hughes@bangor.ac.uk [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Cahier, Benjamin [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Martinazzo, Rocco [Dipartimento di Chimica Università degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Tamura, Hiroyuki [WPI-Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt/Main (Germany)

2014-10-17

Highlights: • Quantum dynamical study of exciton dissociation at a heterojunction interface. • The non-Markovian quantum dynamics involves a highly structured spectral density. • Spectral density is reconstructed from an effective mode transformation of the Hamiltonian. • The dynamics is studied using the hierarchical equations of motion approach. • It was found that the temperature has little effect on the charge transfer. - Abstract: We extend our recent quantum dynamical study of the exciton dissociation and charge transfer at an oligothiophene–fullerene heterojunction interface (Tamura et al., 2012) [6] by investigating the process using the non-perturbative hierarchical equations of motion (HEOM) approach. Based upon an effective mode reconstruction of the spectral density the effect of temperature on the charge transfer is studied using reduced density matrices. It was found that the temperature had little effect on the charge transfer and a coherent dynamics persists over the first few tens of femtoseconds, indicating that the primary charge transfer step proceeds by an activationless pathway.

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

International Nuclear Information System (INIS)

Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

2017-01-01

In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

International Nuclear Information System (INIS)

Smith, Kyle K. G.; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J.

2015-01-01

We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics

Current fluctuations and statistics during a large deviation event in an exactly solvable transport model

International Nuclear Information System (INIS)

Hurtado, Pablo I; Garrido, Pedro L

2009-01-01

We study the distribution of the time-integrated current in an exactly solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and the system statistics during a large deviation event. In this way we unveil a relation between system statistics at the end of a large deviation event and for intermediate times. The mid-time statistics is independent of the sign of the current, a reflection of the time-reversal symmetry of microscopic dynamics, while the end-time statistics does depend on the current sign, and also on its microscopic definition. We compare our exact results with simulations based on the direct evaluation of large deviation functions, analyzing the finite-size corrections of this simulation method and deriving detailed bounds for its applicability. We also show how the Gallavotti–Cohen fluctuation theorem can be used to determine the range of validity of simulation results

Exact vacuum polarization in 1 + 1 dimensional finite nuclei

International Nuclear Information System (INIS)

Ferree, T.C.

1992-01-01

There is considerable interest in the use of renormalizable quantum field theories to describe nuclear structure. In particular, theories which employ hadronic degrees of freedom are used widely and lead to efficient models which allow self-consistent solutions of the many-body problem. An interesting feature inherent to relativistic field theories (like QHD) is the presence of an infinite sea of negative energy fermion (nucleon) states, which interact dynamically with positive energy fermions via other fields. Such interactions give rise to, for example, vacuum polarization effects, in which virtual particle-antiparticle pairs interact with positive energy valence nucleons as well as with each other, and can significantly influence the ground and excited states of nuclear systems. Several authors have addressed this question in various approximations for finite nuclei, mostly based on extensions of results derived for a uniform system of nucleons. Some attempts have also been made to include vacuum effects in finite systems exactly, but the presence of a vector potential can be problematic when working in a spectral representation. In this paper, the author presents a computational method by which vacuum polarization effects in finite nuclei can be calculated exactly in the RHA by employing matrix diagonalization methods in a discrete Fourier representation of the Dirac equation, and an approximate method for including deep negative energy states based on a derivative expansion of the effective action. This efficient approach is shown to provide well-behaved vacuum polarization densities which remain so even in the presence of strong vector potential

Rotational excitation of H2O by para-H2 from an adiabatically reduced dimensional potential.

Science.gov (United States)

Scribano, Yohann; Faure, Alexandre; Lauvergnat, David

2012-03-07

Cross sections and rate coefficients for low lying rotational transitions in H(2)O colliding with para-hydrogen pH(2) are computed using an adiabatic approximation which reduces the dimensional dynamics from a 5D to a 3D problem. Calculations have been performed at the close-coupling level using the recent potential of Valiron et al. [J. Chem. Phys. 129, 134306 (2008)]. A good agreement is found between the reduced adiabatic calculations and the 5D exact calculations, with an impressive time saving and memory gain. This adiabatic reduction of dimensionality seems very promising for scattering studies involving the excitation of a heavy target molecule by a light molecular projectile. © 2012 American Institute of Physics

Exact scale-invariant background of gravitational waves from cosmic defects.

Science.gov (United States)

Figueroa, Daniel G; Hindmarsh, Mark; Urrestilla, Jon

2013-03-08

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction.

New exact solutions of the(2+1-dimensional Broer-Kaup equation by the consistent Riccati expansion method

Directory of Open Access Journals (Sweden)

Jiang Ying

2017-01-01

Full Text Available In this work, we study the (2+1-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

Science.gov (United States)

Sulc, Miroslav; Hernandez, Henar; Martinez, Todd J.; Vanicek, Jiri

2014-03-01

We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that cellularization yields further acceleration [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here we focus on increasing its accuracy by first implementing an exact Gaussian basis method (GBM) combining the accuracy of quantum dynamics and efficiency of classical dynamics. The DR is then derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These include the Gaussian DR (GDR), an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussians evolving classically with an average Hamiltonian. The methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0 /S1 model, and quartic oscillator. Both the GBM and the GDR are shown to increase the accuracy of the DR. Surprisingly, in chaotic systems the GDR can outperform the presumably more accurate GBM, in which the two bases evolve separately. This research was supported by the Swiss NSF Grant No. 200021_124936/1 and NCCR Molecular Ultrafast Science & Technology (MUST), and by the EPFL.

Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

International Nuclear Information System (INIS)

Goyal, N; Gupta, R K

2012-01-01

We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.

Exact solution for the generalized Telegraph Fisher's equation

International Nuclear Information System (INIS)

Abdusalam, H.A.; Fahmy, E.S.

2009-01-01

In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.

Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Institute of Scientific and Technical Information of China (English)

WANG ShunJin; ZHANG Hua

2007-01-01

Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Institute of Scientific and Technical Information of China (English)

2007-01-01

Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

Exact solution of the hidden Markov processes

Science.gov (United States)

Saakian, David B.

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

Dissipative motion perturbation theory and exact solutions

International Nuclear Information System (INIS)

Lodder, J.J.

1976-06-01

Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion

Thermal quantum time-correlation functions from classical-like dynamics

Science.gov (United States)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Exact Theory of Compressible Fluid Turbulence

Science.gov (United States)

Drivas, Theodore; Eyink, Gregory

2017-11-01

We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.

Exact Cover Problem in Milton Babbitt's All-partition Array

OpenAIRE

Bemman, Brian; Meredith, David

2015-01-01

One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclu- sively partitions A. We provide a backtracking algorithm for solving ...

Exact theory of freeze-out

International Nuclear Information System (INIS)

Cannoni, Mirco

2015-01-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x * = m χ /T * . The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y 0 , is where the maximum departure of the WIMPs abundance Y from the thermal value Y 0 is reached. For each mass m χ and total annihilation cross section left angle σ ann υ r right angle, the temperature x * and the actual WIMPs abundance Y(x * ) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x * . The matching of the two abundances at x * is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)

Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters: Preprint

Energy Technology Data Exchange (ETDEWEB)

Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Purba, Victor [University of Minnesota; Jafarpour, Saber [University of California, Santa Barbara; Bullo, Francesco [University of California, Santa Barbara; Dhople, Sairaj [University of Minnesota

2017-08-31

Given that next-generation infrastructures will contain large numbers of grid-connected inverters and these interfaces will be satisfying a growing fraction of system load, it is imperative to analyze the impacts of power electronics on such systems. However, since each inverter model has a relatively large number of dynamic states, it would be impractical to execute complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. That is, we show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as an individual inverter in the paralleled system. Numerical simulations validate the reduced-order models.

Exact-exchange-based quasiparticle calculations

International Nuclear Information System (INIS)

Aulbur, Wilfried G.; Staedele, Martin; Goerling, Andreas

2000-01-01

One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society

Can quantum transition state theory be defined as an exact t = 0+ limit?

Science.gov (United States)

Jang, Seogjoo; Voth, Gregory A.

2016-02-01

The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA's proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0+ limit of HA's QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals [S. Jang, A. V. Sinitskiy, and G. A. Voth, J. Chem. Phys. 140, 154103 (2014)]. It is shown

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

Science.gov (United States)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Convergent dynamics for multistable delayed neural networks

International Nuclear Information System (INIS)

Shih, Chih-Wen; Tseng, Jui-Pin

2008-01-01

This investigation aims at developing a methodology to establish convergence of dynamics for delayed neural network systems with multiple stable equilibria. The present approach is general and can be applied to several network models. We take the Hopfield-type neural networks with both instantaneous and delayed feedbacks to illustrate the idea. We shall construct the complete dynamical scenario which comprises exactly 2 n stable equilibria and exactly (3 n − 2 n ) unstable equilibria for the n-neuron network. In addition, it is shown that every solution of the system converges to one of the equilibria as time tends to infinity. The approach is based on employing the geometrical structure of the network system. Positively invariant sets and componentwise dynamical properties are derived under the geometrical configuration. An iteration scheme is subsequently designed to confirm the convergence of dynamics for the system. Two examples with numerical simulations are arranged to illustrate the present theory

Exact work

International Nuclear Information System (INIS)

Zeger, J.

1993-01-01

Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

An exact fermion-pair to boson mapping

International Nuclear Information System (INIS)

Johnson, C.W.

1993-01-01

I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model

The exact mass-gaps of the principal chiral models

CERN Document Server

Hollowood, Timothy J

1994-01-01

An exact expression for the mass-gap, the ratio of the physical particle mass to the $\\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.

An Exact Solution of the Binary Singular Problem

Directory of Open Access Journals (Sweden)

Baiqing Sun

2014-01-01

Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.

Parallel Implementation of Gamma-Point Pseudopotential Plane-Wave DFT with Exact Exchange

International Nuclear Information System (INIS)

Bylaska, Eric J.; Tsemekhman, Kiril L.; Baden, Scott B.; Weare, John H.; Jonsson, Hannes

2011-01-01

One of the more persistent failures of conventional density functional theory (DFT) methods has been their failure to yield localized charge states such as polarons, excitons and solitons in solid-state and extended systems. It has been suggested that conventional DFT functionals, which are not self-interaction free, tend to favor delocalized electronic states since self-interaction creates a Coulomb barrier to charge localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid-DFT, e.g. B3LYP and PBE0) have shown promise in localizing charge states and predicting accurate band gaps and reaction barriers. We have developed a parallel algorithm for implementing exact exchange into pseudopotential plane-wave density functional theory and we have implemented it in the NWChem program package. The technique developed can readily be employed in plane-wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car-Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite.

Exact soliton-like solutions of perturbed phi4-equation

International Nuclear Information System (INIS)

Gonzalez, J.A.

1986-05-01

Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)

A dynamic counterpart of Lamb vector in viscous compressible aerodynamics

International Nuclear Information System (INIS)

Liu, L Q; Wu, J Z; Shi, Y P; Zhu, J Y

2014-01-01

The Lamb vector is known to play a key role in incompressible fluid dynamics and vortex dynamics. In particular, in low-speed steady aerodynamics it is solely responsible for the total force acting on a moving body, known as the vortex force, with the classic two-dimensional (exact) Kutta–Joukowski theorem and three-dimensional (linearized) lifting-line theory as the most famous special applications. In this paper we identify an innovative dynamic counterpart of the Lamb vector in viscous compressible aerodynamics, which we call the compressible Lamb vector. Mathematically, we present a theorem on the dynamic far-field decay law of the vorticity and dilatation fields, and thereby prove that the generalized Lamb vector enjoys exactly the same integral properties as the Lamb vector does in incompressible flow, and hence the vortex-force theory can be generalized to compressible flow with exactly the same general formulation. Moreover, for steady flow of polytropic gas, we show that physically the force exerted on a moving body by the gas consists of a transverse force produced by the original Lamb vector and a new longitudinal force that reflects the effects of compression and irreversible thermodynamics. (paper)

Inverse Schroedinger equation and the exact wave function

International Nuclear Information System (INIS)

Nakatsuji, Hiroshi

2002-01-01

Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

Quasiparticle many-body dynamics of the Anderson model

International Nuclear Information System (INIS)

Kuzemskij, A.L.

1996-01-01

The paper addresses the many-body quasiparticle dynamics of the Anderson impurity model at finite temperatures in the framework of the equation-of-motion method. We find a new exact identity relating the one-particle and many-particle Green's Functions. Using this identity we present a consistent and general scheme for a construction of generalised mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation. A new approach for the complex expansion for the single-particle propagator in terms of the Coulomb repulsion U and hybridization V is proposed. Using the exact identity, the essentially new many-body dynamical solution of SIAM has been derived. This approach offers a new way for the systematic construction of the approximative interpolating dynamical solutions of the strongly correlated electron systems. 47 refs

Exact infinite-time statistics of the Loschmidt echo for a quantum quench.

Science.gov (United States)

Campos Venuti, Lorenzo; Jacobson, N Tobias; Santra, Siddhartha; Zanardi, Paolo

2011-07-01

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.

Exact theory of freeze-out

Energy Technology Data Exchange (ETDEWEB)

Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x{sub *} = m{sub χ}/T{sub *}. The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y{sub 0}, is where the maximum departure of the WIMPs abundance Y from the thermal value Y{sub 0} is reached. For each mass m{sub χ} and total annihilation cross section left angle σ{sub ann}υ{sub r} right angle, the temperature x{sub *} and the actual WIMPs abundance Y(x{sub *}) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x{sub *}. The matching of the two abundances at x{sub *} is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)

Exactly marginal deformations from exceptional generalised geometry

Energy Technology Data Exchange (ETDEWEB)

Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)

2017-01-27

We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.

Exact partial solution to the steady-state, compressible fluid flow problems of jet formation and jet penetration

International Nuclear Information System (INIS)

Karpp, R.R.

1980-10-01

This report treats analytically the problem of the symmetric impact of two compressible fluid streams. The flow is assumed to be steady, plane, inviscid, and subsonic and that the compressible fluid is of the Chaplygin (tangent gas) type. In the analysis, the governing equations are first transformed to the hodograph plane where an exact, closed-form solution is obtained by standard techniques. The distributions of fluid properties along the plane of symmetry as well as the shapes of the boundary streamlines are exactly determined by transforming the solution back to the physical plane. The problem of a compressible fluid jet penetrating into an infinite target of similar material is also exactly solved by considering a limiting case of this solution. This new compressible flow solution reduces to the classical result of incompressible flow theory when the sound speed of the fluid is allowed to approach infinity. Several illustrations of the differences between compressible and incompressible flows of the type considered are presented

Exact solutions of nonlinear differential equations using continued fractions

International Nuclear Information System (INIS)

Ditto, W.L.; Pickett, T.J.

1990-01-01

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method

Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

Science.gov (United States)

Krumm, F.; Vogel, W.

2018-04-01

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.

Dynamic Forces between the Rails and the Wheels of Railway Vehicle

Directory of Open Access Journals (Sweden)

Zdravko Peran

2016-02-01

Full Text Available The process of acquisition of the measured dynamic values of forces between the rails and the wheels on the real measurement train and the train tracks. The conversion of the measured values into the matrices and vectors enables numerous exact qualitative and quantitative studies of the dynamic phenomena behaviour. The paper shows the possibilities of using MATLAB computer tool. All the commands in the software are given and explained. Calculating of the empirical, normal and cumulative distribution on an example of the lateral force is given in detail. The new software is exactly verified mathematically and qualified for any further use. The developed software is the tool for the development of other two phases: software for the exact automatic evaluation of the maximum values of the dynamic values and software for the automatic approval of vehicles and railway due to the driving safety, loading tracks and driving comfort compared to the limited values regarding UI C CODE 518.

Upper bounds on minimum cardinality of exact and approximate reducts

KAUST Repository

Chikalov, Igor

2010-01-01

In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞.

Science.gov (United States)

Maraga, Anna; Chiocchetta, Alessio; Mitra, Aditi; Gambassi, Andrea

2015-10-01

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Reduced Order Models for Dynamic Behavior of Elastomer Damping Devices

Science.gov (United States)

Morin, B.; Legay, A.; Deü, J.-F.

2016-09-01

In the context of passive damping, various mechanical systems from the space industry use elastomer components (shock absorbers, silent blocks, flexible joints...). The material of these devices has frequency, temperature and amplitude dependent characteristics. The associated numerical models, using viscoelastic and hyperelastic constitutive behaviour, may become computationally too expensive during a design process. The aim of this work is to propose efficient reduced viscoelastic models of rubber devices. The first step is to choose an accurate material model that represent the viscoelasticity. The second step is to reduce the rubber device finite element model to a super-element that keeps the frequency dependence. This reduced model is first built by taking into account the fact that the device's interfaces are much more rigid than the rubber core. To make use of this difference, kinematical constraints enforce the rigid body motion of these interfaces reducing the rubber device model to twelve dofs only on the interfaces (three rotations and three translations per face). Then, the superelement is built by using a component mode synthesis method. As an application, the dynamic behavior of a structure supported by four hourglass shaped rubber devices under harmonic loads is analysed to show the efficiency of the proposed approach.

Exact solutions of some nonlinear partial differential equations using ...

Indian Academy of Sciences (India)

The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

A Reduced-Order Model for Evaluating the Dynamic Response of Multilayer Plates to Impulsive Loads

Science.gov (United States)

2016-04-12

A REDUCED-ORDER MODEL FOR EVALUATING THE DYNAMIC RESPONSE OF MULTILAYER PLATES TO IMPULSIVE LOADS Weiran Jiang, Alyssa Bennett, Nickolas...innovative multilayer materials or structures to optimize the dynamic performance as a mechanism to absorb and spread energy from an impulsive load...models. • Optimizing the structural weight and levels of protection of the multilayer plates with a good combination of materials. Technical Approach 2016

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ-Expansion Method Implementation

Directory of Open Access Journals (Sweden)

Nur Alam

2016-02-01

Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

Science.gov (United States)

Marsili, Matteo; Challet, Damien; Zecchina, Riccardo

2000-06-01

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable - which plays a role similar to price - whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the “thermodynamic” limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even “infinitesimally” for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a “price taker” behavior if agents account for their market impact.

Exact Cover Problem in Milton Babbitt's All-partition Array

DEFF Research Database (Denmark)

Bemman, Brian; Meredith, David

2015-01-01

One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set...

Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations

International Nuclear Information System (INIS)

Roux, Sebastien; Desbat, Laurent; Koenig, Anne; Grangeat, Pierre

2004-01-01

This work is dedicated to the reduction of reconstruction artefacts due to motion occurring during the acquisition of computerized tomographic projections. This problem has to be solved when imaging moving organs such as the lungs or the heart. The proposed method belongs to the class of motion compensation algorithms, where the model of motion is included in the reconstruction formula. We address two fundamental questions. First what conditions on the deformation are required for the reconstruction of the object from projections acquired sequentially during the deformation, and second how do we reconstruct the object from those projections. Here we answer these questions in the particular case of 2D general time-dependent affine deformations, assuming the motion parameters are known. We treat the problem of admissibility conditions on the deformation in the parallel-beam and fan-beam cases. Then we propose exact reconstruction methods based on rebinning or sequential FBP formulae for each of these geometries and present reconstructed images obtained with the fan-beam algorithm on simulated data

Nonequilibrium dynamics of polariton entanglement in a cluster of coupled traps

Energy Technology Data Exchange (ETDEWEB)

Quiroga, L [Departamento de Fisica, Universidad de Los Andes, A.A.4976, Bogota D.C. (Colombia); Tejedor, C, E-mail: lquiroga@uniandes.edu.c [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, Cantoblanco, E-28049, Madrid (Spain)

2009-05-01

We study in detail the generation and relaxation of quantum coherences (entanglement) in a system of coupled polariton traps. By exploiting a Lie algebraic based super-operator technique we provide an analytical exact solution for the Markovian dissipative dynamics (Master equation) of such system which is valid for arbitrary cluster size, polariton-polariton interaction strength, temperature and initial state. Based on the exact solution of the Master equation at T = OK, we discuss how dissipation affects the quantum entanglement dynamics of coupled polariton systems.

On exact correlation functions in SU(N) $ \\mathcal{N}=2 $ superconformal QCD

CERN Document Server

Baggio, Marco; Papadodimas, Kyriakos

2015-01-01

We consider the exact coupling constant dependence of extremal correlation functions of ${\\cal N} = 2$ chiral primary operators in 4d ${\\cal N} = 2$ superconformal gauge theories with gauge group SU(N) and N_f=2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt* equations. In the case at hand, the tt* equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equations to a sequence of decoupled semi-infinite Toda chains, similar to the one encountered previously in the special case of SU(2) gauge group. This ansatz requires a surprising new non-renormalization theorem in ${\\cal N} = 2$ superconformal field theories. We derive a general 3-loop perturbative formula for 2- and 3-point functions in the ${\\cal N} = 2$ chiral ring of the SU(N) theory, and in all explicitly computed exampl...

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

Science.gov (United States)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

Stochastic epidemic-type model with enhanced connectivity: exact solution

International Nuclear Information System (INIS)

Williams, H T; Mazilu, I; Mazilu, D A

2012-01-01

We present an exact analytical solution to a one-dimensional model of the susceptible–infected–recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions. Our results compare well with those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic-type models

Dolan-Grady relations and noncommutative quasi-exactly solvable systems

International Nuclear Information System (INIS)

Klishevich, Sergey M; Plyushchay, Mikhail S

2003-01-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems

Energy vs. density on paths toward exact density functionals

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2018-01-01

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...

Exact Synthesis of Reversible Circuits Using A* Algorithm

Science.gov (United States)

Datta, K.; Rathi, G. K.; Sengupta, I.; Rahaman, H.

2015-06-01

With the growing emphasis on low-power design methodologies, and the result that theoretical zero power dissipation is possible only if computations are information lossless, design and synthesis of reversible logic circuits have become very important in recent years. Reversible logic circuits are also important in the context of quantum computing, where the basic operations are reversible in nature. Several synthesis methodologies for reversible circuits have been reported. Some of these methods are termed as exact, where the motivation is to get the minimum-gate realization for a given reversible function. These methods are computationally very intensive, and are able to synthesize only very small functions. There are other methods based on function transformations or higher-level representation of functions like binary decision diagrams or exclusive-or sum-of-products, that are able to handle much larger circuits without any guarantee of optimality or near-optimality. Design of exact synthesis algorithms is interesting in this context, because they set some kind of benchmarks against which other methods can be compared. This paper proposes an exact synthesis approach based on an iterative deepening version of the A* algorithm using the multiple-control Toffoli gate library. Experimental results are presented with comparisons with other exact and some heuristic based synthesis approaches.

Exact braneworld cosmology induced from bulk black holes

International Nuclear Information System (INIS)

Gregory, James P; Padilla, Antonio

2002-01-01

We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black-hole spacetime. We find that the bulk Weyl tensor gives rise to nonlinear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the 'unconventional' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black-hole-driven cosmologies have the benefit that there is no ambiguity in splitting the braneworld energy momentum into tension and additional matter. We propose a new, enlarged relationship between the two descriptions of braneworld cosmology. We also study the exact thermodynamics of the field theory and present a generalized Cardy-Verlinde formula in this set-up

Reducing traffic in DHT-based discovery protocols for dynamic resources

Science.gov (United States)

Carlini, Emanuele; Coppola, Massimo; Laforenza, Domenico; Ricci, Laura

Existing peer-to-peer approaches for resource location based on distributed hash tables focus mainly on optimizing lookup query resolution. The underlying assumption is that the arrival ratio of lookup queries is higher than the ratio of resource publication operations. We propose a set of optimization strategies to reduce the network traffic generated by the data publication and update process when resources have dynamic-valued attributes. We aim at reducing the publication overhead of supporting multi-attribute range queries. We develop a model predicting the bandwidth reduction, and we assign proper values to the model variables on the basis of real data measurements. We further validate these results by a set of simulations. Our experiments are designed to reproduce the typical behaviour of the resulting scheme within large distributed resource location system, like the resource location service of the XtreemOS Grid-enabled Operating System.

System and method for reducing combustion dynamics and NO.sub.x in a combustor

Science.gov (United States)

Uhm, Jong H.; Johnson, Thomas Edward

2015-11-20

A system for reducing combustion dynamics and NO.sub.x in a combustor includes a tube bundle that extends radially across at least a portion of the combustor, wherein the tube bundle comprises an upstream surface axially separated from a downstream surface. A shroud circumferentially surrounds the upstream and downstream surfaces. A plurality of tubes extends through the tube bundle from the upstream surface through the downstream surface, wherein the downstream surface is stepped to produce tubes having different lengths through the tube bundle. A method for reducing combustion dynamics and NO.sub.x in a combustor includes flowing a working fluid through a plurality of tubes radially arranged between an upstream surface and a downstream surface of an end cap that extends radially across at least a portion of the combustor, wherein the downstream surface is stepped.

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

Science.gov (United States)

Dimitroglou Rizell, Georgios

2015-04-01

We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

International Nuclear Information System (INIS)

Longhi, Stefano

2014-01-01

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H -hat (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H -hat (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization

Exact Relativistic `Antigravity' Propulsion

Science.gov (United States)

Felber, Franklin S.

2006-01-01

The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

Lattice sigma models with exact supersymmetry

International Nuclear Information System (INIS)

Simon Catterall; Sofiane Ghadab

2004-01-01

We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

Kiss, István Z; Simon, Péter L

2017-01-01

This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...

Benchmarking GW against exact diagonalization for semiempirical models

DEFF Research Database (Denmark)

Kaasbjerg, Kristen; Thygesen, Kristian Sommer

2010-01-01

We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW capt...... (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene....

Exactly solvable energy-dependent potentials

International Nuclear Information System (INIS)

Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.

2009-01-01

We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.

New exact travelling wave solutions for the Ostrovsky equation

International Nuclear Information System (INIS)

Kangalgil, Figen; Ayaz, Fatma

2008-01-01

In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation

Backbone dynamics of oxidized and reduced D. vulgaris flavodoxin in solution

International Nuclear Information System (INIS)

Hrovat, Andrea; Bluemel, Markus; Loehr, Frank; Mayhew, Stephen G.; Rueterjans, Heinz

1997-01-01

Recombinant Desulfovibrio vulgaris flavodoxin was produced in Escherichia coli. A complete backbone NMR assignment for the two-electron reduced protein revealed significant changes of chemical shift values compared to the oxidized protein, in particular for the flavine mononucleotide (FMN)-binding site. A comparison of homo- and heteronuclear NOESY spectra for the two redox states led to the assumption that reduction is not accompanied by significant changes of the global fold of the protein.The backbone dynamics of both the oxidized and reduced forms of D. vulgaris flavodoxin were investigated using two-dimensional 15 N- 1 H correlation NMR spectroscopy.T 1 , T 2 and NOE data are obtained for 95% of the backbone amide groups in both redox states. These values were analysed in terms of the 'model-free' approach introduced by Lipari and Szabo [(1982) J. Am. Chem. Soc., 104, 4546-;4559, 4559-;4570]. A comparison of the two redox states indicates that in the reduced species significantly more flexibility occurs in the two loop regions enclosing FMN.Also, a higher amplitude of local motion could be found for the N(3)H group of FMN bound to the reduced protein compared to the oxidized state

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

Directory of Open Access Journals (Sweden)

Feng-Tao He

2013-01-01

Full Text Available We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1 if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton’s width increases, while its amplitude and wave velocity reduce. (2 If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton’s width increases, while its amplitude and the wave velocity reduce.

Pressure of a partially ionized hydrogen gas : numerical results from exact low temperature expansions

OpenAIRE

Alastuey , Angel; Ballenegger , Vincent

2010-01-01

8 pages; International audience; We consider a partially ionized hydrogen gas at low densities, where it reduces almost to an ideal mixture made with hydrogen atoms in their ground-state, ionized protons and ionized electrons. By performing systematic low-temperature expansions within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential, exact formulae for the first five leading corrections to the ideal Saha equation ...

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Lattice fluid dynamics from perfect discretizations of continuum flows

International Nuclear Information System (INIS)

Katz, E.; Wiese, U.

1998-01-01

We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes and naturally exist on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e., grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with a square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation and is shown to represent the continuum flow exactly. For nonsquare cross sections one can use a numerical iterative procedure to derive flow equations that are approximately perfect. copyright 1998 The American Physical Society

Exact Algorithms for Solving Stochastic Games

DEFF Research Database (Denmark)

Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels

2012-01-01

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

Reduced-Order Computational Model for Low-Frequency Dynamics of Automobiles

Directory of Open Access Journals (Sweden)

A. Arnoux

2013-01-01

Full Text Available A reduced-order model is constructed to predict, for the low-frequency range, the dynamical responses in the stiff parts of an automobile constituted of stiff and flexible parts. The vehicle has then many elastic modes in this range due to the presence of many flexible parts and equipment. A nonusual reduced-order model is introduced. The family of the elastic modes is not used and is replaced by an adapted vector basis of the admissible space of global displacements. Such a construction requires a decomposition of the domain of the structure in subdomains in order to control the spatial wave length of the global displacements. The fast marching method is used to carry out the subdomain decomposition. A probabilistic model of uncertainties is introduced. The parameters controlling the level of uncertainties are estimated solving a statistical inverse problem. The methodology is validated with a large computational model of an automobile.

The asymptotic and exact Fisher information matrices of a vector ARMA process

NARCIS (Netherlands)

Klein, A.; Melard, G.; Saidi, A.

2008-01-01

The exact Fisher information matrix of a Gaussian vector autoregressive-moving average (VARMA) process has been considered for a time series of length N in relation to the exact maximum likelihood estimation method. In this paper it is shown that the Gaussian exact Fisher information matrix

Exact 2-point function in Hermitian matrix model

International Nuclear Information System (INIS)

Morozov, A.; Shakirov, Sh.

2009-01-01

J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.

Exact solutions in string-motivated scalar-field cosmology

International Nuclear Information System (INIS)

Oezer, M.; Taha, M.O.

1992-01-01

Two exact cosmological solutions to a scalar-field potential motivated by six-dimensional (6D) Einstein-Maxwell theory are given. The resulting pure scalar-field cosmology is free of singularity and causality problems but conserves entropy. These solutions are then extended into exact cosmological solutions for a decaying scalar field with an approximate two-loop 4D string potential. The resulting cosmology is, for both solutions, free of cosmological problems and close to the standard cosmology of the radiation era

Exactly soluble matrix models

International Nuclear Information System (INIS)

Raju Viswanathan, R.

1991-09-01

We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs

On a method of construction of exact solutions for equations of two-dimensional hydrodynamics of incompressible liquids

International Nuclear Information System (INIS)

Yurov, A.V.; Yurova, A.A.

2006-01-01

The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru

Linear orbit parameters for the exact equations of motion

International Nuclear Information System (INIS)

Parzen, G.

1995-01-01

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived

Fuzziness and Foundations of Exact and Inexact Sciences

CERN Document Server

Dompere, Kofi Kissi

2013-01-01

The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space i...

Dolan Grady relations and noncommutative quasi-exactly solvable systems

Science.gov (United States)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Fast Exact Euclidean Distance (FEED) Transformation

NARCIS (Netherlands)

Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.

2004-01-01

Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number

Mean-field dynamics of a population of stochastic map neurons

Science.gov (United States)

Franović, Igor; Maslennikov, Oleg V.; Bačić, Iva; Nekorkin, Vladimir I.

2017-07-01

We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.

Exact Results in Non-Supersymmetric Large N Orientifold Field Theories

CERN Document Server

Armoni, Adi; Veneziano, Gabriele

2003-01-01

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N=1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N).

On nonlinear differential equation with exact solutions having various pole orders

International Nuclear Information System (INIS)

Kudryashov, N.A.

2015-01-01

We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

Exact ∇{sup 4}R{sup 4} couplings and helicity supertraces

Energy Technology Data Exchange (ETDEWEB)

Bossard, Guillaume [Centre de Physique Théorique, Ecole Polytechnique, Université Paris-Saclay,91128 Palaiseau Cedex (France); Pioline, Boris [Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589,Université Pierre et Marie Curie,4 place Jussieu, 75252 Paris cedex 05 (France); CERN, Theoretical Physics Department,1211 Geneva 23 (Switzerland)

2017-01-12

In type II string theory compactified on a d-dimensional torus T{sup d} down to D=10−d dimensions, the R{sup 4} and ∇{sup 4}R{sup 4} four-graviton couplings are known exactly, for all values of the moduli, in terms of certain Eisenstein series of the U-duality group E{sub d}(ℤ). In the limit where one circle in the torus becomes large, these couplings are expected to reduce to their counterpart in dimension D+1, plus threshold effects and exponentially suppressed corrections corresponding to BPS black holes in dimension D+1 whose worldline winds around the circle. By combining the weak coupling and large radius limits, we determine these exponentially suppressed corrections exactly, and demonstrate that the contributions of 1/4-BPS black holes to the ∇{sup 4}R{sup 4} coupling are proportional to the appropriate helicity supertrace. Mathematically, our results provide the complete Fourier expansion of the next-to-minimal theta series of E{sub d+1}(ℤ) with respect to the maximal parabolic subgroup with Levi component E{sub d} for d≤6, and the complete Abelian part of the Fourier expansion of the same for d=7.

Exact docking flight controller for autonomous aerial refueling with back-stepping based high order sliding mode

Science.gov (United States)

Su, Zikang; Wang, Honglun; Li, Na; Yu, Yue; Wu, Jianfa

2018-02-01

Autonomous aerial refueling (AAR) exact docking control has always been an intractable problem due to the strong nonlinearity, the tight coupling of the 6 DOF aircraft model and the complex disturbances of the multiple environment flows. In this paper, the strongly coupled nonlinear 6 DOF model of the receiver aircraft which considers the multiple flow disturbances is established in the affine nonlinear form to facilitate the nonlinear controller design. The items reflecting the influence of the unknown flow disturbances in the receiver dynamics are taken as the components of the "lumped disturbances" together with the items which have no linear correlation with the virtual control variables. These unmeasurable lumped disturbances are estimated and compensated by a specially designed high order sliding mode observer (HOSMO) with excellent estimation property. With the compensation of the estimated lumped disturbances, a back-stepping high order sliding mode based exact docking flight controller is proposed for AAR in the presence of multiple flow disturbances. Extensive simulation results demonstrate the feasibility and superiority of the proposed docking controller.

Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field

International Nuclear Information System (INIS)

Yuece, Cem

2003-01-01

In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems

CERN Document Server

Li, Tatsien; Gu, Qilong

2016-01-01

This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...

Exact sampling of graphs with prescribed degree correlations

Science.gov (United States)

Bassler, Kevin E.; Del Genio, Charo I.; Erdős, Péter L.; Miklós, István; Toroczkai, Zoltán

2015-08-01

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree and conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is {O}({NM}) where N is the number of nodes and M is the number of edges.

arXiv Integrable flows between exact CFTs

CERN Document Server

Georgiou, George

2017-11-14

We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k$_{1}$ and k$_{2}$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k$_{1}$ and k$_{2}$ − k$_{1}$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.

Exact computation of the 9-j symbols

International Nuclear Information System (INIS)

Lai Shantao; Chiu Jingnan

1992-01-01

A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)

Exact deconstruction of the 6D (2,0) theory

Science.gov (United States)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Exact deconstruction of the 6D (2,0) theory

International Nuclear Information System (INIS)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodriguez-Gomez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2 , starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 x T 2 . In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach

Directory of Open Access Journals (Sweden)

Suchart Limkatanyu

2013-01-01

Full Text Available This paper alternatively derives the exact element stiffness equation for a beam on Kerr-type foundation. The shear coupling between the individual Winkler-spring components and the peripheral discontinuity at the boundaries between the loaded and the unloaded soil surfaces are taken into account in this proposed model. The element flexibility matrix is derived based on the virtual force principle and forms the core of the exact element stiffness matrix. The sixth-order governing differential compatibility of the problem is revealed using the virtual force principle and solved analytically to obtain the exact force interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix based on the exact force interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. One numerical example is utilized to confirm the accuracy and the efficiency of the proposed beam element on Kerr-type foundation and to show a more realistic distribution of interactive foundation force.

Coulomb interactions via local dynamics: a molecular-dynamics algorithm

International Nuclear Information System (INIS)

Pasichnyk, Igor; Duenweg, Burkhard

2004-01-01

We derive and describe in detail a recently proposed method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. We focus on the molecular dynamics version of the method and show that it is intimately related to the Car-Parrinello approach, while being equivalent to solving Maxwell's equations with a freely adjustable speed of light. Unphysical self-energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green function. The method can be straightforwardly parallelized using standard domain decomposition. Some preliminary benchmark results are presented

Exact results for integrable asymptotically-free field theories

CERN Document Server

Evans, J M; Evans, Jonathan M; Hollowood, Timothy J

1995-01-01

An account is given of a technique for testing the equivalence between an exact factorizable S-matrix and an asymptotically-free Lagrangian field theory in two space-time dimensions. The method provides a way of resolving CDD ambiguities in the S-matrix and it also allows for an exact determination of the physical mass in terms of the Lambda parameter of perturbation theory. The results for various specific examples are summarized. (To appear in the Proceedings of the Conference on Recent Developments in Quantum Field Theory and Statistical Mechanics, ICTP, Trieste, Easter 1995).

Accelerating exact schedulability analysis for fixed-priority pre-emptive scheduling

NARCIS (Netherlands)

Hang, Y.; Jiale, Z.; Keskin, U.; Bril, R.J.

2010-01-01

The schedulability analysis for fixed-priority preemptive scheduling (FPPS) plays a significant role in the real-time systems domain. The so-called Hyperplanes Exact Test (HET) [1] is an example of an exact schedulability test for FPPS. In this paper, we aim at improving the efficiency of HET by

Exact WKB analysis and cluster algebras

International Nuclear Information System (INIS)

Iwaki, Kohei; Nakanishi, Tomoki

2014-01-01

We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)

Exactly energy conserving semi-implicit particle in cell formulation

International Nuclear Information System (INIS)

Lapenta, Giovanni

2017-01-01

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These

Exactly energy conserving semi-implicit particle in cell formulation

Energy Technology Data Exchange (ETDEWEB)

Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be

2017-04-01

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These

Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming

DEFF Research Database (Denmark)

Christensen, Tue; Andersen, Kim Allan; Klose, Andreas

2013-01-01

This paper considers a minimum-cost network flow problem in a bipartite graph with a single sink. The transportation costs exhibit a staircase cost structure because such types of transportation cost functions are often found in practice. We present a dynamic programming algorithm for solving...... this so-called single-sink, fixed-charge, multiple-choice transportation problem exactly. The method exploits heuristics and lower bounds to peg binary variables, improve bounds on flow variables, and reduce the state-space variable. In this way, the dynamic programming method is able to solve large...... instances with up to 10,000 nodes and 10 different transportation modes in a few seconds, much less time than required by a widely used mixed-integer programming solver and other methods proposed in the literature for this problem....

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

Science.gov (United States)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

International Nuclear Information System (INIS)

Rivera, R.; Villarroel, D.

2002-01-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics

Exact axially symmetric galactic dynamos

Science.gov (United States)

Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.

2018-05-01

We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.

Perturbation analysis of transient population dynamics using matrix projection models

DEFF Research Database (Denmark)

Stott, Iain

2016-01-01

Non-stable populations exhibit short-term transient dynamics: size, growth and structure that are unlike predicted long-term asymptotic stable, stationary or equilibrium dynamics. Understanding transient dynamics of non-stable populations is important for designing effective population management...... these methods to know exactly what is being measured. Despite a wealth of existing methods, I identify some areas that would benefit from further development....

Dynamic characteristics of mirrors' kinematic mount

International Nuclear Information System (INIS)

Wu Wenkai; Du Qiang; Li Jingze; Chen Gang; Chen Xiaojuan; Xu Yuanli

2002-01-01

Applying exact constrain design principles, kinematic mount for precision positioning large aperture mirrors is designed; theoretical method is introduced to analyze its dynamic characteristics and the result of the experiment for mirrors, stability; accordingly, the methods to improve design are put forward

Dynamic model-based N management reduces surplus nitrogen and improves the environmental performance of corn production

Science.gov (United States)

Sela, S.; Woodbury, P. B.; van Es, H. M.

2018-05-01

The US Midwest is the largest and most intensive corn (Zea mays, L.) production region in the world. However, N losses from corn systems cause serious environmental impacts including dead zones in coastal waters, groundwater pollution, particulate air pollution, and global warming. New approaches to reducing N losses are urgently needed. N surplus is gaining attention as such an approach for multiple cropping systems. We combined experimental data from 127 on-farm field trials conducted in seven US states during the 2011–2016 growing seasons with biochemical simulations using the PNM model to quantify the benefits of a dynamic location-adapted management approach to reduce N surplus. We found that this approach allowed large reductions in N rate (32%) and N surplus (36%) compared to existing static approaches, without reducing yield and substantially reducing yield-scaled N losses (11%). Across all sites, yield-scaled N losses increased linearly with N surplus values above ~48 kg ha‑1. Using the dynamic model-based N management approach enabled growers to get much closer to this target than using existing static methods, while maintaining yield. Therefore, this approach can substantially reduce N surplus and N pollution potential compared to static N management.

Exact deconstruction of the 6D (2,0) theory

Energy Technology Data Exchange (ETDEWEB)

Hayling, J.; Papageorgakis, C. [Queen Mary Univ. of London (United Kingdom). CRST and School of Physics and Astronomy; Pomoni, E. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Rodriguez-Gomez, D. [Oviedo Univ. (Spain). Dept. of Physics

2017-06-15

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T{sup 2}, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S{sup 4} to the (2,0) partition function on S{sup 4} x T{sup 2}. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Hand-held dynamic visual noise reduces naturally occurring food cravings and craving-related consumption.

Science.gov (United States)

Kemps, Eva; Tiggemann, Marika

2013-09-01

This study demonstrated the applicability of the well-established laboratory task, dynamic visual noise, as a technique for reducing naturally occurring food cravings and subsequent food intake. Dynamic visual noise was delivered on a hand-held computer device. Its effects were assessed within the context of a diary study. Over a 4-week period, 48 undergraduate women recorded their food cravings and consumption. Following a 2-week baseline, half the participants watched the dynamic visual noise display whenever they experienced a food craving. Compared to a control group, these participants reported less intense cravings. They were also less likely to eat following a craving and consequently consumed fewer total calories following craving. These findings hold promise for curbing unwanted food cravings and craving-driven consumption in real-world settings. Copyright © 2013 Elsevier Ltd. All rights reserved.

New exact wave solutions for Hirota equation

Indian Academy of Sciences (India)

2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.

TVT-Exact and midurethral sling (SLING-IUFT) operative procedures: a randomized study.

Science.gov (United States)

Aniuliene, Rosita; Aniulis, Povilas; Skaudickas, Darijus

2015-01-01

The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients - using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact - at 94.5% and SLING-IUFT - at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness.

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Model checking exact cost for attack scenarios

DEFF Research Database (Denmark)

Aslanyan, Zaruhi; Nielson, Flemming

2017-01-01

Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....

Exact nonparametric confidence bands for the survivor function.

Science.gov (United States)

Matthews, David

2013-10-12

A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan-Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden-Decker-Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin's lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. It was begun while the author was visiting the Department of Statistics, University of Auckland, and completed during a subsequent sojourn at the Medical Research Council Biostatistics Unit in Cambridge. The support of both institutions, in addition to that of NSERC and the University of Waterloo, is greatly appreciated.

Learning reduced kinetic Monte Carlo models of complex chemistry from molecular dynamics.

Science.gov (United States)

Yang, Qian; Sing-Long, Carlos A; Reed, Evan J

2017-08-01

We propose a novel statistical learning framework for automatically and efficiently building reduced kinetic Monte Carlo (KMC) models of large-scale elementary reaction networks from data generated by a single or few molecular dynamics simulations (MD). Existing approaches for identifying species and reactions from molecular dynamics typically use bond length and duration criteria, where bond duration is a fixed parameter motivated by an understanding of bond vibrational frequencies. In contrast, we show that for highly reactive systems, bond duration should be a model parameter that is chosen to maximize the predictive power of the resulting statistical model. We demonstrate our method on a high temperature, high pressure system of reacting liquid methane, and show that the learned KMC model is able to extrapolate more than an order of magnitude in time for key molecules. Additionally, our KMC model of elementary reactions enables us to isolate the most important set of reactions governing the behavior of key molecules found in the MD simulation. We develop a new data-driven algorithm to reduce the chemical reaction network which can be solved either as an integer program or efficiently using L1 regularization, and compare our results with simple count-based reduction. For our liquid methane system, we discover that rare reactions do not play a significant role in the system, and find that less than 7% of the approximately 2000 reactions observed from molecular dynamics are necessary to reproduce the molecular concentration over time of methane. The framework described in this work paves the way towards a genomic approach to studying complex chemical systems, where expensive MD simulation data can be reused to contribute to an increasingly large and accurate genome of elementary reactions and rates.

Exact dimension estimation of interacting qubit systems assisted by a single quantum probe

Science.gov (United States)

Sone, Akira; Cappellaro, Paola

2017-12-01

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.

Ecoflex. Dynamic traffic management based on measured air quality; Ecoflex. Dynamisch verkeersmanagement op basis van gemeten luchtkwaliteit

Energy Technology Data Exchange (ETDEWEB)

Voogt, M.; Van Baalen, J.; Stelwage, U.; Weststrate, H. [TNO Urban Environment and Safety, Delft (Netherlands); De Koning, A.; Turksma, S. [Peek Traffic, Amersfoort (Netherlands)

2012-02-15

Local air quality measurements can be used as input for a dynamic traffic management system. This makes it possible to deploy emission reducing measures exactly when they are needed. This concept has been demonstrated by TNO and Peek in the EcoFLEX project. [Dutch] Lokale luchtkwaliteitsmetingen kunnen worden gebruikt als input voor een dynamisch verkeersmanagementysteem. Zo wordt het mogelijk om emissiereducerende maatregelen juist dan in te zetten wanneer deze nodig zijn. Dit concept is door TNO en Peek gedemonstreerd in het EcoFLEX-project.

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Directory of Open Access Journals (Sweden)

Armando Martínez-Pérez

2017-10-01

Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

New Exact Solutions for (1 + 1)-Dimensional Dispersion-Less System

International Nuclear Information System (INIS)

Naranmandula; Hu Jianguo; Bao Gang; Tubuxin

2008-01-01

Using improved homogeneous balance method, we obtain complex function form new exact solutions for the (1+1)-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately

An Exact Confidence Region in Multivariate Calibration

OpenAIRE

Mathew, Thomas; Kasala, Subramanyam

1994-01-01

In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.

Exact geodesic distances in FLRW spacetimes

Science.gov (United States)

Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

2017-11-01

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

Dynamics of a clamped–clamped microbeam resonator considering fabrication imperfections

KAUST Repository

Bataineh, Ahmad M.

2014-10-18

We present an investigation into the static and dynamic behavior of an electrostatically actuated clamped–clamped polysilicon microbeam resonator accounting for its fabrication imperfections, which are commonly encountered in similar microstructures. These are mainly because of the initial deformation of the beam due to stress gradient and its flexible anchors. First, we show experimental data of the microbeam when driven electrically by varying the amplitude and frequency of the voltage loads. The results reveal several interesting nonlinear phenomena of jumps, hysteresis, and softening behaviors. Theoretical investigation is then conducted to model the microbeam, and hence, interpret the experimental data. We solve the Eigen value problem governing the natural frequencies analytically. We then utilize a Galerkin-based procedure to derive a reduced order model, which is then used to simulate both the static and dynamic responses. To achieve good matching between theory and experiment, we show that the exact profile of the deformed beam needs to be utilized in the reduced order model, as measured from the optical profiler, combined with a shooting technique simulation, which is capable of tracing the resonant frequency branches under very-low damping conditions.

Exact analytic solutions generated from stipulated Morse and trigonometric Scarf potentials

International Nuclear Information System (INIS)

Saikia, N; Ahmed, S A S

2011-01-01

The extended transformation method has been applied to the exactly solvable stipulated Morse potential and trigonometric Scarf potential, to generate a set of exactly solvable quantum systems (QSs) in any chosen dimension. Bound state solutions of the exactly solvable potentials are given. The generated QSs are generally of Sturmian form. We also report a system case-specific regrouping technique to convert a Sturmian QS to a normal QS. A second-order application of the transformation method is given. The normalizability of the generated QSs is generally given in Sturmian form.

Exact ground and excited states of an antiferromagnetic quantum spin model

International Nuclear Information System (INIS)

Bose, I.

1989-08-01

A quasi-one-dimensional spin model which consists of a chain of octahedra of spins has been suggested for which a certain parameter regime of the Hamiltonian, the ground state, can be written down exactly. The ground state is highly degenerate and can be other than a singlet. Also, several excited states can be constructed exactly. The ground state is a local RVB state for which resonance is confined to rings of spins. Some exact numerical results for an octahedron of spins have also been reported. (author). 16 refs, 2 figs, 1 tab

Asymptotically exact calculation of the exchange energies of one-active-electron diatomic ions with the surface integral method

International Nuclear Information System (INIS)

Scott, Tony C; Aubert-Frecon, Monique; Hadinger, Gisele; Andrae, Dirk; Grotendorst, Johannes; III, John D Morgan

2004-01-01

We present a general procedure, based on the Holstein-Herring method, for calculating exactly the leading term in the exponentially small exchange energy splitting between two asymptotically degenerate states of a diatomic molecule or molecular ion. The general formulae we have derived are shown to reduce correctly to the previously known exact results for the specific cases of the lowest Σ and Π states of H + 2 . We then apply our general formulae to calculate the exchange energy splittings between the lowest states of the diatomic alkali cations K + 2 , Rb + 2 and Cs + 2 , which are isovalent to H + 2 . Our results are found to be in very good agreement with the best available experimental data and ab initio calculations

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Directory of Open Access Journals (Sweden)

Emrullah Yaşar

Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions

Corollary from the Exact Expression for Enthalpy of Vaporization

OpenAIRE

A. A. Sobko

2011-01-01

A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic paramet...

Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

International Nuclear Information System (INIS)

Niven, Robert K.

2005-01-01

The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

Exact penalty results for mathematical programs with vanishing constraints

Czech Academy of Sciences Publication Activity Database

Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří

2010-01-01

Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf

Riemann zeta function from wave-packet dynamics

DEFF Research Database (Denmark)

Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.

2010-01-01

We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...

Decay of autoionizing states in time-dependent density functional and reduced density matrix functional theory

Energy Technology Data Exchange (ETDEWEB)

Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Exact Slater integrals

International Nuclear Information System (INIS)

Golden, L.B.

1968-01-01

In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)

Constructing the reduced dynamical models of interannual climate variability from spatial-distributed time series

Science.gov (United States)

Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander

2016-04-01

We suggest a method for empirical forecast of climate dynamics basing on the reconstruction of reduced dynamical models in a form of random dynamical systems [1,2] derived from observational time series. The construction of proper embedding - the set of variables determining the phase space the model works in - is no doubt the most important step in such a modeling, but this task is non-trivial due to huge dimension of time series of typical climatic fields. Actually, an appropriate expansion of observational time series is needed yielding the number of principal components considered as phase variables, which are to be efficient for the construction of low-dimensional evolution operator. We emphasize two main features the reduced models should have for capturing the main dynamical properties of the system: (i) taking into account time-lagged teleconnections in the atmosphere-ocean system and (ii) reflecting the nonlinear nature of these teleconnections. In accordance to these principles, in this report we present the methodology which includes the combination of a new way for the construction of an embedding by the spatio-temporal data expansion and nonlinear model construction on the basis of artificial neural networks. The methodology is aplied to NCEP/NCAR reanalysis data including fields of sea level pressure, geopotential height, and wind speed, covering Northern Hemisphere. Its efficiency for the interannual forecast of various climate phenomena including ENSO, PDO, NAO and strong blocking event condition over the mid latitudes, is demonstrated. Also, we investigate the ability of the models to reproduce and predict the evolution of qualitative features of the dynamics, such as spectral peaks, critical transitions and statistics of extremes. This research was supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS) [1] Y. I. Molkov, E. M. Loskutov, D. N. Mukhin, and A. M. Feigin, "Random

Exact results for the Floquet coin toss for driven integrable models

Science.gov (United States)

Bhattacharya, Utso; Maity, Somnath; Banik, Uddipan; Dutta, Amit

2018-05-01

We study an integrable Hamiltonian reducible to free fermions, which is subjected to an imperfect periodic driving with the amplitude of driving (or kicking), randomly chosen from a binary distribution like a coin-toss problem. The randomness present in the driving protocol destabilizes the periodic steady state reached in the limit of perfectly periodic driving, leading to a monotonic rise of the stroboscopic residual energy with the number of periods (N ) for such Hamiltonians. We establish that a minimal deviation from the perfectly periodic driving in the present case using such protocols would always result in a bounded heating up of the system with N to an asymptotic finite value. Exploiting the completely uncorrelated nature of the randomness and the knowledge of the stroboscopic Floquet operator in the perfectly periodic situation, we provide an exact analytical formalism to derive the disorder averaged expectation value of the residual energy through a disorder operator. This formalism not only leads to an immense numerical simplification, but also enables us to derive an exact analytical form for the residual energy in the asymptotic limit which is universal, i.e., independent of the bias of coin-toss and the protocol chosen. Furthermore, this formalism clearly establishes the nature of the monotonic growth of the residual energy at intermediate N while clearly revealing the possible nonuniversal behavior of the same.

Exactly solvable models in many-body theory

CERN Document Server

March, N H

2016-01-01

The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation

Energy Technology Data Exchange (ETDEWEB)

Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt (Germany); Martinazzo, Rocco [Dipartimento di Chimica, Universita degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Hughes, Keith H. [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom)

2012-10-14

A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.

Exactness of supersymmetric WKB method for translational shape invariant potentials

International Nuclear Information System (INIS)

Cheng, K M; Leung, P T; Pang, C S

2003-01-01

By examining the generic form of the superpotential of translational shape invariant potentials (TSIPs), we explicitly show the exactness of the lowest order supersymmetric WKB (SWKB) formula for TSIPs. Remarkably, our method applies to both unbroken and broken supersymmetric systems. We also demonstrate the equivalence of one-parameter and multi-parameter TSIPs, thus establishing the exactness of the SWKB formula for all TSIPs

Exactness of supersymmetric WKB method for translational shape invariant potentials

CERN Document Server

Cheng, K M; Pang, C S

2003-01-01

By examining the generic form of the superpotential of translational shape invariant potentials (TSIPs), we explicitly show the exactness of the lowest order supersymmetric WKB (SWKB) formula for TSIPs. Remarkably, our method applies to both unbroken and broken supersymmetric systems. We also demonstrate the equivalence of one-parameter and multi-parameter TSIPs, thus establishing the exactness of the SWKB formula for all TSIPs.

Dynamical and hamiltonian dilations of stochastic processes

International Nuclear Information System (INIS)

Baumgartner, B.; Gruemm, H.-R.

1982-01-01

This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Analysis of fast neutrons elastic moderator through exact solutions involving synthetic-kernels

International Nuclear Information System (INIS)

Moura Neto, C.; Chung, F.L.; Amorim, E.S.

1979-07-01

The computation difficulties in the transport equation solution applied to fast reactors can be reduced by the development of approximate models, assuming that the continuous moderation holds. Two approximations were studied. The first one was based on an expansion in Taylor's series (Fermi, Wigner, Greuling and Goertzel models), and the second involving the utilization of synthetic Kernels (Walti, Turinsky, Becker and Malaviya models). The flux obtained by the exact method is compared with the fluxes from the different models based on synthetic Kernels. It can be verified that the present study is realistic for energies smaller than the threshold for inelastic scattering, as well as in the resonance region. (Author) [pt

Strategies for Reduced-Order Models in Uncertainty Quantification of Complex Turbulent Dynamical Systems

Science.gov (United States)

Qi, Di

Turbulent dynamical systems are ubiquitous in science and engineering. Uncertainty quantification (UQ) in turbulent dynamical systems is a grand challenge where the goal is to obtain statistical estimates for key physical quantities. In the development of a proper UQ scheme for systems characterized by both a high-dimensional phase space and a large number of instabilities, significant model errors compared with the true natural signal are always unavoidable due to both the imperfect understanding of the underlying physical processes and the limited computational resources available. One central issue in contemporary research is the development of a systematic methodology for reduced order models that can recover the crucial features both with model fidelity in statistical equilibrium and with model sensitivity in response to perturbations. In the first part, we discuss a general mathematical framework to construct statistically accurate reduced-order models that have skill in capturing the statistical variability in the principal directions of a general class of complex systems with quadratic nonlinearity. A systematic hierarchy of simple statistical closure schemes, which are built through new global statistical energy conservation principles combined with statistical equilibrium fidelity, are designed and tested for UQ of these problems. Second, the capacity of imperfect low-order stochastic approximations to model extreme events in a passive scalar field advected by turbulent flows is investigated. The effects in complicated flow systems are considered including strong nonlinear and non-Gaussian interactions, and much simpler and cheaper imperfect models with model error are constructed to capture the crucial statistical features in the stationary tracer field. Several mathematical ideas are introduced to improve the prediction skill of the imperfect reduced-order models. Most importantly, empirical information theory and statistical linear response theory are

Exact coefficients for higher dimensional operators with sixteen supersymmetries

Energy Technology Data Exchange (ETDEWEB)

Chen, Wei-Ming [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Wen, Congkao [INFN Sezione di Roma “Tor Vergata' ,Via della Ricerca Scientifica, 00133 Roma (Italy)

2015-09-15

We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F{sup n} with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F{sup 4}. As the F{sup 4} coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.

Dynamics of Phenol Degrading—Iron Reducing Bacteria in Intensive Rice Croopping System

Institute of Scientific and Technical Information of China (English)

LUWENJING; W.REICHARDT; 等

2001-01-01

Field and greenhouse experiments were conducted to investigate the effects of cropping season,nitrogen fertilizer input and aerated fallow o the dynamics of phenol degrading-iron reducing bacteria(PD-IRB)in tropical irrigated rice(Oryza sativa L.)systems,The PD-IRB population density was monitored at different stages of rice growth in two cropping seasons (dry and early wet) in a continuous annual triple rice cropping system under irrigated condition,In this system,the high nitrogen input (195 and 135 kg N ha-1 in dry and ewt seasons ,respectively)plots and control plots receiving no N fertilizer were compared to investigate the effect of nitrogen rate on population size.The phenol degrading-iron reducing bacteria (PD-IRB)were abundant in soils under croppin systems of tropical irrigated rice.However,density of the bacterial populations varied with rice growth stages.Cropping seasons,rhizosphere,and aerated fallow could affect the dynamics of PD-IRB,In the field trial,viable counts of PD-IRB in the topsoil layer(15 cm)ranged between 102 and 108 cells per gram of dry soil.A steep increase in viable counts during the second half of the cropping season suggested that the population density of PD-IRB increased ant advanced crop-growth stages.Population growth of PD-IRB was accelerated during the dry season compared to the wet season,In the greenhouse experiment,the adjacent aerated fallow revealed 1-2 orders of magnitude higher in most probable number(MPN)of PD-IRB than the wet fallow treated plots.As a prominent group of Fe reducing bacteria,PD-IRB predominated in the rhizosphere of rice,since maximum MPN of PD-IRB (2.62×108 g-1 soil) was found in rhizosphere soil.Mineral N fertilizer rates showed no significant effect on PD-IRB population density.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

Science.gov (United States)

Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

2017-06-01

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

Exact results relating spin-orbit interactions in two-dimensional strongly correlated systems

Science.gov (United States)

Kucska, Nóra; Gulácsi, Zsolt

2018-06-01

A 2D square, two-bands, strongly correlated and non-integrable system is analysed exactly in the presence of many-body spin-orbit interactions via the method of Positive Semidefinite Operators. The deduced exact ground states in the high concentration limit are strongly entangled, and given by the spin-orbit coupling are ferromagnetic and present an enhanced carrier mobility, which substantially differs for different spin projections. The described state emerges in a restricted parameter space region, which however is clearly accessible experimentally. The exact solutions are provided via the solution of a matching system of equations containing 74 coupled, non-linear and complex algebraic equations. In our knowledge, other exact results for 2D interacting systems with spin-orbit interactions are not present in the literature.

Euclidean shortest paths exact or approximate algorithms

CERN Document Server

Li, Fajie

2014-01-01

This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.

Effective two-body equations for the four-body problem with exact treatment of (2+2)-subsystem contributions

International Nuclear Information System (INIS)

Haberzettl, H.; Sandhas, W.

1981-01-01

Effective two-body equations for the four-body problem are derived within the general N-body theory of Alt, Grassberger, and Sandhas. In contrast to usual treatments, the final expressions do not require separable (2+2) subamplitudes but incorporate these exactly. All four-body amplitudes can be calculated from the solution of a single integral equation for the reaction (3+1)→(3+1). With single-term separable approximations for the two-particle and the (3+1) subsystem amplitudes the driving terms of the final equations are seen to reduce to those of the field-theoretical model by Fonseca and Shanley. Since our results are based on an exact and complete N-body theory, the investigation of subsystem reaction mechanisms is facilitated. As a consequence, we are led to a three-particle propagator which has the right pole behavior and includes exchange effects

Comments on exact quantization conditions and non-perturbative topological strings

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2015-12-01

We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined topological strings in the Nekrasov-Shatashvili limit. We find that the quantization conditions enjoy an exact S-dual invariance. We also discuss Borel summability of the semi-classical spectrum.

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

Science.gov (United States)

Keck, Maximilian; Montangero, Simone; Santoro, Giuseppe E.; Fazio, Rosario; Rossini, Davide

2017-11-01

We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-product-operator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.

Exact simulation of max-stable processes.

Science.gov (United States)

Dombry, Clément; Engelke, Sebastian; Oesting, Marco

2016-06-01

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.

New explicit and exact solutions of the Benney–Kawahara–Lin equation

International Nuclear Information System (INIS)

Yuan-Xi, Xie

2009-01-01

In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney–Kawahara–Lin equation and derive its many explicit and exact solutions which are all new solutions. (general)

Dynamics of coupled electron-nuclei-systems in laser fields

International Nuclear Information System (INIS)

Falge, Mirjam

2012-01-01

This work aimed at the theoretical analysis of high harmonic generation in molecules and the influence of coupled electron and nuclear dynamics on ultra-short pulse ionization processes. In the first part of this thesis, the isotope effect and influence of vibrational excitation on high harmonic generation were investigated for the isotope pairs H 2 O/D 2 O and H 2 /D 2 . It was shown that on the one hand high harmonic intensities strongly depend on the vibrational quantum number of the initial state of the water molecule and on the other hand the spectra of H 2 O and D 2 O exhibit a clear isotope effect for certain vibrationally excited states. Also it was shown that high harmonics of vibrationally excited states show an even more pronounced isotope effect than the ground state. The second and third part of this work treats the influence of coupled electron and nuclear dynamics on photoelectron spectra. In order to facilitate a numerically exact description of this dynamics, a simple one-dimensional model system (Shin-Metiu model) was used. It consists of only a single electronic and nuclear degree-of-freedom and allows for a switching between adiabatic and strongly non-adiabatic dynamics by its parameterization. This model served for the analysis of the dynamics of three different cases ranging from weak over intermediate to strong electron-nuclear coupling. To investigate the influence of non-adiabatic effects on photoelectron spectra, time-resolved photoelectron spectra were calculated applying two methods: a numerically exact treatment and an adiabatic approach neglecting the electron-nuclear coupling. Subsequently, the dependence of the efficiency of a non-adiabatic transition on the nuclear mass was analysed. To this end, the population dynamics and photoelectron spectra were calculated numerically exactly for a strong electron and nuclear coupling. Thereafter the asymmetry in forward and backward direction of time-resolved photoelectron spectra and the

Exact solution of unsteady flow generated by sinusoidal pressure gradient in a capillary tube

Directory of Open Access Journals (Sweden)

M. Abdulhameed

2015-12-01

Full Text Available In this paper, the mathematical modeling of unsteady second grade fluid in a capillary tube with sinusoidal pressure gradient is developed with non-homogenous boundary conditions. Exact analytical solutions for the velocity profiles have been obtained in explicit forms. These solutions are written as the sum of the steady and transient solutions for small and large times. For growing times, the starting solution reduces to the well-known periodic solution that coincides with the corresponding solution of a Newtonian fluid. Graphs representing the solutions are discussed.

Dynamic visual noise reduces confidence in short-term memory for visual information.

Science.gov (United States)

Kemps, Eva; Andrade, Jackie

2012-05-01

Previous research has shown effects of the visual interference technique, dynamic visual noise (DVN), on visual imagery, but not on visual short-term memory, unless retention of precise visual detail is required. This study tested the prediction that DVN does also affect retention of gross visual information, specifically by reducing confidence. Participants performed a matrix pattern memory task with three retention interval interference conditions (DVN, static visual noise and no interference control) that varied from trial to trial. At recall, participants indicated whether or not they were sure of their responses. As in previous research, DVN did not impair recall accuracy or latency on the task, but it did reduce recall confidence relative to static visual noise and no interference. We conclude that DVN does distort visual representations in short-term memory, but standard coarse-grained recall measures are insensitive to these distortions.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

Science.gov (United States)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Asymptotically exact solution of a local copper-oxide model

International Nuclear Information System (INIS)

Zhang Guangming; Yu Lu.

1994-03-01

We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities. (author). 15 refs, 1 fig

String propagation in an exact four-dimensional black hole background

International Nuclear Information System (INIS)

Mahapatra, S.

1997-01-01

We study string propagation in an exact, stringy, four-dimensional dyonic black hole background. The exact solutions in terms of elliptic functions describing string configurations in the J=0 limit are obtained by solving the string equations of motion and constraints. By using the covariant formalism, we also investigate the propagation of physical perturbations along the string in the given curved background. copyright 1997 The American Physical Society

Compiling Relational Bayesian Networks for Exact Inference

DEFF Research Database (Denmark)

Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan

2004-01-01

We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...

Exact Turbulence Law in Collisionless Plasmas: Hybrid Simulations

Science.gov (United States)

Hellinger, P.; Verdini, A.; Landi, S.; Franci, L.; Matteini, L.

2017-12-01

An exact vectorial law for turbulence in homogeneous incompressible Hall-MHD is derived and tested in two-dimensional hybrid simulations of plasma turbulence. The simulations confirm the validity of the MHD exact law in the kinetic regime, the simulated turbulence exhibits a clear inertial range on large scales where the MHD cascade flux dominates. The simulation results also indicate that in the sub-ion range the cascade continues via the Hall term and that the total cascade rate tends to decrease at around the ion scales, especially in high-beta plasmas. This decrease is like owing to formation of non-thermal features, such as collisionless ion energization, that can not be retained in the Hall MHD approximation.

Structural and dynamic analysis of an ultra short intracavity directional coupler

Science.gov (United States)

Gravé, Ilan; Griffel, Giora; Daou, Youssef; Golan, Gadi

1997-01-01

A recently proposed intracavity directional coupler is analysed. Exact analytic expressions for important parameters such as the transmission ratio, the coupling length, and the photon lifetime are given. We show that by controlling the mirror reflectivities of the cavity, it is theoretically possible to reduce the coupling length to a zero limit. The photon lifetime, which governs the dynamic properties of the structure, sets an upper frequency limit of a few hundreds of GHz, which is well over the bandwidth limitation of microwave lumped or travelling wave electrodes. This novel family of intracavity couplers has important applications in the realization of integrated optics circuits for high-speed computing, data processing, and communication.

Exact solutions of a nonpolynomially nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R.; Tan, H.S.

2007-01-01

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

Fractal diffusion coefficient from dynamical zeta functions

Energy Technology Data Exchange (ETDEWEB)

Cristadoro, Giampaolo [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D 01187 Dresden (Germany)

2006-03-10

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero. (letter to the editor)

Fractal diffusion coefficient from dynamical zeta functions

International Nuclear Information System (INIS)

Cristadoro, Giampaolo

2006-01-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero. (letter to the editor)

An exactly solvable model for first- and second-order transitions

International Nuclear Information System (INIS)

Klushin, L I; Skvortsov, A M; Gorbunov, A A

1998-01-01

The possibility of an exact analytical description of first-order and second-order transitions is demonstrated using a specific microscopic model. Predictions using the exactly calculated partition function are compared with those based on the Landau and Yang-Lee approaches. The model employed is an adsorbed polymer chain with an arbitrary number of links and an external force applied to its end, for which the variation of the partition function with the adsorption interaction parameter and the magnitude of the applied force is calculated. In the thermodynamic limit, the system has one isotropic and two anisotropic, ordered phases, each of which is characterized by two order parameters and between which first-order and second-order transitions occur and a bicritical point exists. The Landau free energy is found exactly as a function of each order parameter separately and, near the bicritical point, as a function of both of them simultaneously. An exact analytical formula is found for the distribution of the complex zeros of the partition function in first-order and second-order phase transitions. Hypotheses concerning the way in which the free energy and the positions of the complex zeros scale with the number of particles N in the system are verified. (reviews of topical problems)

Bifurcations and new exact travelling wave solutions for the ...

Indian Academy of Sciences (India)

2016-10-17

Oct 17, 2016 ... Abstract. By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, ...

Bifurcations and new exact travelling wave solutions for the ...

Indian Academy of Sciences (India)

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and ...

Exactly solvable position dependent mass schroedinger equation

International Nuclear Information System (INIS)

Koc, R.; Tuetuencueler, H.; Koercuek, E.

2002-01-01

Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems

Compiling Relational Bayesian Networks for Exact Inference

DEFF Research Database (Denmark)

Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark

2006-01-01

We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...

Simulation of dynamics behaviors for shipping equipment support with system dynamics analysis approach

Directory of Open Access Journals (Sweden)

Yang Song

2015-05-01

Full Text Available Purpose: The exactly and precisely supply of carrying spare parts has a crucial impact on support and could improve the performance of equipment. Spare parts support is the crux work which will be limited by spare parts allocation and support cost input. Reasonable support strategy can help in making good use of available resources and support the equipment in normal operational status. The purpose of this paper is to propose a dynamics model of spare parts support process based on considering the interaction of multiple factors, and explores the regulation of dynamics behavior in the system. In order to achieve the optimization strategy to improve the effect of support so that will enhance the relevant support parameters of equipment. Design/methodology/approach: Meditate the feedback relationship among some important factors of support that involve support cost, support time and maintenance ability. System dynamics theory is adopted to propose a dynamics model of spare parts support process, on the analysis of multiple factors and casual relationship to find some major ones which have crucial impact on spare parts support. Spare parts support cost and availability was regarded as the control objective, moreover, adjust the control paramours and improve the effect of cannibalization and lateral supply scheduling strategy for spares support. Findings: The factors of spare parts supply, demand and maintenance have relationship of control feedback, and adjust the value of some crucial factors can reduce the support cost and improve the availability value. The main finding is that adopting cannibalization strategy under condition of available materials can relieve the mission and operational availability decline caused by shortage of spare parts. Combining the lateral supply and cannibalization strategy can reduce the inventory of warship carrying spare parts. Practical implications: By controlling the value of key factors regarding aspect of spare

Exact rebinning methods for three-dimensional PET.

Science.gov (United States)

Liu, X; Defrise, M; Michel, C; Sibomana, M; Comtat, C; Kinahan, P; Townsend, D

1999-08-01

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.

Exact critical properties of two-dimensional polymer networks from conformal invariance

International Nuclear Information System (INIS)

Duplantier, B.

1988-03-01

An infinity of exact critical exponents for two-dimensional self-avoiding walks can be derived from conformal invariance and Coulomb gas techniques applied to the O(n) model and to the Potts model. They apply to polymer networks of any topology, for which a general scaling theory is given, valid in any dimension d. The infinite set of exponents has also been calculated to O(ε 2 ), for d=4-ε. The 2D study also includes other universality classes like the dense polymers, the Hamiltonian walks, the polymers at their θ-point. Exact correlation functions can be further given for Hamiltonian walks, and exact winding angle probability distributions for the self-avoiding walks

Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

Science.gov (United States)

Saveliev, V. L.; Gorokhovski, M. A.

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

DYNAMICS OF FINANCIAL SYSTEM: A SYSTEM DYNAMICS APPROACH

Directory of Open Access Journals (Sweden)

Girish K Nair

2013-01-01

Full Text Available There are several ratios which define the financial health of an organization but the importance of Net cash flow, Gross income, Net income, Pending bills, Receivable bills, Debt, and Book value can never be undermined as they give the exact picture of the financial condition. While there are several approaches to study the dynamics of these variables, system dynamics based modelling and simulation is one of the modern techniques. The paper explores this method to simulate the before mentioned parameters during production capacity expansion in an electronic industry. Debt and Book value have shown a non-linear pattern of variation which is discussed. The model can be used by the financial experts as a decision support tool in arriving at conclusions in connection to the expansion plans of the organization.

Reduced Insulin/IGF-1 Signaling Restores the Dynamic Properties of Key Stress Granule Proteins during Aging

Directory of Open Access Journals (Sweden)

Marie C. Lechler

2017-01-01

Full Text Available Summary: Low-complexity “prion-like” domains in key RNA-binding proteins (RBPs mediate the reversible assembly of RNA granules. Individual RBPs harboring these domains have been linked to specific neurodegenerative diseases. Although their aggregation in neurodegeneration has been extensively characterized, it remains unknown how the process of aging disturbs RBP dynamics. We show that a wide variety of RNA granule components, including stress granule proteins, become highly insoluble with age in C. elegans and that reduced insulin/insulin-like growth factor 1 (IGF-1 daf-2 receptor signaling efficiently prevents their aggregation. Importantly, stress-granule-related RBP aggregates are associated with reduced fitness. We show that heat shock transcription factor 1 (HSF-1 is a main regulator of stress-granule-related RBP aggregation in both young and aged animals. During aging, increasing DAF-16 activity restores dynamic stress-granule-related RBPs, partly by decreasing the buildup of other misfolded proteins that seed RBP aggregation. Longevity-associated mechanisms found to maintain dynamic RBPs during aging could be relevant for neurodegenerative diseases. : Lechler et al. show that RNA-binding proteins (RBPs including stress granule proteins are prone to aggregate with age in C. elegans. Aggregation of stress granule RBPs with “prion-like” domains is associated with reduced fitness. Their aggregation is prevented by longevity pathways and promoted by the aggregation of other misfolded proteins. Keywords: neurodegenerative diseases, Caenorhabditis elegans, protein aggregation, aging, RNA-binding proteins, stress granules, HSF-1, DAF-2, longevity

A BEHAVIORAL-APPROACH TO LINEAR EXACT MODELING

NARCIS (Netherlands)

ANTOULAS, AC; WILLEMS, JC

1993-01-01

The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The main contribution of this paper is the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling

KAUST Repository

Ruzziconi, Laura

2013-06-10

We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.

Dynamic and static correlation functions in the inhomogeneous Hartree-Fock-state approach with random-phase-approximation fluctuations

International Nuclear Information System (INIS)

Lorenzana, J.; Grynberg, M.D.; Yu, L.; Yonemitsu, K.; Bishop, A.R.

1992-11-01

The ground state energy, and static and dynamic correlation functions are investigated in the inhomogeneous Hartree-Fock (HF) plus random phase approximation (RPA) approach applied to a one-dimensional spinless fermion model showing self-trapped doping states at the mean field level. Results are compared with homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous HF ground state allows the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground state energy agrees well with the exact results at strong and weak coupling limits. We also compare it with a related quasi-boson approach. The instability towards self-trapped behaviour is signaled by a RPA mode with frequency approaching zero. (author). 21 refs, 10 figs

Nonlinear dynamic characterization of two-dimensional materials

NARCIS (Netherlands)

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

Effect of thermally reduced graphene oxide on dynamic mechanical properties of carbon fiber/epoxy composite

Science.gov (United States)

Adak, Nitai Chandra; Chhetri, Suman; Murmu, Naresh Chandra; Samanta, Pranab; Kuila, Tapas

2018-03-01

The Carbon fiber (CF)/epoxy composites are being used in the automotive and aerospace industries owing to their high specific mechanical strength to weight ratio compared to the other conventional metal and alloys. However, the low interfacial adhesion between fiber and polymer matrix results the inter-laminar fracture of the composites. Effects of different carbonaceous nanomaterials i.e., carbon nanotubes (CNT), graphene nanosheets (GNPs), graphene oxide (GO) etc. on the static mechanical properties of the composites were investigated in detail. Only a few works focused on the improvement of the dynamic mechanical of the CF/epoxy composites. Herein, the effect of thermally reduced grapheme oxide (TRGO) on the dynamic mechanical properties of the CF/epoxy composites was investigated. At first, GO was synthesized using modified Hummers method and then reduced the synthesized GO inside a vacuum oven at 800 °C for 5 min. The prepared TRGO was dispersed in the epoxy resin to modify the epoxy matrix. Then, a number of TRGO/CF/epoxy laminates were manufactured incorporating different wt% of TRGO by vacuum assisted resin transfer molding (VARTM) technique. The developed laminates were cured at room temperature for 24 h and then post cured at 120 °C for 2 h. The dynamic mechanical analyzer (DMA 8000 Perkin Elmer) was used to examine the dynamic mechanical properties of the TRGO/CF/epoxy composites according to ASTM D7028. The dimension of the specimen was 44×10×2.4 mm3 for the DMA test. This test was carried out under flexural loading mode (duel cantilever) at a frequency of 1 Hz and amplitude of 50 μm. The temperature was ramped from 30 to 200 °C with a heating rate of 5 °C min-1. The dynamic mechanical analysis of the 0.2 wt% TRGO incorporated CF/epoxy composites showed ~ 96% enhancement in storage modulus and ~ 12 °C increments in glass transition temperature (Tg) compared to the base CF/epoxy composites. The fiber-matrix interaction was studied by Cole

The Problem of Understanding of Nature in Exact Science

Directory of Open Access Journals (Sweden)

Leo Näpinen

2014-10-01

Full Text Available In this short inquiry I would like to defend the statement that exact science deals with the explanation of models, but not with the understanding (comprehending of nature. By the word ‘nature’ I mean nature as physis (as a self-moving and self-developing living organism to which humans also belong, not nature as natura naturata (as a nonevolving creature created by someone or something. The Estonian philosopher of science Rein Vihalemm (2008 has shown with his conception of phi-science (φ-science that exact science is itself an idealized model or theoretical object derived from Galilean mathematical physics.

Quasi-exact solvability of the one-dimensional Holstein model

International Nuclear Information System (INIS)

Pan Feng; Dai Lianrong; Draayer, J P

2006-01-01

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is solved by using a Bethe ansatz in analogue to that for the one-dimensional spinless Fermi-Hubbard model. Excitation energies and the corresponding wavefunctions of the model are determined by a set of partial differential equations. It is shown that the model is, at least, quasi-exactly solvable for the two-site case, when the phonon frequency, the electron-phonon coupling strength and the hopping integral satisfy certain relations. As examples, some quasi-exact solutions of the model for the two-site case are derived. (letter to the editor)

Disease clusters, exact distributions of maxima, and P-values.

Science.gov (United States)

Grimson, R C

1993-10-01

This paper presents combinatorial (exact) methods that are useful in the analysis of disease cluster data obtained from small environments, such as buildings and neighbourhoods. Maxwell-Boltzmann and Fermi-Dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns (space and/or time) in these environments. The methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring. One of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models.

Clock Math — a System for Solving SLEs Exactly

Directory of Open Access Journals (Sweden)

Jakub Hladík

2013-01-01

Full Text Available In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers.

Exact solution of matricial Φ23 quantum field theory

Science.gov (United States)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

Exact Tests for Two-Way Contingency Tables with Structural Zeros

Directory of Open Access Journals (Sweden)

Luke J. West

2008-11-01

Full Text Available Fisher's exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher's exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test is implemented in the form of a new R package, aylmer.

Monte Carlo study of four-spinon dynamic structure function in antiferromagnetic Heisenberg model

International Nuclear Information System (INIS)

Si-Lakhal, B.; Abada, A.

2003-11-01

Using Monte Carlo integration methods, we describe the behavior of the exact four-s pinon dynamic structure function S 4 in the antiferromagnetic spin 1/2 Heisenberg quantum spin chain as a function of the neutron energy ω and momentum transfer k. We also determine the fourspinon continuum, the extent of the region in the (k, ω) plane outside which S 4 is identically zero. In each case, the behavior of S 4 is shown to be consistent with the four-spinon continuum and compared to the one of the exact two-spinon dynamic structure function S 2 . Overall shape similarity is noted. (author)

Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

International Nuclear Information System (INIS)

Plunien, G.; Beier, T.; Soff, G.

1998-01-01

We present a calculation scheme for the two-loop vacuum polarization correction of order α 2 to the Lamb shift of hydrogenlike high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in (Zα). By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuumpolarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogenlike lead and uranium are presented. (orig.)

Dynamics of actin cables in polarized growth of the filamentous fungus Aspergillus nidulans

Directory of Open Access Journals (Sweden)

Anna eBergs

2016-05-01

Full Text Available Highly polarized growth of filamentous fungi requires a continuous supply of proteins and lipids to the hyphal tip. This transport is managed by vesicle trafficking via the actin and microtubule cytoskeletons and their associated motor proteins. Particularly, actin cables originating from the hyphal tip are essential for hyphal growth. Although specific marker proteins to visualize actin cables have been developed in filamentous fungi, the exact organization and dynamics of actin cables has remained elusive. Here we visualized actin cables using tropomyosin (TpmA and Lifeact fused to fluorescent proteins in Aspergillus nidulans and studied the dynamics and regulation. GFP tagged TpmA visualized dynamic actin cables formed from the hyphal tip with cycles of elongation and shrinkage. The elongation and shrinkage rates of actin cables were similar and approximately 0.6 μm/s. Comparison of actin markers revealed that high concentrations of Lifeact reduced actin dynamics. Simultaneous visualization of actin cables and microtubules suggests temporally and spatially coordinated polymerization and depolymerization between the two cytoskeletons. Our results provide new insights into the molecular mechanism of ordered polarized growth regulated by actin cables and microtubules.

Exact collisional moments for plasma fluid theories

Science.gov (United States)

Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi

2017-10-01

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.

PLNoise: a package for exact numerical simulation of power-law noises

Science.gov (United States)

Milotti, Edoardo

2006-08-01

Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1uk/summaries/ADXV_v1_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell, ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes

Exact Solution of Fractional Diffusion Model with Source Term used in Study of Concentration of Fission Product in Uranium Dioxide Particle

International Nuclear Information System (INIS)

Fang Chao; Cao Jianzhu; Sun Lifeng

2011-01-01

The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide (UO 2 ) particle is built. The adsorption effect of the fission product on the surface of the UO 2 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor. (nuclear physics)

Entanglement dynamics after quantum quenches in generic integrable systems

Directory of Open Access Journals (Sweden)

Vincenzo Alba, Pasquale Calabrese

2018-03-01

Full Text Available The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data

Science.gov (United States)

Gibbons, T. J.; Öztürk, E.; Sims, N. D.

2018-01-01

Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

Exact solution of two interacting run-and-tumble random walkers with finite tumble duration

International Nuclear Information System (INIS)

Slowman, A B; Evans, M R; Blythe, R A

2017-01-01

We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, poisson-distributed, tumble duration so that a particle remains stationary whilst tumbling, thus generalising the persistent random walker model. We present the exact solution for the nonequilibrium stationary state of this system in the case of two random walkers. We find this to be characterised by two lengthscales, one arising from the jamming of approaching particles, and the other from one particle moving when the other is tumbling. The first of these lengthscales vanishes in a scaling limit where the continuous-space dynamics is recovered whilst the second remains finite. Thus the nonequilibrium stationary state reveals a rich structure of attractive, jammed and extended pieces. (paper)

Exact renormalization group as a scheme for calculations

International Nuclear Information System (INIS)

Mack, G.

1985-10-01

In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)

Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap

International Nuclear Information System (INIS)

Sowinski, Tomasz; Brewczyk, Miroslaw; Gajda, Mariusz; RzaPzewski, Kazimierz

2010-01-01

We study dynamics of two interacting ultracold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the δ-like potential, we study the time evolution of an initially separable state of two particles. The corresponding time-dependent single-particle density matrix is obtained and diagonalized, and single-particle orbitals are found. This allows us to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled, then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.

Optimization of Algorithms Using Extensions of Dynamic Programming

KAUST Repository

AbouEisha, Hassan M.

2017-04-09

We study and answer questions related to the complexity of various important problems such as: multi-frontal solvers of hp-adaptive finite element method, sorting and majority. We advocate the use of dynamic programming as a viable tool to study optimal algorithms for these problems. The main approach used to attack these problems is modeling classes of algorithms that may solve this problem using a discrete model of computation then defining cost functions on this discrete structure that reflect different complexity measures of the represented algorithms. As a last step, dynamic programming algorithms are designed and used to optimize those models (algorithms) and to obtain exact results on the complexity of the studied problems. The first part of the thesis presents a novel model of computation (element partition tree) that represents a class of algorithms for multi-frontal solvers along with cost functions reflecting various complexity measures such as: time and space. It then introduces dynamic programming algorithms for multi-stage and bi-criteria optimization of element partition trees. In addition, it presents results based on optimal element partition trees for famous benchmark meshes such as: meshes with point and edge singularities. New improved heuristics for those benchmark meshes were ob- tained based on insights of the optimal results found by our algorithms. The second part of the thesis starts by introducing a general problem where different problems can be reduced to and show how to use a decision table to model such problem. We describe how decision trees and decision tests for this table correspond to adaptive and non-adaptive algorithms for the original problem. We present exact bounds on the average time complexity of adaptive algorithms for the eight elements sorting problem. Then bounds on adaptive and non-adaptive algorithms for a variant of the majority problem are introduced. Adaptive algorithms are modeled as decision trees whose depth

AESS: Accelerated Exact Stochastic Simulation

Science.gov (United States)

Jenkins, David D.; Peterson, Gregory D.

2011-12-01

The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution

Exact goodness-of-fit tests for Markov chains.

Science.gov (United States)

Besag, J; Mondal, D

2013-06-01

Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps. © 2013, The International Biometric Society.

New types of exact solutions for a breaking soliton equation

International Nuclear Information System (INIS)

Mei Jianqin; Zhang Hongqing

2004-01-01

In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations

Reduced effects of pictorial distinctiveness on false memory following dynamic visual noise.

Science.gov (United States)

Parker, Andrew; Kember, Timothy; Dagnall, Neil

2017-07-01

High levels of false recognition for non-presented items typically occur following exposure to lists of associated words. These false recognition effects can be reduced by making the studied items more distinctive by the presentation of pictures during encoding. One explanation of this is that during recognition, participants expect or attempt to retrieve distinctive pictorial information in order to evaluate the study status of the test item. If this involves the retrieval and use of visual imagery, then interfering with imagery processing should reduce the effectiveness of pictorial information in false memory reduction. In the current experiment, visual-imagery processing was disrupted at retrieval by the use of dynamic visual noise (DVN). It was found that effects of DVN dissociated true from false memory. Memory for studied words was not influenced by the presence of an interfering noise field. However, false memory was increased and the effects of picture-induced distinctiveness was eliminated. DVN also increased false recollection and remember responses to unstudied items.

Dynamical chiral bag model

International Nuclear Information System (INIS)

Colanero, K.; Chu, M.-C.

2002-01-01

We study a dynamical chiral bag model, in which massless fermions are confined within an impenetrable but movable bag coupled to meson fields. The self-consistent motion of the bag is obtained by solving the equations of motion exactly assuming spherical symmetry. When the bag interacts with an external meson wave we find three different kinds of resonances: fermionic, geometric, and σ resonances. We discuss the phenomenological implications of our results

Dynamics of a spherical minority game

International Nuclear Information System (INIS)

Galla, T; Coolen, A C C; Sherrington, D

2003-01-01

We present an exact dynamical solution of a spherical version of the batch minority game (MG) with random external information. The control parameters in this model are the ratio of the number of possible values for the public information over the number of agents, and the radius of the spherical constraint on the microscopic degrees of freedom. We find a phase diagram with three phases: two without anomalous response (an oscillating versus a frozen state) and a further frozen phase with divergent integrated response. In contrast to standard MG versions, we can also calculate the volatility exactly. Our study reveals similarities between the spherical and the conventional MG, but also intriguing differences. Numerical simulations confirm our analytical results

Extended Plefka expansion for stochastic dynamics

International Nuclear Information System (INIS)

Bravi, B; Sollich, P; Opper, M

2016-01-01

We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry. (paper)

Extended Plefka expansion for stochastic dynamics

Science.gov (United States)

Bravi, B.; Sollich, P.; Opper, M.

2016-05-01

We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry.

Exact-to-precision generalized perturbation theory for source-driven systems

International Nuclear Information System (INIS)

Wang Congjian; Abdel-Khalik, Hany S.

2011-01-01

Highlights: ► We present a new development in higher order generalized perturbation theory. ► The method addresses the explosion in the flux phase space, input parameters, and responses. ► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method. ► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method. ► The accuracy of the method is compared to exact direct perturbations and first-order GPT. - Abstract: Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.

Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

International Nuclear Information System (INIS)

Yomba, Emmanuel; Kofane, Timoleon Crepin

2003-01-01

The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

Particle Tracking in Circular Accelerators Using the Exact Hamiltonian in SixTrack

CERN Document Server

Fjellstrom, Mattias; Hansson, Johan

2013-12-13

Particle motion in accelerators is in general complex. Tracking codes are developed to simulate beam dynamics in accelerators. SixTrack is a long lived particle tracking code maintained at CERN, the European Organization for Nuclear Research. A particle accelerator consists of a large number of magnets and other electromagnetic devices that guide the particle through the accelerator. Each device defines its own equation of motion, which often cannot be solved exactly. For this purpose, a number of approximations are introduced in order to facilitate the solution and to speed up the computation. In a high-energy accelerator, the particle has small transverse momentum components. This is exploited in the small-angle approximation. In this approximation the equations of motion are expanded to a low order in the transverse momentum components. In low-energy particle accelerators, or in tracking with large momentum deviations, this approximation is invalid. The equations of motion of a particle passing through a f...

The generalized tanh method to obtain exact solutions of nonlinear partial differential equation

OpenAIRE

Gómez, César

2007-01-01

In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.

Atomic quantum simulation of the lattice gauge-Higgs model: Higgs couplings and emergence of exact local gauge symmetry.

Science.gov (United States)

Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo

2013-09-13

Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.

Exact constants in approximation theory

CERN Document Server

Korneichuk, N

1991-01-01

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

Dynamics of a Bouncing Ball

Science.gov (United States)

Liang, Shiuan-Ni; Lan, Boon Leong

The dynamics of a bouncing ball undergoing repeated inelastic impacts with a table oscillating vertically in a sinusoidal fashion is studied using Newtonian mechanics and general relativistic mechanics. An exact mapping describes the bouncing ball dynamics in each theory. We show, contrary to expectation, that the trajectories predicted by Newtonian mechanics and general relativistic mechanics from the same parameters and initial conditions for the ball bouncing at low speed in a weak gravitational field can rapidly disagree completely. The bouncing ball system could be realized experimentally to test which of the two different predicted trajectories is correct.

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

International Nuclear Information System (INIS)

Liu Chunping; Liu Xiaoping

2004-01-01

First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

One-component plasma dynamical structure factor and the plasma dispersion: Method of moments

International Nuclear Information System (INIS)

Adamjan, S.V.; Tkachenko, I.M.; Meyer, T.

1989-01-01

The molecular dynamics data of Hansen, McDonald and Pollock on the dynamical properties of the classical one-component plasma (OCP) are compared with the results based on an approximation formula for the dielectric function satisfying all known sum rules and exact relations using HNC plasma static properties. (author)

Automatic differentiation tools in the dynamic simulation of chemical engineering processes

Directory of Open Access Journals (Sweden)

Castro M.C.

2000-01-01

Full Text Available Automatic Differentiation is a relatively recent technique developed for the differentiation of functions applicable directly to the source code to compute the function written in standard programming languages. That technique permits the automatization of the differentiation step, crucial for dynamic simulation and optimization of processes. The values for the derivatives obtained with AD are exact (to roundoff. The theoretical exactness of the AD comes from the fact that it uses the same rules of differentiation as in differential calculus, but these rules are applied to an algorithmic specification of the function rather than to a formula. The main purpose of this contribution is to discuss the impact of Automatic Differentiation in the field of dynamic simulation of chemical engineering processes. The influence of the differentiation technique on the behavior of the integration code, the performance of the generated code and the incorporation of AD tools in consistent initialization tools are discussed from the viewpoint of dynamic simulation of typical models in chemical engineering.

Exact, almost and delayed fault detection: An observer based approach

DEFF Research Database (Denmark)

Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.

1999-01-01

This paper consider the problem of fault detection and isolation in continuous- and discrete-time systems while using zero or almost zero threshold. A number of different fault detections and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability...... conditions are given for the formulated design problems together with methods for appropriate design of observer based fault detectors. The l-step delayed fault detection problem is also considered for discrete-time systems . Moreover, certain indirect fault detection methods such as unknown input observers...

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring [PowerPoint

Energy Technology Data Exchange (ETDEWEB)

Roettgen, Dan [Wisc; Seeger, Benjamin [Stuttgart; Tai, Wei Che [Washington; Baek, Seunghun [Michigan; Dossogne, Tilan [Liege; Allen, Matthew S [Wisc; Kuether, Robert J.; Brake, Matthew Robert; Mayes, Randall L.

2016-01-01

Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.

Formulations and exact algorithms for the vehicle routing problem with time windows

DEFF Research Database (Denmark)

Kallehauge, Brian

2008-01-01

In this paper we review the exact algorithms proposed in the last three decades for the solution of the vehicle routing problem with time windows (VRPTW). The exact algorithms for the VRPTW are in many aspects inherited from work on the traveling salesman problem (TSP). In recognition of this fact...