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

PubMed

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

2015-06-28

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.

Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems.

PubMed

Paganin, David M; Beltran, Mario A; Petersen, Timothy C

2018-03-01

We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.

Microscopic derivation of particle-based coarse-grained dynamics: Exact expression for memory function

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-03-01

We consider the generalized Langevin equations of motion describing exactly the particle-based coarse-grained dynamics in the classical microscopic ensemble that were derived recently within the Mori-Zwanzig formalism based on new projection operators [S. Izvekov, J. Chem. Phys. 138(13), 134106 (2013)]. The fundamental difference between the new family of projection operators and the standard Zwanzig projection operator used in the past to derive the coarse-grained equations of motion is that the new operators average out the explicit irrelevant trajectories leading to the possibility of solving the projected dynamics exactly. We clarify the definition of the projection operators and revisit the formalism to compute the projected dynamics exactly for the microscopic system in equilibrium. The resulting expression for the projected force is in the form of a "generalized additive fluctuating force" describing the departure of the generalized microscopic force associated with the coarse-grained coordinate from its projection. Starting with this key expression, we formulate a new exact formula for the memory function in terms of microscopic and coarse-grained conservative forces. We conclude by studying two independent limiting cases of practical importance: the Markov limit (vanishing correlations of projected force) and the limit of weak dependence of the memory function on the particle momenta. We present computationally affordable expressions which can be efficiently evaluated from standard molecular dynamics simulations.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

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

NASA Astrophysics Data System (ADS)

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.

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation.

PubMed

Hele, Timothy J H; Ananth, Nandini

2016-12-22

We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Exact and Heuristic Algorithms for Runway Scheduling

NASA Technical Reports Server (NTRS)

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.

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

Delving Into Dissipative Quantum Dynamics: From Approximate to Numerically Exact Approaches

NASA Astrophysics Data System (ADS)

Chen, Hsing-Ta

In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Pade-resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin-boson model, and non-crossing approximations (NCA) for the Anderson-Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin-boson model. I propose well-defined criteria for assessing the accuracy of Pade-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Pade approximation is reliable. I continue the investigation of spin-boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin-boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. Finally, I investigate the dynamical interplay between the electron-electron interaction and the electron-phonon coupling within the Anderson-Holstein model via two complementary NCAs: the first is constructed around the weak-coupling limit and the second around the polaron limit. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. I find the two NCAs disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The complementary frameworks used here pave the way for numerically exact methods based on inchworm dQMC algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

The probabilistic convolution tree: efficient exact Bayesian inference for faster LC-MS/MS protein inference.

PubMed

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 O(k log(k)2) and the space to O(k log(k)) where k 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.

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

PubMed Central

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

Parallel dynamics between non-Hermitian and Hermitian systems

NASA Astrophysics Data System (ADS)

Wang, P.; Lin, S.; Jin, L.; Song, Z.

2018-06-01

We reveals a connection between non-Hermitian and Hermitian systems by studying the connection between a family of non-Hermitian and Hermitian Hamiltonians based on exact solutions. In general, for a dynamic process in a non-Hermitian system H , there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate system H†. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H , and we present the relations between {H ,H ,H†} .

Solving Integer Programs from Dependence and Synchronization Problems

DTIC Science & Technology

1993-03-01

DEFF.NSNE Solving Integer Programs from Dependence and Synchronization Problems Jaspal Subhlok March 1993 CMU-CS-93-130 School of Computer ScienceT IC...method Is an exact and efficient way of solving integer programming problems arising in dependence and synchronization analysis of parallel programs...7/;- p Keywords: Exact dependence tesing, integer programming. parallelilzng compilers, parallel program analysis, synchronization analysis Solving

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1996-01-01

The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated 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 was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

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

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

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

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{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -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 themore » 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.« less

Entanglement dynamics in a non-Markovian environment: An exactly solvable model

NASA Astrophysics Data System (ADS)

Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.

2012-05-01

We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

Dynamic pattern matcher using incomplete data

NASA Technical Reports Server (NTRS)

Johnson, Gordon G. (Inventor); Wang, Lui (Inventor)

1993-01-01

This invention relates generally to pattern matching systems, and more particularly to a method for dynamically adapting the system to enhance the effectiveness of a pattern match. Apparatus and methods for calculating the similarity between patterns are known. There is considerable interest, however, in the storage and retrieval of data, particularly, when the search is called or initiated by incomplete information. For many search algorithms, a query initiating a data search requires exact information, and the data file is searched for an exact match. Inability to find an exact match thus results in a failure of the system or method.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

NASA Astrophysics Data System (ADS)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

PLNoise: a package for exact numerical simulation of power-law noises

NASA Astrophysics Data System (ADS)

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 -1<β⩽1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/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 in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press, Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. Nature of problem: Exact generation of different types of Gaussian colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701]. Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing. Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy. Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 4 in this work, the generation routine took on average about 7 ms for each sample.

COMPUTATIONAL FLUID DYNAMICS MODELING OF SCALED HANFORD DOUBLE SHELL TANK MIXING - CFD MODELING SENSITIVITY STUDY RESULTS

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

JACKSON VL

2011-08-31

The primary purpose of the tank mixing and sampling demonstration program is to mitigate the technical risks associated with the ability of the Hanford tank farm delivery and celtification systems to measure and deliver a uniformly mixed high-level waste (HLW) feed to the Waste Treatment and Immobilization Plant (WTP) Uniform feed to the WTP is a requirement of 24590-WTP-ICD-MG-01-019, ICD-19 - Interface Control Document for Waste Feed, although the exact definition of uniform is evolving in this context. Computational Fluid Dynamics (CFD) modeling has been used to assist in evaluating scaleup issues, study operational parameters, and predict mixing performance atmore » full-scale.« less

Approximation algorithms for scheduling unrelated parallel machines with release dates

NASA Astrophysics Data System (ADS)

Avdeenko, T. V.; Mesentsev, Y. A.; Estraykh, I. V.

2017-01-01

In this paper we propose approaches to optimal scheduling of unrelated parallel machines with release dates. One approach is based on the scheme of dynamic programming modified with adaptive narrowing of search domain ensuring its computational effectiveness. We discussed complexity of the exact schedules synthesis and compared it with approximate, close to optimal, solutions. Also we explain how the algorithm works for the example of two unrelated parallel machines and five jobs with release dates. Performance results that show the efficiency of the proposed approach have been given.

Heuristic algorithms for solving of the tool routing problem for CNC cutting machines

NASA Astrophysics Data System (ADS)

Chentsov, P. A.; Petunin, A. A.; Sesekin, A. N.; Shipacheva, E. N.; Sholohov, A. E.

2015-11-01

The article is devoted to the problem of minimizing the path of the cutting tool to shape cutting machines began. This problem can be interpreted as a generalized traveling salesman problem. Earlier version of the dynamic programming method to solve this problem was developed. Unfortunately, this method allows to process an amount not exceeding thirty circuits. In this regard, the task of constructing quasi-optimal route becomes relevant. In this paper we propose options for quasi-optimal greedy algorithms. Comparison of the results of exact and approximate algorithms is given.

Analysis of dynamic system response to product random processes

NASA Technical Reports Server (NTRS)

Sidwell, K.

1978-01-01

The response of dynamic systems to the product of two independent Gaussian random processes is developed by use of the Fokker-Planck and associated moment equations. The development is applied to the amplitude modulated process which is used to model atmospheric turbulence in aeronautical applications. The exact solution for the system response is compared with the solution obtained by the quasi-steady approximation which omits the dynamic properties of the random amplitude modulation. The quasi-steady approximation is valid as a limiting case of the exact solution for the dynamic response of linear systems to amplitude modulated processes. In the nonlimiting case the quasi-steady approximation can be invalid for dynamic systems with low damping.

Comparative Effects of Different Balance-Training-Progression Styles on Postural Control and Ankle Force Production: A Randomized Controlled Trial.

PubMed

Cuğ, Mutlu; Duncan, Ashley; Wikstrom, Erik

2016-02-01

Despite the effectiveness of balance training, the exact parameters needed to maximize the benefits of such programs remain unknown. One such factor is how individuals should progress to higher levels of task difficulty within a balance-training program. Yet no investigators have directly compared different balance-training-progression styles. To compare an error-based progression (ie, advance when proficient at a task) with a repetition-based progression (ie, advance after a set amount of repetitions) style during a balance-training program in healthy individuals. Randomized controlled trial. Research laboratory. A total of 28 (16 women, 12 men) physically healthy young adults (age = 21.57 ± 3.95 years, height = 171.60 ± 11.03 cm, weight = 72.96 ± 16.18 kg, body mass index = 24.53 ± 3.7). All participants completed 12 supervised balance-training sessions over 4 weeks. Each session consisted of a combination of dynamic unstable-surface tasks that incorporated a BOSU ball and lasted about 30 minutes. Static balance from an instrumented force plate, dynamic balance as measured via the Star Excursion Balance Test, and ankle force production in all 4 cardinal planes of motion as measured with a handheld dynamometer before and after the intervention. Selected static postural-control outcomes, dynamic postural control, and ankle force production in all planes of motion improved (P < .05). However, no differences between the progression styles were observed (P > .05) for any of the outcome measures. A 4-week balance-training program consisting of dynamic unstable-surface exercises on a BOSU ball improved dynamic postural control and ankle force production in healthy young adults. These results suggest that an error-based balance-training program is comparable with but not superior to a repetition-based balance-training program in improving postural control and ankle force production in healthy young adults.

Wheat forecast economics effect study. [value of improved information on crop inventories, production, imports and exports

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Rouhani, R.; Jones, S.; Schick, I.

1980-01-01

A model to assess the value of improved information regarding the inventories, productions, exports, and imports of crop on a worldwide basis is discussed. A previously proposed model is interpreted in a stochastic control setting and the underlying assumptions of the model are revealed. In solving the stochastic optimization problem, the Markov programming approach is much more powerful and exact as compared to the dynamic programming-simulation approach of the original model. The convergence of a dual variable Markov programming algorithm is shown to be fast and efficient. A computer program for the general model of multicountry-multiperiod is developed. As an example, the case of one country-two periods is treated and the results are presented in detail. A comparison with the original model results reveals certain interesting aspects of the algorithms and the dependence of the value of information on the incremental cost function.

Exact solutions for species tree inference from discordant gene trees.

PubMed

Chang, Wen-Chieh; Górecki, Paweł; Eulenstein, Oliver

2013-10-01

Phylogenetic analysis has to overcome the grant challenge of inferring accurate species trees from evolutionary histories of gene families (gene trees) that are discordant with the species tree along whose branches they have evolved. Two well studied approaches to cope with this challenge are to solve either biologically informed gene tree parsimony (GTP) problems under gene duplication, gene loss, and deep coalescence, or the classic RF supertree problem that does not rely on any biological model. Despite the potential of these problems to infer credible species trees, they are NP-hard. Therefore, these problems are addressed by heuristics that typically lack any provable accuracy and precision. We describe fast dynamic programming algorithms that solve the GTP problems and the RF supertree problem exactly, and demonstrate that our algorithms can solve instances with data sets consisting of as many as 22 taxa. Extensions of our algorithms can also report the number of all optimal species trees, as well as the trees themselves. To better asses the quality of the resulting species trees that best fit the given gene trees, we also compute the worst case species trees, their numbers, and optimization score for each of the computational problems. Finally, we demonstrate the performance of our exact algorithms using empirical and simulated data sets, and analyze the quality of heuristic solutions for the studied problems by contrasting them with our exact solutions.

Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations

NASA Astrophysics Data System (ADS)

Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.

2018-05-01

The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

Surface dynamics of micellar diblock copolymer films

NASA Astrophysics Data System (ADS)

Song, Sanghoon; Cha, Wonsuk; Kim, Hyunjung; Jiang, Zhang; Narayanan, Suresh

2011-03-01

We studied the structure and surface dynamics of poly(styrene)-b-poly(dimethylsiloxane) (PS-b-PDMS) diblock copolymer films with micellar PDMS surrounded by PS shells. By `in-situ' high resolution synchrotron x-ray reflectivity and diffuse scattering, we obtained exact thickness, electron density and surface tension. A segregation layer near the top surface was appeared with increasing temperature Surface dynamics were measured as a function of film thickness and temperature by x-ray photon correlation spectroscopy. The best fit to relaxation time constants as a function of in-plane wavevectors were analyzed with a theory based on capillary waves with hydrodynamics with bilayer model Finally the viscosities for the top segregated layer as well as for the bottom layer are obtained at given temperatures This work was supported by National Research Foundation of Korea (R15-2008-006-01001-0), Seoul Research and Business Development Program (10816), and Sogang University Research Grant (2010).

Component model reduction via the projection and assembly method

NASA Technical Reports Server (NTRS)

Bernard, Douglas E.

1989-01-01

The problem of acquiring a simple but sufficiently accurate model of a dynamic system is made more difficult when the dynamic system of interest is a multibody system comprised of several components. A low order system model may be created by reducing the order of the component models and making use of various available multibody dynamics programs to assemble them into a system model. The difficulty is in choosing the reduced order component models to meet system level requirements. The projection and assembly method, proposed originally by Eke, solves this difficulty by forming the full order system model, performing model reduction at the the system level using system level requirements, and then projecting the desired modes onto the components for component level model reduction. The projection and assembly method is analyzed to show the conditions under which the desired modes are captured exactly; to the numerical precision of the algorithm.

Computer program determines exact two-sided tolerance limits for normal distributions

NASA Technical Reports Server (NTRS)

Friedman, H. A.; Webb, S. R.

1968-01-01

Computer program determines by numerical integration the exact statistical two-sided tolerance limits, when the proportion between the limits is at least a specified number. The program is limited to situations in which the underlying probability distribution for the population sampled is the normal distribution with unknown mean and variance.

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

PubMed

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

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

NASA Technical Reports Server (NTRS)

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.

Einstein-aether theory: dynamics of relativistic particles with spin or polarization in a Gödel-type universe

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

Balakin, Alexander B.; Popov, Vladimir A., E-mail: alexander.balakin@kpfu.ru, E-mail: vladipopov@mail.ru

In the framework of the Einstein-aether theory we consider a cosmological model, which describes the evolution of the unit dynamic vector field with activated rotational degree of freedom. We discuss exact solutions of the Einstein-aether theory, for which the space-time is of the Gödel-type, the velocity four-vector of the aether motion is characterized by a non-vanishing vorticity, thus the rotational vectorial modes can be associated with the source of the universe rotation. The main goal of our paper is to study the motion of test relativistic particles with a vectorial internal degree of freedom (spin or polarization), which is coupledmore » to the unit dynamic vector field. The particles are considered as the test ones in the given space-time background of the Gödel-type; the spin (polarization) coupling to the unit dynamic vector field is modeled using exact solutions of three types. The first exact solution describes the aether with arbitrary Jacobson's coupling constants; the second one relates to the case, when the Jacobson's constant responsible for the vorticity is vanishing; the third exact solution is obtained using three constraints for the coupling constants. The analysis of the exact expressions, which are obtained for the particle momentum and for the spin (polarization) four-vector components, shows that the interaction of the spin (polarization) with the unit vector field induces a rotation, which is additional to the geodesic precession of the spin (polarization) associated with the universe rotation as a whole.« less

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

PubMed

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

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

Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu

The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packetmore » in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.« less

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

NASA Technical Reports Server (NTRS)

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 master equation and non-Markovian decoherence dynamics of Majorana zero modes under gate-induced charge fluctuations

NASA Astrophysics Data System (ADS)

Lai, Hon-Lam; Yang, Pei-Yun; Huang, Yu-Wei; Zhang, Wei-Min

2018-02-01

In this paper, we use the exact master equation approach to investigate the decoherence dynamics of Majorana zero modes in the Kitaev model, a 1D p -wave spinless topological superconducting chain (TSC) that is disturbed by gate-induced charge fluctuations. The exact master equation is derived by extending Feynman-Vernon influence functional technique to fermionic open systems involving pairing excitations. We obtain the exact master equation for the zero-energy Bogoliubov quasiparticle (bogoliubon) in the TSC, and then transfer it into the master equation for the Majorana zero modes. Within this exact master equation formalism, we can describe in detail the non-Markovian decoherence dynamics of the zero-energy bogoliubon as well as Majorana zero modes under local perturbations. We find that at zero temperature, local charge fluctuations induce level broadening to one of the Majorana zero modes but there is an isolated peak (localized bound state) located at zero energy that partially protects the Majorana zero mode from decoherence. At finite temperatures, the zero-energy localized bound state does not precisely exist, but the coherence of the Majorana zero mode can still be partially but weakly protected, due to the sharp dip of the spectral density near the zero frequency. The decoherence will be enhanced as one increases the charge fluctuations and/or the temperature of the gate.

SSRscanner: a program for reporting distribution and exact location of simple sequence repeats.

PubMed

Anwar, Tamanna; Khan, Asad U

2006-02-20

Simple sequence repeats (SSRs) have become important molecular markers for a broad range of applications, such as genome mapping and characterization, phenotype mapping, marker assisted selection of crop plants and a range of molecular ecology and diversity studies. These repeated DNA sequences are found in both prokaryotes and eukaryotes. They are distributed almost at random throughout the genome, ranging from mononucleotide to trinucleotide repeats. They are also found at longer lengths (> 6 repeating units) of tracts. Most of the computer programs that find SSRs do not report its exact position. A computer program SSRscanner was written to find out distribution, frequency and exact location of each SSR in the genome. SSRscanner is user friendly. It can search repeats of any length and produce outputs with their exact position on chromosome and their frequency of occurrence in the sequence. This program has been written in PERL and is freely available for non-commercial users by request from the authors. Please contact the authors by E-mail: huzzi99@hotmail.com.

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

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.

Dynamical Response of Networks Under External Perturbations: Exact Results

NASA Astrophysics Data System (ADS)

Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.

2015-04-01

We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.

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

NASA Astrophysics Data System (ADS)

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.

Nonequilibrium Green's functions and atom-surface dynamics: Simple views from a simple model system

NASA Astrophysics Data System (ADS)

Boström, E.; Hopjan, M.; Kartsev, A.; Verdozzi, C.; Almbladh, C.-O.

2016-03-01

We employ Non-equilibrium Green's functions (NEGF) to describe the real-time dynamics of an adsorbate-surface model system exposed to ultrafast laser pulses. For a finite number of electronic orbitals, the system is solved exactly and within different levels of approximation. Specifically i) the full exact quantum mechanical solution for electron and nuclear degrees of freedom is used to benchmark ii) the Ehrenfest approximation (EA) for the nuclei, with the electron dynamics still treated exactly. Then, using the EA, electronic correlations are treated with NEGF within iii) 2nd Born and with iv) a recently introduced hybrid scheme, which mixes 2nd Born self-energies with non-perturbative, local exchange- correlation potentials of Density Functional Theory (DFT). Finally, the effect of a semi-infinite substrate is considered: we observe that a macroscopic number of de-excitation channels can hinder desorption. While very preliminary in character and based on a simple and rather specific model system, our results clearly illustrate the large potential of NEGF to investigate atomic desorption, and more generally, the non equilibrium dynamics of material surfaces subject to ultrafast laser fields.

Game-theoretic analysis of dynamic traffic equilibria.

DOT National Transportation Integrated Search

2014-03-01

Dynamic traffic assignment has grown steadily in popularity and use since its inception. It has become an : important and permanent tool in transportation agencies across the country. However, the exact nature of : dynamic traffic equilibrium, includ...

OPTRAN- OPTIMAL LOW THRUST ORBIT TRANSFERS

NASA Technical Reports Server (NTRS)

Breakwell, J. V.

1994-01-01

OPTRAN is a collection of programs that solve the problem of optimal low thrust orbit transfers between non-coplanar circular orbits for spacecraft with chemical propulsion systems. The programs are set up to find Hohmann-type solutions, with burns near the perigee and apogee of the transfer orbit. They will solve both fairly long burn-arc transfers and "divided-burn" transfers. Program modeling includes a spherical earth gravity model and propulsion system models for either constant thrust or constant acceleration. The solutions obtained are optimal with respect to fuel use: i.e., final mass of the spacecraft is maximized with respect to the controls. The controls are the direction of thrust and the thrust on/off times. Two basic types of programs are provided in OPTRAN. The first type is for "exact solution" which results in complete, exact tkme-histories. The exact spacecraft position, velocity, and optimal thrust direction are given throughout the maneuver, as are the optimal thrust switch points, the transfer time, and the fuel costs. Exact solution programs are provided in two versions for non-coplanar transfers and in a fast version for coplanar transfers. The second basic type is for "approximate solutions" which results in approximate information on the transfer time and fuel costs. The approximate solution is used to estimate initial conditions for the exact solution. It can be used in divided-burn transfers to find the best number of burns with respect to time. The approximate solution is useful by itself in relatively efficient, short burn-arc transfers. These programs are written in FORTRAN 77 for batch execution and have been implemented on a DEC VAX series computer with the largest program having a central memory requirement of approximately 54K of 8 bit bytes. The OPTRAN program were developed in 1983.

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

NASA Astrophysics Data System (ADS)

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.

Dynamics of a spin-boson model with structured spectral density

NASA Astrophysics Data System (ADS)

Kurt, Arzu; Eryigit, Resul

2018-05-01

We report the results of a study of the dynamics of a two-state system coupled to an environment with peaked spectral density. An exact analytical expression for the bath correlation function is obtained. Validity range of various approximations to the correlation function for calculating the population difference of the system is discussed as function of tunneling splitting, oscillator frequency, coupling constant, damping rate and the temperature of the bath. An exact expression for the population difference, for a limited range of parameters, is derived.

Linearizing feedforward/feedback attitude control

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Bach, Ralph E.

1991-01-01

An approach to attitude control theory is introduced in which a linear form is postulated for the closed-loop rotation error dynamics, then the exact control law required to realize it is derived. The nonminimal (four-component) quaternion form is used to attitude because it is globally nonsingular, but the minimal (three-component) quaternion form is used for attitude error because it has no nonlinear constraints to prevent the rotational error dynamics from being linearized, and the definition of the attitude error is based on quaternion algebra. This approach produces an attitude control law that linearizes the closed-loop rotational error dynamics exactly, without any attitude singularities, even if the control errors become large.

Exact and Approximate Solutions for Transient Squeezing Flow

NASA Astrophysics Data System (ADS)

Lang, Ji; Santhanam, Sridhar; Wu, Qianhong

2017-11-01

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration is negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear, and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process, and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature, and will have a broad impact in industrial and biomedical applications. This work is supported by National Science Foundation CBET Fluid Dynamics Program under Award #1511096, and supported by the Seed Grant from The Villanova Center for the Advancement of Sustainability in Engineering (VCASE).

Comparative Effects of Different Balance-Training–Progression Styles on Postural Control and Ankle Force Production: A Randomized Controlled Trial

PubMed Central

Cuğ, Mutlu; Duncan, Ashley; Wikstrom, Erik

2016-01-01

Context:  Despite the effectiveness of balance training, the exact parameters needed to maximize the benefits of such programs remain unknown. One such factor is how individuals should progress to higher levels of task difficulty within a balance-training program. Yet no investigators have directly compared different balance-training–progression styles. Objective:  To compare an error-based progression (ie, advance when proficient at a task) with a repetition-based progression (ie, advance after a set amount of repetitions) style during a balance-training program in healthy individuals. Design:  Randomized controlled trial. Setting:  Research laboratory. Patients or Other Participants:  A total of 28 (16 women, 12 men) physically healthy young adults (age = 21.57 ± 3.95 years, height = 171.60 ± 11.03 cm, weight = 72.96 ± 16.18 kg, body mass index = 24.53 ± 3.7). Intervention(s):  All participants completed 12 supervised balance-training sessions over 4 weeks. Each session consisted of a combination of dynamic unstable-surface tasks that incorporated a BOSU ball and lasted about 30 minutes. Main Outcome Measure(s):  Static balance from an instrumented force plate, dynamic balance as measured via the Star Excursion Balance Test, and ankle force production in all 4 cardinal planes of motion as measured with a handheld dynamometer before and after the intervention. Results:  Selected static postural-control outcomes, dynamic postural control, and ankle force production in all planes of motion improved (P < .05). However, no differences between the progression styles were observed (P > .05) for any of the outcome measures. Conclusions:  A 4-week balance-training program consisting of dynamic unstable-surface exercises on a BOSU ball improved dynamic postural control and ankle force production in healthy young adults. These results suggest that an error-based balance-training program is comparable with but not superior to a repetition-based balance-training program in improving postural control and ankle force production in healthy young adults. PMID:26878257

Exact mapping between different dynamics of isotropically trapped quantum gases

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Pelster, Axel; Anglin, James R.

2016-05-01

Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact theoretical treatment. In this talk, we present a class of exact mappings between all the observables of different experiments, under the experimentally attainable conditions that the gas particles interact via a homogeneously scaling two-body potential which is in general time-dependent, and are confined in an isotropic harmonic trap. We express our result through an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics which makes it general. It applies to arbitrary measurements on possibly multi-component Bose or Fermi gases in arbitrary initial quantum states, no matter how highly excited or far from equilibrium. We use an example to show how the results of two different and currently feasible experiments can be mapped onto each other by our spacetime transformation. DAMOP sorting category: 6.11 Nonlinear dynamics and out-of-equilibrium trapped gases EW acknowledge the financial support from the Alexander von Humboldt foundation.

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

NASA Astrophysics Data System (ADS)

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.

SSRscanner: a program for reporting distribution and exact location of simple sequence repeats

PubMed Central

Anwar, Tamanna; Khan, Asad U

2006-01-01

Simple sequence repeats (SSRs) have become important molecular markers for a broad range of applications, such as genome mapping and characterization, phenotype mapping, marker assisted selection of crop plants and a range of molecular ecology and diversity studies. These repeated DNA sequences are found in both prokaryotes and eukaryotes. They are distributed almost at random throughout the genome, ranging from mononucleotide to trinucleotide repeats. They are also found at longer lengths (> 6 repeating units) of tracts. Most of the computer programs that find SSRs do not report its exact position. A computer program SSRscanner was written to find out distribution, frequency and exact location of each SSR in the genome. SSRscanner is user friendly. It can search repeats of any length and produce outputs with their exact position on chromosome and their frequency of occurrence in the sequence. Availability This program has been written in PERL and is freely available for non-commercial users by request from the authors. Please contact the authors by E-mail: huzzi99@hotmail.com PMID:17597863

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

NASA Astrophysics Data System (ADS)

Moix, Jeremy M.; Cao, Jianshu

2013-10-01

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems.

PubMed

Moix, Jeremy M; Cao, Jianshu

2013-10-07

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods

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

Favata, Marc

2011-01-15

Barack and Sago [Phys. Rev. Lett. 102, 191101 (2009)] have recently computed the shift of the innermost stable circular orbit (ISCO) of the Schwarzschild spacetime due to the conservative self-force that arises from the finite-mass of an orbiting test-particle. This calculation of the ISCO shift is one of the first concrete results of the self-force program, and provides an exact (fully relativistic) point of comparison with approximate post-Newtonian (PN) computations of the ISCO. Here this exact ISCO shift is compared with nearly all known PN-based methods. These include both 'nonresummed' and 'resummed' approaches (the latter reproduce the test-particle limit bymore » construction). The best agreement with the exact (Barack-Sago) result is found when the pseudo-4PN coefficient of the effective-one-body (EOB) metric is fit to numerical relativity simulations. However, if one considers uncalibrated methods based only on the currently known 3PN-order conservative dynamics, the best agreement is found from the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)], which relies only on the (nonresummed) 3PN equations of motion. This method reproduces the exact test-particle limit without any resummation. A comparison of PN methods with the ISCO in the equal-mass case (computed via sequences of numerical relativity initial-data sets) is also performed. Here a (different) nonresummed method also performs very well (as was previously shown). These results suggest that the EOB approach - while exactly incorporating the conservative test-particle dynamics and having several other important advantages - does not (in the absence of calibration) incorporate conservative self-force effects more accurately than standard PN methods. I also consider how the conservative self-force ISCO shift, combined in some cases with numerical relativity computations of the ISCO, can be used to constrain our knowledge of (1) the EOB effective metric, (2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN- and 5PN-order terms in the PN orbital energy. These constraints could help in constructing better gravitational-wave templates. Lastly, I suggest a new method to calibrate unknown PN terms in inspiral templates using numerical-relativity calculations.« less

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model.

PubMed

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-28

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

NASA Astrophysics Data System (ADS)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Three-dimensional structural dynamics of DNA origami Bennett linkages using individual-particle electron tomography

DOE PAGES

Lei, Dongsheng; Marras, Alexander E.; Liu, Jianfang; ...

2018-02-09

Scaffolded DNA origami has proven to be a powerful and efficient technique to fabricate functional nanomachines by programming the folding of a single-stranded DNA template strand into three-dimensional (3D) nanostructures, designed to be precisely motion-controlled. Although two-dimensional (2D) imaging of DNA nanomachines using transmission electron microscopy and atomic force microscopy suggested these nanomachines are dynamic in 3D, geometric analysis based on 2D imaging was insufficient to uncover the exact motion in 3D. In this paper, we use the individual-particle electron tomography method and reconstruct 129 density maps from 129 individual DNA origami Bennett linkage mechanisms at ~6-14 nm resolution. The statisticalmore » analyses of these conformations lead to understanding the 3D structural dynamics of Bennett linkage mechanisms. Moreover, our effort provides experimental verification of a theoretical kinematics model of DNA origami, which can be used as feedback to improve the design and control of motion via optimized DNA sequences and routing.« less

Three-dimensional structural dynamics of DNA origami Bennett linkages using individual-particle electron tomography

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

Lei, Dongsheng; Marras, Alexander E.; Liu, Jianfang

Scaffolded DNA origami has proven to be a powerful and efficient technique to fabricate functional nanomachines by programming the folding of a single-stranded DNA template strand into three-dimensional (3D) nanostructures, designed to be precisely motion-controlled. Although two-dimensional (2D) imaging of DNA nanomachines using transmission electron microscopy and atomic force microscopy suggested these nanomachines are dynamic in 3D, geometric analysis based on 2D imaging was insufficient to uncover the exact motion in 3D. In this paper, we use the individual-particle electron tomography method and reconstruct 129 density maps from 129 individual DNA origami Bennett linkage mechanisms at ~6-14 nm resolution. The statisticalmore » analyses of these conformations lead to understanding the 3D structural dynamics of Bennett linkage mechanisms. Moreover, our effort provides experimental verification of a theoretical kinematics model of DNA origami, which can be used as feedback to improve the design and control of motion via optimized DNA sequences and routing.« less

The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.

2018-03-01

The extended Einstein-Maxwell-aether-axion model describes internal interactions inside the system, which contains gravitational, electromagnetic fields, the dynamic unit vector field describing the velocity of an aether, and the pseudoscalar field associated with the axionic dark matter. The specific feature of this model is that the axion field controls the dynamics of the aether through the guiding functions incorporated into Jacobson’s constitutive tensor. Depending on the state of the axion field, these guiding functions can control and switch on or switch off the influence of acceleration, shear, vorticity and expansion of the aether flow on the state of physical system as a whole. We obtain new exact solutions, which possess the pp-wave symmetry, and indicate them by the term pp-wave aether modes in contrast to the pure pp-waves, which cannot propagate in this field conglomerate. These exact solutions describe a specific dynamic state of the pseudoscalar field, which corresponds to one of the minima of the axion potential and switches off the influence of shear and expansion of the aether flow; the model does not impose restrictions on Jacobson’s coupling constants and on the axion mass. Properties of these new exact solutions are discussed.

JANUS: a bit-wise reversible integrator for N-body dynamics

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2018-01-01

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS , for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formally symplectic and satisfies Liouville's theorem exactly. Its order is even and can be adjusted between two and ten. We discuss the implementation of JANUS and present tests of its accuracy and speed by performing and analysing long-term integrations of the Solar system. We show that JANUS is fast and accurate enough to tackle a broad class of dynamical problems. We also discuss the practical and philosophical implications of running exactly time-reversible simulations.

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

NASA Astrophysics Data System (ADS)

Bukov, Marin; Polkovnikov, Anatoli

2014-10-01

We study the stroboscopic and nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. We show that the former produces the evolution expected in the high-frequency limit only for observables, which commute with the operator to which the driving protocol couples. On the contrary, nonstroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the number operator following a quantum cyclotron orbit on a 2×2 plaquette, as well as the chiral current operator flowing along the legs of a 2×20 ladder. The exact evolution is compared with its stroboscopic and nonstroboscopic counterparts, including finite-frequency corrections.

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

PubMed

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.

Evolution and selection of river networks: Statics, dynamics, and complexity

PubMed Central

Rinaldo, Andrea; Rigon, Riccardo; Banavar, Jayanth R.; Maritan, Amos; Rodriguez-Iturbe, Ignacio

2014-01-01

Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-invariant structure of optimal river patterns. Optimal channel networks (OCNs) are feasible optimal configurations of a spanning network mimicking landscape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless configurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics—every spanning tree is exactly a local minimum of total energy dissipation. It is remarkable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms that are nevertheless characterized by universal statistical features. Such universal features explain very well the statistics of, and the linkages among, the scaling features measured for fluvial landforms across a broad range of scales regardless of geology, exposed lithology, vegetation, or climate, and differ significantly from those of the ground state, known exactly. Results are provided on the emergence of criticality through adaptative evolution and on the yet-unexplored range of applications of the OCN concept. PMID:24550264

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

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

Lack of consensus in social systems

NASA Astrophysics Data System (ADS)

Benczik, I. J.; Benczik, S. Z.; Schmittmann, B.; Zia, R. K. P.

2008-05-01

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.

New version of PLNoise: a package for exact numerical simulation of power-law noises

NASA Astrophysics Data System (ADS)

Milotti, Edoardo

2007-08-01

In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0<α⩽2. Here I extend the algorithm to generate 1/f noises with 2<α⩽4 (black noises). The method is exact in the sense that it produces a sampled process with a theoretically guaranteed range-limited power-law spectrum for any arbitrary sequence of sampling intervals, i.e. the sampling times may be unevenly spaced. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v2_0.html Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland 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 RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run 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 in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press., Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. No. of lines in distributed program, including test data, etc.:2975 No. of bytes in distributed program, including test data, etc.:194 588 Distribution format:tar.gz Catalogue identifier of previous version: ADXV_v1_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212 Does the new version supersede the previous version?: Yes Nature of problem: Exact generation of different types of colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701], possibly followed by an integration step to produce noise with spectral index >2. Reasons for the new version: Extension to 1/f noises with spectral index 2<α⩽4: the new version generates both noises with spectral with spectral index 0<α⩽2 and with 2<α⩽4. Summary of revisions: Although the overall structure remains the same, one routine has been added and several changes have been made throughout the code to include the new integration step. Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing. Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy. Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 3 in the long write-up, the generation routine took on average about 75 μs for each sample.

pycola: N-body COLA method code

NASA Astrophysics Data System (ADS)

Tassev, Svetlin; Eisenstein, Daniel J.; Wandelt, Benjamin D.; Zaldarriagag, Matias

2015-09-01

pycola is a multithreaded Python/Cython N-body code, implementing the Comoving Lagrangian Acceleration (COLA) method in the temporal and spatial domains, which trades accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is especially useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing. The COLA method achieves its speed by calculating the large-scale dynamics exactly using LPT while letting the N-body code solve for the small scales, without requiring it to capture exactly the internal dynamics of halos.

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

NASA Astrophysics Data System (ADS)

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.

Exact finite element method analysis of viscoelastic tapered structures to transient loads

NASA Technical Reports Server (NTRS)

Spyrakos, Constantine Chris

1987-01-01

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Exact and Monte carlo resampling procedures for the Wilcoxon-Mann-Whitney and Kruskal-Wallis tests.

PubMed

Berry, K J; Mielke, P W

2000-12-01

Exact and Monte Carlo resampling FORTRAN programs are described for the Wilcoxon-Mann-Whitney rank sum test and the Kruskal-Wallis one-way analysis of variance for ranks test. The program algorithms compensate for tied values and do not depend on asymptotic approximations for probability values, unlike most algorithms contained in PC-based statistical software packages.

How hairpin vortices emerge from exact invariant solutions

NASA Astrophysics Data System (ADS)

Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania

2017-11-01

Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

Kraken: ultrafast metagenomic sequence classification using exact alignments

PubMed Central

2014-01-01

Kraken is an ultrafast and highly accurate program for assigning taxonomic labels to metagenomic DNA sequences. Previous programs designed for this task have been relatively slow and computationally expensive, forcing researchers to use faster abundance estimation programs, which only classify small subsets of metagenomic data. Using exact alignment of k-mers, Kraken achieves classification accuracy comparable to the fastest BLAST program. In its fastest mode, Kraken classifies 100 base pair reads at a rate of over 4.1 million reads per minute, 909 times faster than Megablast and 11 times faster than the abundance estimation program MetaPhlAn. Kraken is available at http://ccb.jhu.edu/software/kraken/. PMID:24580807

Exact and heuristic algorithms for Space Information Flow.

PubMed

Uwitonze, Alfred; Huang, Jiaqing; Ye, Yuanqing; Cheng, Wenqing; Li, Zongpeng

2018-01-01

Space Information Flow (SIF) is a new promising research area that studies network coding in geometric space, such as Euclidean space. The design of algorithms that compute the optimal SIF solutions remains one of the key open problems in SIF. This work proposes the first exact SIF algorithm and a heuristic SIF algorithm that compute min-cost multicast network coding for N (N ≥ 3) given terminal nodes in 2-D Euclidean space. Furthermore, we find that the Butterfly network in Euclidean space is the second example besides the Pentagram network where SIF is strictly better than Euclidean Steiner minimal tree. The exact algorithm design is based on two key techniques: Delaunay triangulation and linear programming. Delaunay triangulation technique helps to find practically good candidate relay nodes, after which a min-cost multicast linear programming model is solved over the terminal nodes and the candidate relay nodes, to compute the optimal multicast network topology, including the optimal relay nodes selected by linear programming from all the candidate relay nodes and the flow rates on the connection links. The heuristic algorithm design is also based on Delaunay triangulation and linear programming techniques. The exact algorithm can achieve the optimal SIF solution with an exponential computational complexity, while the heuristic algorithm can achieve the sub-optimal SIF solution with a polynomial computational complexity. We prove the correctness of the exact SIF algorithm. The simulation results show the effectiveness of the heuristic SIF algorithm.

Exact calculation of distributions on integers, with application to sequence alignment.

PubMed

Newberg, Lee A; Lawrence, Charles E

2009-01-01

Computational biology is replete with high-dimensional discrete prediction and inference problems. Dynamic programming recursions can be applied to several of the most important of these, including sequence alignment, RNA secondary-structure prediction, phylogenetic inference, and motif finding. In these problems, attention is frequently focused on some scalar quantity of interest, a score, such as an alignment score or the free energy of an RNA secondary structure. In many cases, score is naturally defined on integers, such as a count of the number of pairing differences between two sequence alignments, or else an integer score has been adopted for computational reasons, such as in the test of significance of motif scores. The probability distribution of the score under an appropriate probabilistic model is of interest, such as in tests of significance of motif scores, or in calculation of Bayesian confidence limits around an alignment. Here we present three algorithms for calculating the exact distribution of a score of this type; then, in the context of pairwise local sequence alignments, we apply the approach so as to find the alignment score distribution and Bayesian confidence limits.

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

NASA Astrophysics Data System (ADS)

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.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

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

PubMed

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.

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

NASA Astrophysics Data System (ADS)

Liu, Xinzijian; Liu, Jian

2018-03-01

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.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Path Following in the Exact Penalty Method of Convex Programming.

PubMed

Zhou, Hua; Lange, Kenneth

2015-07-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

Path Following in the Exact Penalty Method of Convex Programming

PubMed Central

Zhou, Hua; Lange, Kenneth

2015-01-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander; Pronina, Ekaterina; Kolomeisky, Anatoly; Artyomov, Maxim

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability p, creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of p<1 a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

The Highly-Automated Airplane: Its Impact on Aviation Safety and an Analysis of Training Philosophy.

DTIC Science & Technology

1997-06-01

equipment. This means more than just knowing how to program the device and being familiar with the functions of varying modes (Patrick, 1996:18). 33...the function that I wanted to use or modify in a flight plan." "Initially it is extremely difficult to figure out exactly how to program or pull up...commented: "Getting used to the EFIS display was the hardest. Initially it is extremely difficult to figure out exactly how to program or pull up the

Oscillations and chaos in neural networks: an exactly solvable model.

PubMed Central

Wang, L P; Pichler, E E; Ross, J

1990-01-01

We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics. Images PMID:2251287

A one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer 3. Numerical methods and comparisons with exact solutions

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

Gelbard, F.; Fitzgerald, J.W.; Hoppel, W.A.

1998-07-01

We present the theoretical framework and computational methods that were used by {ital Fitzgerald} {ital et al.} [this issue (a), (b)] describing a one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer. The concepts and limitations of modeling spatially varying multicomponent aerosols are elucidated. New numerical sectional techniques are presented for simulating multicomponent aerosol growth, settling, and eddy transport, coupled to time-dependent and spatially varying condensing vapor concentrations. Comparisons are presented with new exact solutions for settling and particle growth by simultaneous dynamic condensation of one vapor and by instantaneous equilibration with a spatially varying secondmore » vapor. {copyright} 1998 American Geophysical Union« less

Entanglement dynamics following a sudden quench: An exact solution

NASA Astrophysics Data System (ADS)

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.

Models for the dynamics of dust-like matter in the self-gravity field: The method of hydrodynamic substitutions

NASA Astrophysics Data System (ADS)

Zhuravlev, V. M.

2017-09-01

Models for the dynamics of a dust-like medium in the self-gravity field are investigated. Solutions of the corresponding problems are constructed by the method of hydrodynamic substitutions generalizing the Cole-Hopf substitutions. The method is extended to multidimensional ideal and viscous fluid flows with cylindrical and spherical symmetries for which exact solutions are constructed. Solutions for the dynamics of self-gravitating dust with arbitrary initial distributions of both fluid density and velocity are constructed using special coordinate transformations. In particular, the problem of cosmological expansion is considered in terms of Newton's gravity theory. Models of a one-dimensional viscous dust fluid flow and some problems of gas hydrodynamics are considered. Examples of exact solutions and their brief analysis are provided.

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

Curchod, Basile F. E.; Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de; Gross, E. K. U.

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface—the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrastmore » to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.« less

Object matching using a locally affine invariant and linear programming techniques.

PubMed

Li, Hongsheng; Huang, Xiaolei; He, Lei

2013-02-01

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

[Three-dimensional reconstruction of functional brain images].

PubMed

Inoue, M; Shoji, K; Kojima, H; Hirano, S; Naito, Y; Honjo, I

1999-08-01

We consider PET (positron emission tomography) measurement with SPM (Statistical Parametric Mapping) analysis to be one of the most useful methods to identify activated areas of the brain involved in language processing. SPM is an effective analytical method that detects markedly activated areas over the whole brain. However, with the conventional presentations of these functional brain images, such as horizontal slices, three directional projection, or brain surface coloring, makes understanding and interpreting the positional relationships among various brain areas difficult. Therefore, we developed three-dimensionally reconstructed images from these functional brain images to improve the interpretation. The subjects were 12 normal volunteers. The following three types of images were constructed: 1) routine images by SPM, 2) three-dimensional static images, and 3) three-dimensional dynamic images, after PET images were analyzed by SPM during daily dialog listening. The creation of images of both the three-dimensional static and dynamic types employed the volume rendering method by VTK (The Visualization Toolkit). Since the functional brain images did not include original brain images, we synthesized SPM and MRI brain images by self-made C++ programs. The three-dimensional dynamic images were made by sequencing static images with available software. Images of both the three-dimensional static and dynamic types were processed by a personal computer system. Our newly created images showed clearer positional relationships among activated brain areas compared to the conventional method. To date, functional brain images have been employed in fields such as neurology or neurosurgery, however, these images may be useful even in the field of otorhinolaryngology, to assess hearing and speech. Exact three-dimensional images based on functional brain images are important for exact and intuitive interpretation, and may lead to new developments in brain science. Currently, the surface model is the most common method of three-dimensional display. However, the volume rendering method may be more effective for imaging regions such as the brain.

Linked-List-Based Multibody Dynamics (MBDyn) Engine

NASA Technical Reports Server (NTRS)

MacLean, John; Brain, Thomas; Wuiocho, Leslie; Huynh, An; Ghosh, Tushar

2012-01-01

This new release of MBDyn is a software engine that calculates the dynamics states of kinematic, rigid, or flexible multibody systems. An MBDyn multibody system may consist of multiple groups of articulated chains, trees, or closed-loop topologies. Transient topologies are handled through conservation of energy and momentum. The solution for rigid-body systems is exact, and several configurable levels of nonlinear term fidelity are available for flexible dynamics systems. The algorithms have been optimized for efficiency and can be used for both non-real-time (NRT) and real-time (RT) simulations. Interfaces are currently compatible with NASA's Trick Simulation Environment. This new release represents a significant advance in capability and ease of use. The two most significant new additions are an application programming interface (API) that clarifies and simplifies use of MBDyn, and a link-list infrastructure that allows a single MBDyn instance to propagate an arbitrary number of interacting groups of multibody top ologies. MBDyn calculates state and state derivative vectors for integration using an external integration routine. A Trickcompatible interface is provided for initialization, data logging, integration, and input/output.

Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams. Ph.D. Thesis, 1990 Final Report, May 1990

NASA Technical Reports Server (NTRS)

Watson, Robert A.

1991-01-01

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

NASA Astrophysics Data System (ADS)

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.

Studying relaxation phenomena via effective master equations

NASA Astrophysics Data System (ADS)

Chan, David; Wan, Jones T. K.; Chu, L. L.; Yu, K. W.

2000-04-01

The real-time dynamics of various relaxation phenomena can be conveniently formulated by a master equation with the enumeration of transition rates between given classes of conformations. To study the relaxation time towards equilibrium, it suffices to solve for the second largest eigenvalue of the resulting eigenvalue equation. Generally speaking, there is no analytic solution for the dynamic equation. Mean-field approaches generally yield misleading results while the presumably exact Monte-Carlo methods require prohibitive time steps in most real systems. In this work, we propose an exact decimation procedure for reducing the number of conformations significantly, while there is no loss of information, i.e., the reduced (or effective) equation is an exact transformed version of the original one. However, we have to pay the price: the initial Markovianity of the evolution equation is lost and the reduced equation contains memory terms in the transition rates. Since the transformed equation has significantly reduced number of degrees of freedom, the systems can readily be diagonalized by iterative means, to obtain the exact second largest eigenvalue and hence the relaxation time. The decimation method has been applied to various relaxation equations with generally desirable results. The advantages and limitations of the method will be discussed.

Exact Solutions for Wind-Driven Coastal Upwelling and Downwelling over Sloping Topography

NASA Astrophysics Data System (ADS)

Choboter, P.; Duke, D.; Horton, J.; Sinz, P.

2009-12-01

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping topographies. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is added to allow the cross-shore flow to be geostrophically balanced far from shore. Previously, this model has been used to study upwelling over flat-bottom and sloping topographies, but the novel feature in this work is the discovery of exact solutions for downwelling. These exact solutions are compared to numerical solutions from a primitive-equation ocean model, based on the Princeton Ocean Model, configured in a similar two-dimensional geometry. Many typical features of the evolution of density and velocity during downwelling are displayed by the analytical model.

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

NASA Astrophysics Data System (ADS)

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.

Reduced Dynamics of the Non-holonomic Whipple Bicycle

NASA Astrophysics Data System (ADS)

Boyer, Frédéric; Porez, Mathieu; Mauny, Johan

2018-06-01

Though the bicycle is a familiar object of everyday life, modeling its full nonlinear three-dimensional dynamics in a closed symbolic form is a difficult issue for classical mechanics. In this article, we address this issue without resorting to the usual simplifications on the bicycle kinematics nor its dynamics. To derive this model, we use a general reduction-based approach in the principal fiber bundle of configurations of the three-dimensional bicycle. This includes a geometrically exact model of the contacts between the wheels and the ground, the explicit calculation of the kernel of constraints, along with the dynamics of the system free of any external forces, and its projection onto the kernel of admissible velocities. The approach takes benefits of the intrinsic formulation of geometric mechanics. Along the path toward the final equations, we show that the exact model of the bicycle dynamics requires to cope with a set of non-symmetric constraints with respect to the structural group of its configuration fiber bundle. The final reduced dynamics are simulated on several examples representative of the bicycle. As expected the constraints imposed by the ground contacts, as well as the energy conservation, are satisfied, while the dynamics can be numerically integrated in real time.

Exact mapping of the 2+1 Dirac oscillator onto the Jaynes-Cummings model: Ion-trap experimental proposal

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

Bermudez, A.; Martin-Delgado, M. A.; Solano, E.

2007-10-15

We study the dynamics of the 2+1 Dirac oscillator exactly and find spin oscillations due to a Zitterbewegung of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model, describing the interaction of a two-level atom with a quantized single-mode field. This equivalence allows us to map a series of quantum optical phenomena onto the relativistic oscillator and vice versa. We make a realistic experimental proposal, in reach with current technology, for studying the equivalence of both models using a single trapped ion.

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

PubMed

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.

Towards a true protein movie: a perspective on the potential impact of the ensemble-based structure determination using exact NOEs.

PubMed

Vögeli, Beat; Orts, Julien; Strotz, Dean; Chi, Celestine; Minges, Martina; Wälti, Marielle Aulikki; Güntert, Peter; Riek, Roland

2014-04-01

Confined by the Boltzmann distribution of the energies of the states, a multitude of structural states are inherent to biomolecules. For a detailed understanding of a protein's function, its entire structural landscape at atomic resolution and insight into the interconversion between all the structural states (i.e. dynamics) are required. Whereas dedicated trickery with NMR relaxation provides aspects of local dynamics, and 3D structure determination by NMR is well established, only recently have several attempts been made to formulate a more comprehensive description of the dynamics and the structural landscape of a protein. Here, a perspective is given on the use of exact NOEs (eNOEs) for the elucidation of structural ensembles of a protein describing the covered conformational space. Copyright © 2013 Elsevier Inc. All rights reserved.

Propagation of arbitrary initial wave packets in a quantum parametric oscillator: Instability zones for higher order moments

NASA Astrophysics Data System (ADS)

Biswas, Subhadip; Chattopadhyay, Rohitashwa; Bhattacharjee, Jayanta K.

2018-05-01

We consider the dynamics of a particle in a parametric oscillator with a view to exploring any quantum feature of the initial wave packet that shows divergent (in time) behaviour for parameter values where the classical motion dynamics of the mean position is bounded. We use Ehrenfest's theorem to explore the dynamics of nth order moment which reduces exactly to a linear non autonomous differential equation of order n + 1. It is found that while the width and skewness of the packet is unbounded exactly in the zones where the classical motion is unbounded, the kurtosis of an initially non-gaussian wave packet can become infinitely large in certain additional zones. This implies that the shape of the wave packet can change drastically with time in these zones.

Detecting many-body-localization lengths with cold atoms

NASA Astrophysics Data System (ADS)

Guo, Xuefei; Li, Xiaopeng

2018-03-01

Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.

Quantum regression theorem and non-Markovianity of quantum dynamics

NASA Astrophysics Data System (ADS)

Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano

2014-08-01

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

NASA Technical Reports Server (NTRS)

Storch, J.; Gates, S.

1983-01-01

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

Dynamic stress effects in technical superconductors and the ''training'' problem of superconducting magnets

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

Pasztor, G.; Schmidt, C.

The behavior of NbTi superconductors under dynamic mechanical stress was investigated. A training effect was found in short-sample tests when the conductor was strained in a magnetic field and with a transport current applied. Possible mechanisms are discussed which were proposed to explain training in short samples and in magnets. A stress-induced microplastic as well as an incomplete pseudoelastic behavior of NbTi was detected by monitoring acoustic emission. The experiments support the hypothesis that microplastic or shape memory effects in NbTi involving dislocation processes are responsible for training. The minimum energy needed to induce a normal transition in short-sample testsmore » is calculated with a computer program, which gives the exact solution of the heat equation. A prestrain treatment of the conductor at room temperature is shown to be a simple method of reducing training of short samples and of magnets. This is a direct proof that the same mechanisms are involved in both cases.« less

A refined analysis of composite laminates. [theory of statics and dynamics

NASA Technical Reports Server (NTRS)

Srinivas, S.

1973-01-01

The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.

Resummed tree heptagon

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2018-04-01

The form factor program for the regularized space-time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of 't Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space-time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion-antifermion pairs accounted for in NMHV two-channel conformal blocks.

Exact calculation of loop formation probability identifies folding motifs in RNA secondary structures

PubMed Central

Sloma, Michael F.; Mathews, David H.

2016-01-01

RNA secondary structure prediction is widely used to analyze RNA sequences. In an RNA partition function calculation, free energy nearest neighbor parameters are used in a dynamic programming algorithm to estimate statistical properties of the secondary structure ensemble. Previously, partition functions have largely been used to estimate the probability that a given pair of nucleotides form a base pair, the conditional stacking probability, the accessibility to binding of a continuous stretch of nucleotides, or a representative sample of RNA structures. Here it is demonstrated that an RNA partition function can also be used to calculate the exact probability of formation of hairpin loops, internal loops, bulge loops, or multibranch loops at a given position. This calculation can also be used to estimate the probability of formation of specific helices. Benchmarking on a set of RNA sequences with known secondary structures indicated that loops that were calculated to be more probable were more likely to be present in the known structure than less probable loops. Furthermore, highly probable loops are more likely to be in the known structure than the set of loops predicted in the lowest free energy structures. PMID:27852924

Mesoscale Modeling of Dynamic Compression of Boron Carbide Polycrystals

DTIC Science & Technology

2013-05-01

reported later. Recrystallization has not been reported in the literature and is precluded by the model, meaning : 0 →1 is irreversible. Following...average HEL, above which a measurable strength loss is evident (Vogler et al., 2004), though amorphization has not been definitively proven to cause... definition (A.7) is exact when ı2 E→ 0 (Clayton, 2012). This criterion agrees exactly with that for classical stability under hydrostatic loading

Accurate van der Waals coefficients from density functional theory

PubMed Central

Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn

2012-01-01

The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Exact Solutions for Nonlinear Development of a Kelvin-Helmholtz Instability for the Counterflow of Superfluid and Normal Components of Helium II.

PubMed

Lushnikov, Pavel M; Zubarev, Nikolay M

2018-05-18

Relative motion of the normal and superfluid components of helium II results in the quantum Kelvin-Helmholtz instability (KHI) at their common free surface. We found the integrability and exact growing solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two classical fluids, the dynamics of a helium II free surface allows reduction to the Laplace growth equation, which has an infinite number of exact solutions, including the generic formation of sharp cusps at the free surface in a finite time.

Exact Solutions for Nonlinear Development of a Kelvin-Helmholtz Instability for the Counterflow of Superfluid and Normal Components of Helium II

NASA Astrophysics Data System (ADS)

Lushnikov, Pavel M.; Zubarev, Nikolay M.

2018-05-01

Relative motion of the normal and superfluid components of helium II results in the quantum Kelvin-Helmholtz instability (KHI) at their common free surface. We found the integrability and exact growing solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two classical fluids, the dynamics of a helium II free surface allows reduction to the Laplace growth equation, which has an infinite number of exact solutions, including the generic formation of sharp cusps at the free surface in a finite time.

Improving approximate-optimized effective potentials by imposing exact conditions: Theory and applications to electronic statics and dynamics

NASA Astrophysics Data System (ADS)

Kurzweil, Yair; Head-Gordon, Martin

2009-07-01

We develop a method that can constrain any local exchange-correlation potential to preserve basic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the time-dependent case we enforce translational covariance, zero net force, Levy-Perdew virial theorem, and energy balance. We test our method on the exchange (only) Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results (total energy, Kohn-Sham eigenvalues, polarizability, and hyperpolarizability) indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the time-dependent case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by cw laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI, and TDHF. We found that electron dynamics such as electron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least one order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non-cw driving force.

Improving approximate-optimized effective potentials by imposing exact conditions: Theory and applications to electronic statics and dynamics

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

Kurzweil, Yair; Head-Gordon, Martin

2009-07-15

We develop a method that can constrain any local exchange-correlation potential to preserve basic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the time-dependent case we enforce translational covariance, zero net force, Levy-Perdew virial theorem, and energy balance. We test our method on the exchangemore » (only) Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results (total energy, Kohn-Sham eigenvalues, polarizability, and hyperpolarizability) indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the time-dependent case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by cw laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI, and TDHF. We found that electron dynamics such as electron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least one order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non-cw driving force.« less

A high-performance Fortran code to calculate spin- and parity-dependent nuclear level densities

NASA Astrophysics Data System (ADS)

Sen'kov, R. A.; Horoi, M.; Zelevinsky, V. G.

2013-01-01

A high-performance Fortran code is developed to calculate the spin- and parity-dependent shell model nuclear level densities. The algorithm is based on the extension of methods of statistical spectroscopy and implies exact calculation of the first and second Hamiltonian moments for different configurations at fixed spin and parity. The proton-neutron formalism is used. We have applied the method for calculating the level densities for a set of nuclei in the sd-, pf-, and pf+g- model spaces. Examples of the calculations for 28Si (in the sd-model space) and 64Ge (in the pf+g-model space) are presented. To illustrate the power of the method we estimate the ground state energy of 64Ge in the larger model space pf+g, which is not accessible to direct shell model diagonalization due to the prohibitively large dimension, by comparing with the nuclear level densities at low excitation energy calculated in the smaller model space pf. Program summaryProgram title: MM Catalogue identifier: AENM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 193181 No. of bytes in distributed program, including test data, etc.: 1298585 Distribution format: tar.gz Programming language: Fortran 90, MPI. Computer: Any architecture with a Fortran 90 compiler and MPI. Operating system: Linux. RAM: Proportional to the system size, in our examples, up to 75Mb Classification: 17.15. External routines: MPICH2 (http://www.mcs.anl.gov/research/projects/mpich2/) Nature of problem: Calculating of the spin- and parity-dependent nuclear level density. Solution method: The algorithm implies exact calculation of the first and second Hamiltonian moments for different configurations at fixed spin and parity. The code is parallelized using the Message Passing Interface and a master-slaves dynamical load-balancing approach. Restrictions: The program uses two-body interaction in a restricted single-level basis. For example, GXPF1A in the pf-valence space. Running time: Depends on the system size and the number of processors used (from 1 min to several hours).

First Selection, Then Influence: Developmental Differences in Friendship Dynamics Regarding Academic Achievement

ERIC Educational Resources Information Center

Gremmen, Mariola Claudia; Dijkstra, Jan Kornelis; Steglich, Christian; Veenstra, René

2017-01-01

This study concerns peer selection and influence dynamics in early adolescents' friendships regarding academic achievement. Using longitudinal social network analysis (RSiena), both selection and influence processes were investigated for students' average grades and their cluster-specific grades (i.e., language, exact, and social cluster). Data…

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

Singleton, Jr., Robert; Israel, Daniel M.; Doebling, Scott William

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 returnedmore » 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.« less

Paramedic. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

Florida State Univ., Tallahassee. Center for Instructional Development and Services.

This program guide identifies primary considerations in the organization, operation, and evaluation of a paramedic program. An occupational description and program content are presented. A curriculum framework specifies the exact course title, course number, levels of instruction, major course content, laboratory activities, special notes, major…

Marketing and Distribution. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

Florida State Univ., Tallahassee. Center for Instructional Development and Services.

This program guide identifies primary considerations in the organization, operation, and evaluation of a marketing education program. An occupational description and program content are presented. A curriculum framework specifies the exact course title, course number, levels of instruction, major course content, laboratory activities, special…

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

NASA Astrophysics Data System (ADS)

Kuznetsov, Alexander M.; Medvedev, Igor G.

2006-05-01

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.

Sterols in spermatogenesis and sperm maturation

PubMed Central

Keber, Rok; Rozman, Damjana; Horvat, Simon

2013-01-01

Mammalian spermatogenesis is a complex developmental program in which a diploid progenitor germ cell transforms into highly specialized spermatozoa. One intriguing aspect of sperm production is the dynamic change in membrane lipid composition that occurs throughout spermatogenesis. Cholesterol content, as well as its intermediates, differs vastly between the male reproductive system and nongonadal tissues. Accumulation of cholesterol precursors such as testis meiosis-activating sterol and desmosterol is observed in testes and spermatozoa from several mammalian species. Moreover, cholesterogenic genes, especially meiosis-activating sterol-producing enzyme cytochrome P450 lanosterol 14α-demethylase, display stage-specific expression patterns during spermatogenesis. Discrepancies in gene expression patterns suggest a complex temporal and cell-type specific regulation of sterol compounds during spermatogenesis, which also involves dynamic interactions between germ and Sertoli cells. The functional importance of sterol compounds in sperm production is further supported by the modulation of sterol composition in spermatozoal membranes during epididymal transit and in the female reproductive tract, which is a prerequisite for successful fertilization. However, the exact role of sterols in male reproduction is unknown. This review discusses sterol dynamics in sperm maturation and describes recent methodological advances that will help to illuminate the complexity of sperm formation and function. PMID:23093550

Brock BaseCamp--Outdoor Orientation Programs Come to Canada

ERIC Educational Resources Information Center

O'Connell, Tim

2011-01-01

What exactly is an "outdoor orientation program?" First offered in the United States in the 1930s by Dartmouth College, outdoor orientation programs (OOPs) use adventure programming to help incoming students adjust to university or college. Typically, these programs are conducted in a wilderness or backcountry setting, are several days…

Sliding mode disturbance observer-enhanced adaptive control for the air-breathing hypersonic flight vehicle

NASA Astrophysics Data System (ADS)

An, Hao; Wang, Changhong; Fidan, Baris

2017-10-01

This paper presents a backstepping procedure to design an adaptive controller for the air-breathing hypersonic flight vehicle (AHFV) subject to external disturbances and actuator saturations. In each step, a sliding mode exact disturbance observer (SMEDO) is exploited to exactly estimate the lumped disturbance in finite time. Specific dynamics are introduced to handle the possible actuator saturations. Based on SMEDO and introduced dynamics, an adaptive control law is designed, along with the consideration on ;explosion of complexity; in backstepping design. The developed controller is equipped with fast disturbance rejection and great capability to accommodate the saturated actuators, which also lead to a wider application scope. A simulation study is provided to show the effectiveness and superiority of the proposed controller.

Exact results in 3d N = 2 Spin(7) gauge theories with vector and spinor matters

NASA Astrophysics Data System (ADS)

Nii, Keita

2018-05-01

We study three-dimensional N = 2 Spin(7) gauge theories with N S spinorial matters and with N f vectorial matters. The quantum Coulomb branch on the moduli space of vacua is one- or two-dimensional depending on the matter contents. For particular values of ( N f , N S ), we find s-confinement phases and derive exact superpotentials. The 3d dynamics of Spin(7) is connected to the 4d dynamics via KK-monopoles. Along the Higgs branch of the Spin(7) theories, we obtain 3d N = 2 G 2 or SU(4) theories and some of them lead to new s-confinement phases. As a check of our analysis we compute superconformal indices for these theories.

Exact results for quench dynamics and defect production in a two-dimensional model.

PubMed

Sengupta, K; Sen, Diptiman; Mondal, Shreyoshi

2008-02-22

We show that for a d-dimensional model in which a quench with a rate tau(-1) takes the system across a (d-m)-dimensional critical surface, the defect density scales as n approximately 1/tau(mnu/(znu+1)), where nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d = 2 and m = nu = z = 1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model that can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

DESIGN: a program to create data entry programs

Treesearch

J. Michael Wuerth; David R. Weise

1994-01-01

Scientific data entry can be an exacting process. The specific information needs change from investigation to investigation. A computer program to design custom data screens is described. The program, DESIGN, generates the necessary C programming language source code to create a basic data entry program. Data entry screens can contain multiple nested screens. Users can...

Patient Care Assistant. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

Florida State Univ., Tallahassee. Center for Instructional Development and Services.

This program guide identifies primary considerations in the organization, operation, and evaluation of a patient care assistant program. An occupational description and program content are presented. A curriculum framework specifies the exact course title, course number, levels of instruction, major course content, laboratory activities, special…

The dynamic programming high-order Dynamic Bayesian Networks learning for identifying effective connectivity in human brain from fMRI.

PubMed

Dang, Shilpa; Chaudhury, Santanu; Lall, Brejesh; Roy, Prasun Kumar

2017-06-15

Determination of effective connectivity (EC) among brain regions using fMRI is helpful in understanding the underlying neural mechanisms. Dynamic Bayesian Networks (DBNs) are an appropriate class of probabilistic graphical temporal-models that have been used in past to model EC from fMRI, specifically order-one. High-order DBNs (HO-DBNs) have still not been explored for fMRI data. A fundamental problem faced in the structure-learning of HO-DBN is high computational-burden and low accuracy by the existing heuristic search techniques used for EC detection from fMRI. In this paper, we propose using dynamic programming (DP) principle along with integration of properties of scoring-function in a way to reduce search space for structure-learning of HO-DBNs and finally, for identifying EC from fMRI which has not been done yet to the best of our knowledge. The proposed exact search-&-score learning approach HO-DBN-DP is an extension of the technique which was originally devised for learning a BN's structure from static data (Singh and Moore, 2005). The effectiveness in structure-learning is shown on synthetic fMRI dataset. The algorithm reaches globally-optimal solution in appreciably reduced time-complexity than the static counterpart due to integration of properties. The proof of optimality is provided. The results demonstrate that HO-DBN-DP is comparably more accurate and faster than currently used structure-learning algorithms used for identifying EC from fMRI. The real data EC from HO-DBN-DP shows consistency with previous literature than the classical Granger Causality method. Hence, the DP algorithm can be employed for reliable EC estimates from experimental fMRI data. Copyright © 2017 Elsevier B.V. All rights reserved.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Reaching extended length-scales with temperature-accelerated dynamics

NASA Astrophysics Data System (ADS)

Amar, Jacques G.; Shim, Yunsic

2013-03-01

In temperature-accelerated dynamics (TAD) a high-temperature molecular dynamics (MD) simulation is used to accelerate the search for the next low-temperature activated event. While TAD has been quite successful in extending the time-scales of simulations of non-equilibrium processes, due to the fact that the computational work scales approximately as the cube of the number of atoms, until recently only simulations of relatively small systems have been carried out. Recently, we have shown that by combining spatial decomposition with our synchronous sublattice algorithm, significantly improved scaling is possible. However, in this approach the size of activated events is limited by the processor size while the dynamics is not exact. Here we discuss progress in developing an alternate approach in which high-temperature parallel MD along with localized saddle-point (LSAD) calculations, are used to carry out TAD simulations without restricting the size of activated events while keeping the dynamics ``exact'' within the context of harmonic transition-state theory. In tests of our LSAD method applied to Ag/Ag(100) annealing and Cu/Cu(100) growth simulations we find significantly improved scaling of TAD, while maintaining a negligibly small error in the energy barriers. Supported by NSF DMR-0907399.

Computer program for buckling loads of orthotropic laminated stiffened panels subjected to biaxial in-place loads (BUCLASP 2)

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.

1974-01-01

General-purpose program performs exact instability analyses for structures such as unidirectionally-stiffened, rectangular composite panels. Program was written in FORTRAN IV and COMPASS for CDC-series computers.

Confidence bounds for normal and lognormal distribution coefficients of variation

Treesearch

Steve Verrill

2003-01-01

This paper compares the so-called exact approach for obtaining confidence intervals on normal distribution coefficients of variation to approximate methods. Approximate approaches were found to perform less well than the exact approach for large coefficients of variation and small sample sizes. Web-based computer programs are described for calculating confidence...

A walk through the approximations of ab initio multiple spawning

NASA Astrophysics Data System (ADS)

Mignolet, Benoit; Curchod, Basile F. E.

2018-04-01

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

A walk through the approximations of ab initio multiple spawning.

PubMed

Mignolet, Benoit; Curchod, Basile F E

2018-04-07

Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.

Kerr-like behaviour of second harmonic generation in the far-off resonant regime

NASA Astrophysics Data System (ADS)

Peřinová, Vlasta; Lukš, Antonín; Křepelka, Jaromír; Leoński, Wiesław; Peřina, Jan

2018-05-01

We separate the Kerr-like behaviour of the second-harmonic generation in the far-off resonant regime from the oscillations caused by the time-dependence of the interaction energy. To this purpose, we consider the approximation obtained from the exact dynamics by the method of small rotations. The Floquet-type decomposition of the approximate dynamics comprises the Kerr-like dynamics and oscillations of the same order of magnitude as those assumed for the exact dynamics of the second-harmonic generation. We have found that a superposition of two states of concentrated quantum phase arises in the fundamental mode in the second-harmonic generation in the far-off resonant limit at a later time than a superposition of two coherent states in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes. The quantum phase fluctuation is higher for the same initial coherent amplitudes in the fundamental mode in the second-harmonic generation in the far-off resonant limit than in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes.

Correlated electron-nuclear dynamics with conditional wave functions.

PubMed

Albareda, Guillermo; Appel, Heiko; Franco, Ignacio; Abedi, Ali; Rubio, Angel

2014-08-22

The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.

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

NASA Astrophysics Data System (ADS)

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.

Respiratory Therapy and Respiratory Therapy Technician. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

Florida State Univ., Tallahassee. Center for Instructional Development and Services.

This program guide identifies primary considerations in the organization, operation, and evaluation of respiratory therapy and respiratory therapy technician programs. An occupational description and program content are presented. The curriculum framework specifies the exact course title, course number, levels of instruction, major course content,…

Laser Electro-Optic Technology. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

University of South Florida, Tampa. Dept. of Adult and Vocational Education.

This program guide identifies primary considerations in the organization, operation, and evaluation of a laser electro-optic technology program. An occupational description and program content are presented. A curriculum framework specifies the exact course title, course number, levels of instruction, major course content, laboratory activities,…

Natural Resources and Forest Ecology. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

Florida State Univ., Tallahassee. Center for Instructional Development and Services.

This program guide identifies primary considerations in the organization, operation, and evaluation of a natural resources and forest ecology program. Program content is presented first. A curriculum framework specifies the exact course title, course number, levels of instruction, major course content, laboratory activities, special notes, major…

Receptionist and Communication Systems Operation. Florida Vocational Program Guide.

ERIC Educational Resources Information Center

Florida State Univ., Tallahassee. Center for Instructional Development and Services.

This program guide identifies primary considerations in the organization, operation, and evaluation of a receptionist and communication systems operation program. An occupational description and program content are presented. A curriculum framework specifies the exact course title, course number, levels of instruction, major course content,…

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1999-01-01

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Exact solutions for kinetic models of macromolecular dynamics.

PubMed

Chemla, Yann R; Moffitt, Jeffrey R; Bustamante, Carlos

2008-05-15

Dynamic biological processes such as enzyme catalysis, molecular motor translocation, and protein and nucleic acid conformational dynamics are inherently stochastic processes. However, when such processes are studied on a nonsynchronized ensemble, the inherent fluctuations are lost, and only the average rate of the process can be measured. With the recent development of methods of single-molecule manipulation and detection, it is now possible to follow the progress of an individual molecule, measuring not just the average rate but the fluctuations in this rate as well. These fluctuations can provide a great deal of detail about the underlying kinetic cycle that governs the dynamical behavior of the system. However, extracting this information from experiments requires the ability to calculate the general properties of arbitrarily complex theoretical kinetic schemes. We present here a general technique that determines the exact analytical solution for the mean velocity and for measures of the fluctuations. We adopt a formalism based on the master equation and show how the probability density for the position of a molecular motor at a given time can be solved exactly in Fourier-Laplace space. With this analytic solution, we can then calculate the mean velocity and fluctuation-related parameters, such as the randomness parameter (a dimensionless ratio of the diffusion constant and the velocity) and the dwell time distributions, which fully characterize the fluctuations of the system, both commonly used kinetic parameters in single-molecule measurements. Furthermore, we show that this formalism allows calculation of these parameters for a much wider class of general kinetic models than demonstrated with previous methods.

EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.

ERIC Educational Resources Information Center

Jarvis, John J.; And Others

Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Transverse vibration of Bernoulli Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

NASA Astrophysics Data System (ADS)

Maiz, Santiago; Bambill, Diana V.; Rossit, Carlos A.; Laura, P. A. A.

2007-06-01

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams.

Extended Plefka expansion for stochastic dynamics

NASA Astrophysics Data System (ADS)

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.

Polaron dynamics with a multitude of Davydov D{sub 2} trial states

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

Zhou, Nengji; Department of Physics, Hangzhou Normal University, Hangzhou 310046; Huang, Zhongkai

2015-07-07

We propose an extension to the Davydov D{sub 2} Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the “multi-D{sub 2} Ansatz” is a linear combination of Davydov D{sub 2} trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D{sub 1} and D{sub 2} Ansätze. With an increase in the number ofmore » the Davydov D{sub 2} trial states in the multi-D{sub 2} Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.« less

Opera: reconstructing optimal genomic scaffolds with high-throughput paired-end sequences.

PubMed

Gao, Song; Sung, Wing-Kin; Nagarajan, Niranjan

2011-11-01

Scaffolding, the problem of ordering and orienting contigs, typically using paired-end reads, is a crucial step in the assembly of high-quality draft genomes. Even as sequencing technologies and mate-pair protocols have improved significantly, scaffolding programs still rely on heuristics, with no guarantees on the quality of the solution. In this work, we explored the feasibility of an exact solution for scaffolding and present a first tractable solution for this problem (Opera). We also describe a graph contraction procedure that allows the solution to scale to large scaffolding problems and demonstrate this by scaffolding several large real and synthetic datasets. In comparisons with existing scaffolders, Opera simultaneously produced longer and more accurate scaffolds demonstrating the utility of an exact approach. Opera also incorporates an exact quadratic programming formulation to precisely compute gap sizes (Availability: http://sourceforge.net/projects/operasf/ ).

Opera: Reconstructing Optimal Genomic Scaffolds with High-Throughput Paired-End Sequences

PubMed Central

Gao, Song; Sung, Wing-Kin

2011-01-01

Abstract Scaffolding, the problem of ordering and orienting contigs, typically using paired-end reads, is a crucial step in the assembly of high-quality draft genomes. Even as sequencing technologies and mate-pair protocols have improved significantly, scaffolding programs still rely on heuristics, with no guarantees on the quality of the solution. In this work, we explored the feasibility of an exact solution for scaffolding and present a first tractable solution for this problem (Opera). We also describe a graph contraction procedure that allows the solution to scale to large scaffolding problems and demonstrate this by scaffolding several large real and synthetic datasets. In comparisons with existing scaffolders, Opera simultaneously produced longer and more accurate scaffolds demonstrating the utility of an exact approach. Opera also incorporates an exact quadratic programming formulation to precisely compute gap sizes (Availability: http://sourceforge.net/projects/operasf/). PMID:21929371

Greedy algorithms in disordered systems

NASA Astrophysics Data System (ADS)

Duxbury, P. M.; Dobrin, R.

1999-08-01

We discuss search, minimal path and minimal spanning tree algorithms and their applications to disordered systems. Greedy algorithms solve these problems exactly, and are related to extremal dynamics in physics. Minimal cost path (Dijkstra) and minimal cost spanning tree (Prim) algorithms provide extremal dynamics for a polymer in a random medium (the KPZ universality class) and invasion percolation (without trapping) respectively.

An Exact Solvable Model of Rocket Dynamics in Atmosphere

ERIC Educational Resources Information Center

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…

Exact calculation of loop formation probability identifies folding motifs in RNA secondary structures.

PubMed

Sloma, Michael F; Mathews, David H

2016-12-01

RNA secondary structure prediction is widely used to analyze RNA sequences. In an RNA partition function calculation, free energy nearest neighbor parameters are used in a dynamic programming algorithm to estimate statistical properties of the secondary structure ensemble. Previously, partition functions have largely been used to estimate the probability that a given pair of nucleotides form a base pair, the conditional stacking probability, the accessibility to binding of a continuous stretch of nucleotides, or a representative sample of RNA structures. Here it is demonstrated that an RNA partition function can also be used to calculate the exact probability of formation of hairpin loops, internal loops, bulge loops, or multibranch loops at a given position. This calculation can also be used to estimate the probability of formation of specific helices. Benchmarking on a set of RNA sequences with known secondary structures indicated that loops that were calculated to be more probable were more likely to be present in the known structure than less probable loops. Furthermore, highly probable loops are more likely to be in the known structure than the set of loops predicted in the lowest free energy structures. © 2016 Sloma and Mathews; Published by Cold Spring Harbor Laboratory Press for the RNA Society.

Exact ghost-free bigravitational waves

NASA Astrophysics Data System (ADS)

Ayón-Beato, Eloy; Higuita-Borja, Daniel; Méndez-Zavaleta, Julio A.; Velázquez-Rodríguez, Gerardo

2018-04-01

We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type-N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This entails a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-wave dynamics, using an integral representation originally due to Poisson. Inspired by this progress, we tackle the subtle problem of how matter couples to bigravity and, more concretely, if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported by either a massless free scalar field or a wavefront-homogeneous Maxwell field. Considering the most general allowed Maxwell source instead is a highly nontrivial task, which we accomplish by again exploiting the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this eventually allows us to find the most general configurations for any matter source.

Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

NASA Technical Reports Server (NTRS)

Schlesinger, Robert E.

1990-01-01

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Validation of the SURE Program, phase 1

NASA Technical Reports Server (NTRS)

Dotson, Kelly J.

1987-01-01

Presented are the results of the first phase in the validation of the SURE (Semi-Markov Unreliability Range Evaluator) program. The SURE program gives lower and upper bounds on the death-state probabilities of a semi-Markov model. With these bounds, the reliability of a semi-Markov model of a fault-tolerant computer system can be analyzed. For the first phase in the validation, fifteen semi-Markov models were solved analytically for the exact death-state probabilities and these solutions compared to the corresponding bounds given by SURE. In every case, the SURE bounds covered the exact solution. The bounds, however, had a tendency to separate in cases where the recovery rate was slow or the fault arrival rate was fast.

Quantum Dynamics in the HMF Model

NASA Astrophysics Data System (ADS)

Plestid, Ryan; O'Dell, Duncan

2017-04-01

The Hamiltonian Mean Field (HMF) model represents a paradigm in the study of long-range interactions but has never been realized in a lab. Recently Shutz and Morigi (PRL 113) have come close but ultimately fallen short. Their proposal relied on cavity-induced interactions between atoms. If a design using cold atoms is to be successful, an understanding of quantum effects is essential. I will outline the natural quantum generalization of the HMF assuming a BEC by using a generalized Gross-Pitaevskii equation (gGPE). I will show how quantum effects modify features which are well understood in the classical model. More specifically, by working in the semi-classical regime (strong interparticle interactions) we can identify the universal features predicted by catastrophe theory dressed with quantum interference effects. The stationary states of gGPE can be solved exactly and are found to be described by self-consistent Mathieu functions. Finally, I will discuss the connection between the classical description of the dynamics in terms of the Vlassov equation, and the gGPE. We would like to thank the Government of Ontario's OGS program, NSERC, and the Perimeter Institute of Theoretical Physics.

A design methodology for neutral buoyancy simulation of space operations

NASA Technical Reports Server (NTRS)

Akin, David L.

1988-01-01

Neutral buoyancy has often been used in the past for EVA development activities, but little has been done to provide an analytical understanding of the environment and its correlation with space. This paper covers a set of related research topics at the MIT Space Systems Laboratory, dealing with the modeling of the space and underwater environments, validation of the models through testing in neutral buoyancy, parabolic flight, and space flight experiments, and applications of the models to gain a better design methodology for creating meaningful neutral buoyancy simulations. Examples covered include simulation validation criteria for human body dynamics, and for applied torques in a beam rotation task, which is the pacing crew operation for EVA structural assembly. Extensions of the dynamics models are presented for powered vehicles in the underwater environment, and examples given from the MIT Space Telerobotics Research Program, including the Beam Assembly Teleoperator and the Multimode Proximity Operations Device. Future expansions of the modeling theory are also presented, leading to remote vehicles which behave in neutral buoyancy exactly as the modeled system would in space.

Mad-X a worthy successor for MAD8?

NASA Astrophysics Data System (ADS)

Schmidt, F.

2006-03-01

MAD-X is the successor at CERN to MAD8, a program for accelerator design and simulation with a long history. We had to give up on MAD8 since the code had evolved in such a way that the maintenance and upgrades had become increasingly difficult. In particular, the memory management with the Zebra banks seemed outdated. MAD-X was first released in June, 2002. It offers most of the MAD8 functionality, with some additions, corrections, and extensions. The most important of these extensions is the interface to PTC, the Polymorphic Tracking Code by E. Forest. The most relevant new features of MAD-X are: languages: C, Fortran77, and Fortran90; dynamic memory allocation: in the core program written in C; strictly modular organization, modified and extended input language; symplectic and arbitrary exact description of all elements via PTC; Taylor Maps and Normal Form techniques using PTC. It is also important to note that we have adopted a new style for program development and maintenance that relies heavily on active maintenance of modules by the users themselves. Proposals for collaboration as with KEK, Japan and GSI, Germany are therefore very welcome.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Quantum decay model with exact explicit analytical solution

NASA Astrophysics Data System (ADS)

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.

Motor Programming in Apraxia of Speech

ERIC Educational Resources Information Center

Maas, Edwin; Robin, Donald A.; Wright, David L.; Ballard, Kirrie J.

2008-01-01

Apraxia of Speech (AOS) is an impairment of motor programming. However, the exact nature of this deficit remains unclear. The present study examined motor programming in AOS in the context of a recent two-stage model [Klapp, S. T. (1995). Motor response programming during simple and choice reaction time: The role of practice. "Journal of…

Proceedings of the 1977 MACSYMA users' conference (NASA)

NASA Technical Reports Server (NTRS)

1977-01-01

The MACSYMA program for symbolic and algebraic manipulation enables exact, symbolic mathematical computations to be performed on a computer. This program is rather large, and various approaches to the hardware and software problems are examined.

Numerically Exact Long Time Magnetization Dynamics Near the Nonequilibrium Kondo Regime

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David; Millis, Andrew; Rabani, Eran

2013-03-01

The dynamical and steady-state spin response of the nonequilibrium Anderson impurity model to magnetic fields, bias voltages, and temperature is investigated by a numerically exact method which allows access to unprecedentedly long times. The method is based on using real, continuous time bold Monte Carlo techniques--quantum Monte Carlo sampling of diagrammatic corrections to a partial re-summation--in order to compute the kernel of a memory function, which is then used to determine the reduced density matrix. The method owes its effectiveness to the fact that the memory kernel is dominated by relatively short-time properties even when the system's dynamics are long-ranged. We make predictions regarding the non-monotonic temperature dependence of the system at high bias voltage and the oscillatory quench dynamics at high magnetic fields. We also discuss extensions of the method to the computation of transport properties and correlation functions, and its suitability as an impurity solver free from the need for analytical continuation in the context of dynamical mean field theory. This work is supported by the US Department of Energy under grant DE-SC0006613, by NSF-DMR-1006282 and by the US-Israel Binational Science Foundation. GC is grateful to the Yad Hanadiv-Rothschild Foundation for the award of a Rothschild Fellowship.

Heisenberg operator approach for spin squeezing dynamics

NASA Astrophysics Data System (ADS)

Bhattacherjee, Aranya Bhuti; Sharma, Deepti; Pelster, Axel

2017-12-01

We reconsider the one-axis twisting Hamiltonian, which is commonly used for generating spin squeezing, and treat its dynamics within the Heisenberg operator approach. To this end we solve the underlying Heisenberg equations of motion perturbatively and evaluate the expectation values of the resulting time-dependent Heisenberg operators in order to determine approximately the dynamics of spin squeezing. Comparing our results with those originating from exact numerics reveals that they are more accurate than the commonly used frozen spin approximation.

Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics

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

White, Alexander J.; Center for Nonlinear Studies; Gorshkov, Vyacheslav N.

2014-11-14

Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantummore » mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.« less

Public Sector Employee Assistance Programs.

ERIC Educational Resources Information Center

Kemp, Donna R.; Verlinde, Beverly

This document discusses employee assistance programs (EAPs), programs which have been developed to help employees deal with personal problems that seriously affect job performance. It reviews literature which specifically addresses EAPs in the public sector, noting that there are no exact figures on how many public entities have EAPs. Previous…

7 CFR 1493.260 - Facility payment guarantee.

Code of Federal Regulations, 2013 CFR

2013-01-01

... OF AGRICULTURE EXPORT PROGRAMS CCC EXPORT CREDIT GUARANTEE PROGRAMS CCC Facility Guarantee Program (FGP) Operations § 1493.260 Facility payment guarantee. (a) CCC's maximum obligation. CCC will agree to... fails to pay under the foreign bank letter of credit or related obligation. The exact amount of CCC's...

7 CFR 1493.260 - Facility payment guarantee.

Code of Federal Regulations, 2012 CFR

2012-01-01

... OF AGRICULTURE EXPORT PROGRAMS CCC EXPORT CREDIT GUARANTEE PROGRAMS CCC Facility Guarantee Program (FGP) Operations § 1493.260 Facility payment guarantee. (a) CCC's maximum obligation. CCC will agree to... fails to pay under the foreign bank letter of credit or related obligation. The exact amount of CCC's...

7 CFR 1493.260 - Facility payment guarantee.

Code of Federal Regulations, 2014 CFR

2014-01-01

... OF AGRICULTURE EXPORT PROGRAMS CCC EXPORT CREDIT GUARANTEE PROGRAMS CCC Facility Guarantee Program (FGP) Operations § 1493.260 Facility payment guarantee. (a) CCC's maximum obligation. CCC will agree to... fails to pay under the foreign bank letter of credit or related obligation. The exact amount of CCC's...

AESS: Accelerated Exact Stochastic Simulation

NASA Astrophysics Data System (ADS)

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 method: The Accelerated Exact Stochastic Simulation (AESS) tool provides implementations of a wide variety of popular variations on the Gillespie method. Users can select the specific algorithm considered most appropriate. Comparisons between the methods and with other available implementations indicate that AESS provides the fastest known implementation of Gillespie's method for a variety of test models. Users may wish to execute ensembles of simulations to sweep parameters or to obtain better statistical results, so AESS supports acceleration of ensembles of simulation using parallel processing with MPI, SSE vector units on x86 processors, and/or using NVIDIA GPUs with CUDA.

Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane

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

Liu, Jian, E-mail: jianliupku@pku.edu.cn; State Key Joint Laboratory of Environmental Simulation and Pollution Control, College of Environmental Sciences and Engineering, Peking University, Beijing 100871; Zhang, Zhijun

Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Importance of the correlation contribution for local hybrid functionals: range separation and self-interaction corrections.

PubMed

Arbuznikov, Alexei V; Kaupp, Martin

2012-01-07

Local hybrid functionals with their position-dependent exact-exchange admixture are a conceptually simple and promising extension of the concept of a hybrid functional. Local hybrids based on a simple mixing of the local spin density approximation (LSDA) with exact exchange have been shown to be successful for thermochemistry, reaction barriers, and a range of other properties. So far, the combination of this generation of local hybrids with an LSDA correlation functional has been found to give the most favorable results for atomization energies, for a range of local mixing functions (LMFs) governing the exact-exchange admixture. Here, we show that the choice of correlation functional to be used with local hybrid exchange crucially influences the parameterization also of the exchange part as well as the overall performance. A novel ansatz for the correlation part of local hybrids is suggested based on (i) range-separation of LSDA correlation into short-range (SR) and long-range (LR) parts, and (ii) partial or full elimination of the one-electron self-correlation from the SR part. It is shown that such modified correlation functionals allow overall larger exact exchange admixture in thermochemically competitive local hybrids than before. This results in improvements for reaction barriers and for other properties crucially influenced by self-interaction errors, as demonstrated by a number of examples. Based on the range-separation approach, a fresh view on the breakdown of the correlation energy into dynamical and non-dynamical parts is suggested.

Binocular video ophthalmoscope for simultaneous recording of sequences of the human retina to compare dynamic parameters

NASA Astrophysics Data System (ADS)

Tornow, Ralf P.; Milczarek, Aleksandra; Odstrcilik, Jan; Kolar, Radim

2017-07-01

A parallel video ophthalmoscope was developed to acquire short video sequences (25 fps, 250 frames) of both eyes simultaneously with exact synchronization. Video sequences were registered off-line to compensate for eye movements. From registered video sequences dynamic parameters like cardiac cycle induced reflection changes and eye movements can be calculated and compared between eyes.

Heteroclinic switching between chimeras

NASA Astrophysics Data System (ADS)

Bick, Christian

2018-05-01

Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. We give exact results how such global dynamics can arise in paradigmatic phase oscillator networks: Higher-order network interactions give rise to metastable chimeras—localized frequency synchrony patterns—which are joined by heteroclinic connections. Moreover, we illuminate the mechanisms that underly the switching dynamics in these experimentally accessible networks.

Viscous versus inviscid exact coherent states in high Reynolds number wall flows

NASA Astrophysics Data System (ADS)

Montemuro, Brandon; Klewicki, Joe; White, Chris; Chini, Greg

2017-11-01

Streamwise-averaged motions consisting of streamwise-oriented streaks and vortices are key components of exact coherent states (ECS) arising in incompressible wall-bounded shear flows. These invariant solutions are believed to provide a scaffold in phase space for the turbulent dynamics realized at large Reynolds number Re . Nevertheless, many ECS, including upper-branch states, have a large- Re asymptotic structure in which the effective Reynolds number governing the streak and roll dynamics is order unity. Although these viscous ECS very likely play a role in the dynamics of the near-wall region, they cannot be relevant to the inertial layer, where the leading-order mean dynamics are known to be inviscid. In particular, viscous ECS cannot account for the observed regions of quasi-uniform streamwise momentum and interlaced internal shear layers (or `vortical fissures') within the inertial layer. In this work, a large- Re asymptotic analysis is performed to extend the existing self-sustaining-process/vortex-wave-interaction theory to account for largely inviscid ECS. The analysis highlights feedback mechanisms between the fissures and uniform momentum zones that can enable their self-sustenance at extreme Reynolds number. NSF CBET Award 1437851.

Multi-state trajectory approach to non-adiabatic dynamics: General formalism and the active state trajectory approximation

NASA Astrophysics Data System (ADS)

Tao, Guohua

2017-07-01

A general theoretical framework is derived for the recently developed multi-state trajectory (MST) approach from the time dependent Schrödinger equation, resulting in equations of motion for coupled nuclear-electronic dynamics equivalent to Hamilton dynamics or Heisenberg equation based on a new multistate Meyer-Miller (MM) model. The derived MST formalism incorporates both diabatic and adiabatic representations as limiting cases and reduces to Ehrenfest or Born-Oppenheimer dynamics in the mean-field or the single-state limits, respectively. In the general multistate formalism, nuclear dynamics is represented in terms of a set of individual state-specific trajectories, while in the active state trajectory (AST) approximation, only one single nuclear trajectory on the active state is propagated with its augmented images running on all other states. The AST approximation combines the advantages of consistent nuclear-coupled electronic dynamics in the MM model and the single nuclear trajectory in the trajectory surface hopping (TSH) treatment and therefore may provide a potential alternative to both Ehrenfest and TSH methods. The resulting algorithm features in a consistent description of coupled electronic-nuclear dynamics and excellent numerical stability. The implementation of the MST approach to several benchmark systems involving multiple nonadiabatic transitions and conical intersection shows reasonably good agreement with exact quantum calculations, and the results in both representations are similar in accuracy. The AST treatment also reproduces the exact results reasonably, sometimes even quantitatively well, with a better performance in the adiabatic representation.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

PubMed

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

NASA Astrophysics Data System (ADS)

Dowell, David H.; Zhou, Feng; Schmerge, John

2018-01-01

Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam's horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel their emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.

Foundations and latest advances in replica exchange transition interface sampling.

PubMed

Cabriolu, Raffaela; Skjelbred Refsnes, Kristin M; Bolhuis, Peter G; van Erp, Titus S

2017-10-21

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations.

Exact subthreshold integration with continuous spike times in discrete-time neural network simulations.

PubMed

Morrison, Abigail; Straube, Sirko; Plesser, Hans Ekkehard; Diesmann, Markus

2007-01-01

Very large networks of spiking neurons can be simulated efficiently in parallel under the constraint that spike times are bound to an equidistant time grid. Within this scheme, the subthreshold dynamics of a wide class of integrate-and-fire-type neuron models can be integrated exactly from one grid point to the next. However, the loss in accuracy caused by restricting spike times to the grid can have undesirable consequences, which has led to interest in interpolating spike times between the grid points to retrieve an adequate representation of network dynamics. We demonstrate that the exact integration scheme can be combined naturally with off-grid spike events found by interpolation. We show that by exploiting the existence of a minimal synaptic propagation delay, the need for a central event queue is removed, so that the precision of event-driven simulation on the level of single neurons is combined with the efficiency of time-driven global scheduling. Further, for neuron models with linear subthreshold dynamics, even local event queuing can be avoided, resulting in much greater efficiency on the single-neuron level. These ideas are exemplified by two implementations of a widely used neuron model. We present a measure for the efficiency of network simulations in terms of their integration error and show that for a wide range of input spike rates, the novel techniques we present are both more accurate and faster than standard techniques.

Foundations and latest advances in replica exchange transition interface sampling

NASA Astrophysics Data System (ADS)

Cabriolu, Raffaela; Skjelbred Refsnes, Kristin M.; Bolhuis, Peter G.; van Erp, Titus S.

2017-10-01

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations.

Analysis of the behavior of a wiper blade around the reversal in consideration of dynamic and static friction

NASA Astrophysics Data System (ADS)

Unno, M.; Shibata, A.; Yabuno, H.; Yanagisawa, D.; Nakano, T.

2017-04-01

Reducing noise generated by automobile windshield wipers during reversals is a desirable feature. For this purpose, details of the behavior of the wiper blade need to be ascertained. In this study, we present theoretical and experimental clarification of this behavior during reversals. Using simulation algorithms to consider exactly the effects of dynamic and static friction, we determined theoretical predictions for the vibrational response caused by friction and the response frequency and compared these results with experimental ones obtained from a mock-up incorporating an actual wiper blade. We introduce an analytical link model with two degrees of freedom and consider two types of states at the blade tip. In the stick and the slip states, static friction and dynamic friction, respectively, act on the blade tip. In the theoretical approach, the static friction is expressed by a set-valued function. The transition between the two states is repeated and an evaluation of an exact transition time leads to an accurate prediction of the behavior of the wiper system. In the analysis, the slack variable method is used to find the exact transition time. Assuming low blade speeds during reversal, a parameter study indicates that the blade tip transitions between slip and stick states and the frequency of the vibration caused by this transitions is close to the natural frequency of the neck of the wiper blade. The theoretical predictions are in good agreement with experimental observations.

Simulation program for estimating statistical power of Cox's proportional hazards model assuming no specific distribution for the survival time.

PubMed

Akazawa, K; Nakamura, T; Moriguchi, S; Shimada, M; Nose, Y

1991-07-01

Small sample properties of the maximum partial likelihood estimates for Cox's proportional hazards model depend on the sample size, the true values of regression coefficients, covariate structure, censoring pattern and possibly baseline hazard functions. Therefore, it would be difficult to construct a formula or table to calculate the exact power of a statistical test for the treatment effect in any specific clinical trial. The simulation program, written in SAS/IML, described in this paper uses Monte-Carlo methods to provide estimates of the exact power for Cox's proportional hazards model. For illustrative purposes, the program was applied to real data obtained from a clinical trial performed in Japan. Since the program does not assume any specific function for the baseline hazard, it is, in principle, applicable to any censored survival data as long as they follow Cox's proportional hazards model.

CALL on Mac.

ERIC Educational Resources Information Center

Fukuzawa, Jeannette L.; Lubin, Jan M.

Five computer programs for the Macintosh that are geared for Computer-Assisted Language Learning (CALL) are described. All five programs allow the teacher to input material. The first program allows entry of new vocabulary lists including definition, a sentence in which the exact word is used, a fill-in-the-blank exercise, and the word's phonetics…

Matrix pentagons

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2017-10-01

The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang-Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.

A program for performing exact quantum dynamics calculations using cylindrical polar coordinates: A nanotube application

NASA Astrophysics Data System (ADS)

Skouteris, Dimitris; Gervasi, Osvaldo; Laganà, Antonio

2009-03-01

A program that uses the time-dependent wavepacket method to study the motion of structureless particles in a force field of quasi-cylindrical symmetry is presented here. The program utilises cylindrical polar coordinates to express the wavepacket, which is subsequently propagated using a Chebyshev expansion of the Schrödinger propagator. Time-dependent exit flux as well as energy-dependent S matrix elements can be obtained for all states of the particle (describing its angular momentum component along the nanotube axis and the excitation of the radial degree of freedom in the cylinder). The program has been used to study the motion of an H atom across a carbon nanotube. Program summaryProgram title: CYLWAVE Catalogue identifier: AECL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3673 No. of bytes in distributed program, including test data, etc.: 35 237 Distribution format: tar.gz Programming language: Fortran 77 Computer: RISC workstations Operating system: UNIX RAM: 120 MBytes Classification: 16.7, 16.10 External routines: SUNSOFT performance library (not essential) TFFT2D.F (Temperton Fast Fourier Transform), BESSJ.F (from Numerical Recipes, for the calculation of Bessel functions) (included in the distribution file). Nature of problem: Time evolution of the state of a structureless particle in a quasicylindrical potential. Solution method: Time dependent wavepacket propagation. Running time: 50000 secs. The test run supplied with the distribution takes about 10 minutes to complete.

a Numerical Comparison of Langrange and Kane's Methods of AN Arm Segment

NASA Astrophysics Data System (ADS)

Rambely, Azmin Sham; Halim, Norhafiza Ab.; Ahmad, Rokiah Rozita

A 2-D model of a two-link kinematic chain is developed using two dynamics equations of motion, namely Kane's and Lagrange Methods. The dynamics equations are reduced to first order differential equation and solved using modified Euler and fourth order Runge Kutta to approximate the shoulder and elbow joint angles during a smash performance in badminton. Results showed that Runge-Kutta produced a better and exact approximation than that of modified Euler and both dynamic equations produced better absolute errors.

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Dynamic Stiffness Modeling of Composite Plate and Shell Assemblies

DTIC Science & Technology

2013-12-09

FA8655-10-1-3084 Report 6 Dynamic Stiffness Modelling of Plate and Shell Assemblies 4 Introduction Aerospace structures are generally made up of thin ...Sound and Vibration, 294(1- 2):131–161, 2006. [23] Y. F. Xing and B. Liu. New exact solutions for free vibrations of thin orthotropic rectangular plates ...Structures, 89(5–6):467–475, 2011. [80] A.Y.T. Leung. Dynamic stiffness analysis of laminated composite plates . Thin - Walled Structures, 25:109–133, 1996

Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng

2018-01-01

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

Diffusion in Deterministic Interacting Lattice Systems

NASA Astrophysics Data System (ADS)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

A linear model of population dynamics

NASA Astrophysics Data System (ADS)

Lushnikov, A. A.; Kagan, A. I.

2016-08-01

The Malthus process of population growth is reformulated in terms of the probability w(n,t) to find exactly n individuals at time t assuming that both the birth and the death rates are linear functions of the population size. The master equation for w(n,t) is solved exactly. It is shown that w(n,t) strongly deviates from the Poisson distribution and is expressed in terms either of Laguerre’s polynomials or a modified Bessel function. The latter expression allows for considerable simplifications of the asymptotic analysis of w(n,t).

Is There A Mechanics of Mind?

NASA Astrophysics Data System (ADS)

Jones, Robert

2008-04-01

In his book ``Extending Mechanics to Minds'' (Cambridge U. Press, 2006) Jon Doyle suggests that the human mind operates according to mechanical principles. Now in contemporary cognitive science operations in the cognitive or ``knowledge level'' are performed by lower level components of the program level. This decomposition continues from the program level down through the logic level, circuit level, and device level. Each level has its own components and each is described by its own laws of operation (Unified Theories of Cognition, Allen Newell, Harvard U. Press, 1990). The circuit and device levels could just as easily by fabricated out of mechanical elements such as linkage differentials and racks and pinions (Mechanisms and Dynamics of Machinery, Mabie and Ocvirk, John Wiley and Sons, 1975, ch. 8). These mechanisms would then be exactly those governed by the mechanical principles that Doyle focuses on. But Doyle's mistake is to apply the same laws to the cognitive level. Rather, I believe, the cognitive level is best described by operations like knowledge base search, analogy, classification, compression, etc. (R. Jones, Trans. of the Kansas Acad. of Sci., vol. 109, no. 3/4, pg 159, 2006).

Exact milestoning

PubMed Central

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. PMID:25747056

Exact symmetries in the velocity fluctuations of a hot Brownian swimmer

NASA Astrophysics Data System (ADS)

Falasco, Gianmaria; Pfaller, Richard; Bregulla, Andreas P.; Cichos, Frank; Kroy, Klaus

2016-09-01

Symmetries constrain dynamics. We test this fundamental physical principle, experimentally and by molecular dynamics simulations, for a hot Janus swimmer operating far from thermal equilibrium. Our results establish scalar and vectorial steady-state fluctuation theorems and a thermodynamic uncertainty relation that link the fluctuating particle current to its entropy production at an effective temperature. A Markovian minimal model elucidates the underlying nonequilibrium physics.

Exact coherent structures and chaotic dynamics in a model of cardiac tissue

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

Byrne, Greg; Marcotte, Christopher D.; Grigoriev, Roman O., E-mail: roman.grigoriev@physics.gatech.edu

Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low- and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are referred to as exact coherent structures (ECS) and play an important role in both initiating and sustaining turbulence. The nature of ECS and their role in organizing spatiotemporally chaotic dynamics, however, is reasonably well understood only for systems on relatively small spatial domains lacking continuous Euclidean symmetries. Construction of ECS on large domains and in the presence of continuous translational and/or rotational symmetries remains a challenge. This ismore » especially true for models of excitable media which display spiral turbulence and for which the standard approach to computing ECS completely breaks down. This paper uses the Karma model of cardiac tissue to illustrate a potential approach that could allow computing a new class of ECS on large domains of arbitrary shape by decomposing them into a patchwork of solutions on smaller domains, or tiles, which retain Euclidean symmetries locally.« less

Review of probabilistic analysis of dynamic response of systems with random parameters

NASA Technical Reports Server (NTRS)

Kozin, F.; Klosner, J. M.

1989-01-01

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence

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

Alonso, J. L.; Instituto de Biocomputacion y Fisica de Sistemas Complejos; Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, E-50018 Zaragoza

2012-08-07

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamicsmore » makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.« less

Momentum-space cluster dual-fermion method

NASA Astrophysics Data System (ADS)

Iskakov, Sergei; Terletska, Hanna; Gull, Emanuel

2018-03-01

Recent years have seen the development of two types of nonlocal extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations nonperturbatively. On the other hand, diagrammatic extensions, such as the dual-fermion theory, recover long-ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in nonperturbative regimes of phase space. In this paper, we present an exact cluster dual-fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse-graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independently of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual-fermion approximation to the single-particle self-energies and double occupancies.

On the accuracy of the LSC-IVR approach for excitation energy transfer in molecular aggregates

NASA Astrophysics Data System (ADS)

Teh, Hung-Hsuan; Cheng, Yuan-Chung

2017-04-01

We investigate the applicability of the linearized semiclassical initial value representation (LSC-IVR) method to excitation energy transfer (EET) problems in molecular aggregates by simulating the EET dynamics of a dimer model in a wide range of parameter regime and comparing the results to those obtained from a numerically exact method. It is found that the LSC-IVR approach yields accurate population relaxation rates and decoherence rates in a broad parameter regime. However, the classical approximation imposed by the LSC-IVR method does not satisfy the detailed balance condition, generally leading to incorrect equilibrium populations. Based on this observation, we propose a post-processing algorithm to solve the long time equilibrium problem and demonstrate that this long-time correction method successfully removed the deviations from exact results for the LSC-IVR method in all of the regimes studied in this work. Finally, we apply the LSC-IVR method to simulate EET dynamics in the photosynthetic Fenna-Matthews-Olson complex system, demonstrating that the LSC-IVR method with long-time correction provides excellent description of coherent EET dynamics in this typical photosynthetic pigment-protein complex.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

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.

Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

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

Dowell, David H.; Zhou, Feng; Schmerge, John

Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam’s horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel theirmore » emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.« less

Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

DOE PAGES

Dowell, David H.; Zhou, Feng; Schmerge, John

2018-01-17

Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam’s horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel theirmore » emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.« less

Correlated Light-Matter Interactions in Cavity QED

NASA Astrophysics Data System (ADS)

Flick, Johannes; Pellegrini, Camilla; Ruggenthaler, Michael; Appel, Heiko; Tokatly, Ilya; Rubio, Angel

2015-03-01

In the last decade, time-dependent density functional theory (TDDFT) has been successfully applied to a large variety of problems, such as calculations of absorption spectra, excitation energies, or dynamics in strong laser fields. Recently, we have generalized TDDFT to also describe electron-photon systems (QED-TDDFT). Here, matter and light are treated on an equal quantized footing. In this work, we present the first numerical calculations in the framework of QED-TDDFT. We show exact solutions for fully quantized prototype systems consisting of atoms or molecules placed in optical high-Q cavities and coupled to quantized electromagnetic modes. We focus on the electron-photon exchange-correlation (xc) contribution by calculating exact Kohn-Sham potentials using fixed-point inversions and present the performance of the first approximated xc-potential based on an optimized effective potential (OEP) approach. Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, and Fritz-Haber-Institut der MPG, Berlin

Atomic quantum simulation of the lattice gauge-Higgs model: Higgs couplings and emergence of exact local gauge symmetry.

PubMed

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.

[Quantitative Evaluation of Intracardiac Blood Flow by Left Ventricle Dynamic Anatovy Based On Exact Solutions of Non-Stationary Navier-Stocks Equations for Selforganized tornado-Like Flows of Viscous Incompresssible Fluid].

PubMed

Talygin, E A; Zazybo, N A; Zhorzholiany, S T; Krestinich, I M; Mironov, A A; Kiknadze, G I; Bokerya, L A; Gorodkov, A Y; Makarenko, V N; Alexandrova, S A

2016-01-01

New approach to intracardiac blood flow condition analysis based on geometric parameters of left ventricle flow channel has been suggested. Parameters, that used in this method, follow from exact solutions of nonstationary Navier-Stocks equations for selforganized tornado-like flows of viscous incompressible fluid. The main advantage of this method is considering dynamic anatomy of intracardiac cavity and trabeculae relief of left ventricle streamlined surface, both registered in a common mri-process, as flow condition indicator. Calculated quantity options that characterizes blood flow condition can be use as diagnostic criterias for estimation of violation in blood circulation function which entails heart ejection reduction. Developed approach allows to clarify heart jet organization mechanism and estimate the share of the tornado-like flow self-organization in heart ejection structure.

Dynamical analysis of a cubic Liénard system with global parameters

NASA Astrophysics Data System (ADS)

Chen, Hebai; Chen, Xingwu

2015-10-01

In this paper we investigate the dynamical behaviour of a cubic Liénard system with global parameters. After analysing the qualitative properties of all the equilibria and judging the existences of limit cycles and homoclinic loops for the whole parameter plane, we give the bifurcation diagram and phase portraits. Phase portraits are global if there exist limit cycles and local otherwise. We prove that parameters lie in a connected region, not just on a curve, usually in the parameter plane when the system has one homoclinic loop. Moreover, for global parameters we give a positive answer to conjecture 3.2 of (1998 Nonlinearity 11 1505-19) in the case of exactly two equilibria about the existence of some function whose graph is exactly the surface of double limit cycles. Supported by NSFC 11471228, 11172246 and the Fundamental Research Funds for the Central Universities.

Grazing-incidence X-ray diffraction from a crystal with subsurface defects

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

Gaevskii, A. Yu., E-mail: transilv@mail.ru; Golentus, I. E.

2015-03-15

The diffraction of X rays incident on a crystal surface under grazing angles under conditions of total external reflection has been investigated. An approach is proposed in which exact solutions to the dynamic problem of grazing-incidence diffraction in an ideal crystal are used as initial functions to calculate the diffuse component of diffraction in a crystal with defects. The diffuse component of diffraction is calculated for a crystal with surface defects of a dilatation-center type. Exact formulas of the continuum theory which take into account the mirror-image forces are used for defect-induced atomic displacements. Scattering intensity maps near Bragg peaksmore » are constructed for different scan modes, and the conditions for detecting primarily the diffuse component are determined. The results of dynamic calculations of grazing-incidence diffraction in defect-containing crystals are compared with calculations in the kinematic approximation.« less

Noether symmetry approach in the cosmological alpha-attractors

NASA Astrophysics Data System (ADS)

Kaewkhao, Narakorn; Kanesom, Thanyagamon; Channuie, Phongpichit

2018-06-01

In cosmological framework, Noether symmetry technique has revealed a useful tool in order to examine exact solutions. In this work, we first introduce the Jordan-frame Lagrangian and apply the conformal transformation in order to obtain the Lagrangian equivalent to Einstein-frame form. We then analyze the dynamics of the field in the cosmological alpha-attractors using the Noether symmetry approach by focusing on the single field scenario in the Einstein-frame form. We show that with a Noether symmetry the corresponding dynamical system can be completely integrated and the potential exhibited by the symmetry can be exactly obtained. With the proper choice of parameters, the behavior of the scale factor displays an exponential (de Sitter) behavior at the present epoch. Moreover, we discover that the Hubble parameters strongly depends on the initial values of parameters exhibited by the Noether symmetry. Interestingly, it can retardedly evolve and becomes a constant in the present epoch in all cases.

Comparison of the iterated equation of motion approach and the density matrix formalism for the quantum Rabi model

NASA Astrophysics Data System (ADS)

Kalthoff, Mona; Keim, Frederik; Krull, Holger; Uhrig, Götz S.

2017-05-01

The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results.

Efficient steady-state solver for hierarchical quantum master equations

NASA Astrophysics Data System (ADS)

Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2017-07-01

Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.

Dynamic Stability of Uncertain Laminated Beams Under Subtangential Loads

NASA Technical Reports Server (NTRS)

Goyal, Vijay K.; Kapania, Rakesh K.; Adelman, Howard (Technical Monitor); Horta, Lucas (Technical Monitor)

2002-01-01

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.

Spectral functions of strongly correlated extended systems via an exact quantum embedding

NASA Astrophysics Data System (ADS)

Booth, George H.; Chan, Garnet Kin-Lic

2015-04-01

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 109, 186404 (2012), 10.1103/PhysRevLett.109.186404], introduced an approach to quantum cluster embedding methods whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost but was inherently limited by the construction of a bath designed to reproduce ground-state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency-dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the one- (1D) and two-dimensional (2D) Hubbard model, where we obtain zero temperature and thermodynamic limit spectral functions, and show the trivial extension to two-particle Green's functions. This advance therefore extends the scope and applicability of DMET in condensed-matter problems as a computationally tractable route to correlated spectral functions of extended systems and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.

Dynamics of Coupled Electron-Boson Systems with the Multiple Davydov D1 Ansatz and the Generalized Coherent State.

PubMed

Chen, Lipeng; Borrelli, Raffaele; Zhao, Yang

2017-11-22

The dynamics of a coupled electron-boson system is investigated by employing a multitude of the Davydov D 1 trial states, also known as the multi-D 1 Ansatz, and a second trial state based on a superposition of the time-dependent generalized coherent state (GCS Ansatz). The two Ansätze are applied to study population dynamics in the spin-boson model and the Holstein molecular crystal model, and a detailed comparison with numerically exact results obtained by the (multilayer) multiconfiguration time-dependent Hartree method and the hierarchy equations of motion approach is drawn. It is found that the two methodologies proposed here have significantly improved over that with the single D 1 Ansatz, yielding quantitatively accurate results even in the critical cases of large energy biases and large transfer integrals. The two methodologies provide new effective tools for accurate, efficient simulation of many-body quantum dynamics thanks to a relatively small number of parameters which characterize the electron-nuclear wave functions. The wave-function-based approaches are capable of tracking explicitly detailed bosonic dynamics, which is absent by construct in approaches based on the reduced density matrix. The efficiency and flexibility of our methods are also advantages as compared with numerically exact approaches such as QUAPI and HEOM, especially at low temperatures and in the strong coupling regime.

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

PubMed

Hele, Timothy J H; Willatt, Michael J; Muolo, Andrea; Althorpe, Stuart C

2015-04-07

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

A quantum dynamical study of the rotation of the dihydrogen ligand in the Fe(H)2(H2)(PEtPh2)3 coordination complex.

PubMed

Gonzalez, Megan E; Eckert, Juergen; Aquino, Adelia J A; Poirier, Bill

2018-04-21

Progress in the hydrogen fuel field requires a clear understanding and characterization of how materials of interest interact with hydrogen. Due to the inherently quantum mechanical nature of hydrogen nuclei, any theoretical studies of these systems must be treated quantum dynamically. One class of material that has been examined in this context are dihydrogen complexes. Since their discovery by Kubas in 1984, many such complexes have been studied both experimentally and theoretically. This particular study examines the rotational dynamics of the dihydrogen ligand in the Fe(H) 2 (H 2 )(PEtPh 2 ) 3 complex, allowing for full motion in both the rotational degrees of freedom and treating the quantum dynamics (QD) explicitly. A "gas-phase" global potential energy surface is first constructed using density functional theory with the Becke, 3-parameter, Lee-Yang-Parr functional; this is followed by an exact QD calculation of the corresponding rotation/libration states. The results provide insight into the dynamical correlation of the two rotation angles as well as a comprehensive analysis of both ground- and excited-state librational tunneling splittings. The latter was computed to be 6.914 cm -1 -in excellent agreement with the experimental value of 6.4 cm -1 . This work represents the first full-dimensional ab initio exact QD calculation ever performed for dihydrogen ligand rotation in a coordination complex.

A quantum dynamical study of the rotation of the dihydrogen ligand in the Fe(H)2(H2)(PEtPh2)3 coordination complex

NASA Astrophysics Data System (ADS)

Gonzalez, Megan E.; Eckert, Juergen; Aquino, Adelia J. A.; Poirier, Bill

2018-04-01

Progress in the hydrogen fuel field requires a clear understanding and characterization of how materials of interest interact with hydrogen. Due to the inherently quantum mechanical nature of hydrogen nuclei, any theoretical studies of these systems must be treated quantum dynamically. One class of material that has been examined in this context are dihydrogen complexes. Since their discovery by Kubas in 1984, many such complexes have been studied both experimentally and theoretically. This particular study examines the rotational dynamics of the dihydrogen ligand in the Fe(H)2(H2)(PEtPh2)3 complex, allowing for full motion in both the rotational degrees of freedom and treating the quantum dynamics (QD) explicitly. A "gas-phase" global potential energy surface is first constructed using density functional theory with the Becke, 3-parameter, Lee-Yang-Parr functional; this is followed by an exact QD calculation of the corresponding rotation/libration states. The results provide insight into the dynamical correlation of the two rotation angles as well as a comprehensive analysis of both ground- and excited-state librational tunneling splittings. The latter was computed to be 6.914 cm-1—in excellent agreement with the experimental value of 6.4 cm-1. This work represents the first full-dimensional ab initio exact QD calculation ever performed for dihydrogen ligand rotation in a coordination complex.

Resumming the large-N approximation for time evolving quantum systems

NASA Astrophysics Data System (ADS)

Mihaila, Bogdan; Dawson, John F.; Cooper, Fred

2001-05-01

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is L(x,ẋ)=(12)∑Ni=1x˙2i-(g/8N)[∑Ni=1x2i- r20]2. The key to these approximations is to treat both the x propagator and the x2 propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the x2 propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact x2 propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest N better than the dynamic Debye screening approximation.

Global ice sheet/RSL simulations using the higher-order Ice Sheet System Model.

NASA Astrophysics Data System (ADS)

Larour, E. Y.; Ivins, E. R.; Adhikari, S.; Schlegel, N.; Seroussi, H. L.; Morlighem, M.

2017-12-01

Relative sea-level rise is driven by processes that are intimately linked to the evolution ofglacial areas and ice sheets in particular. So far, most Earth System models capable of projecting theevolution of RSL on decadal to centennial time scales have relied on offline interactions between RSL andice sheets. In particular, grounding line and calving front dynamics have not been modeled in a way that istightly coupled with Elasto-Static Adjustment (ESA) and/or Glacial-Isostatic Adjustment (GIA). Here, we presenta new simulation of the entire Earth System in which both Greenland and Antarctica ice sheets are tightly coupledto an RSL model that includes both ESA and GIA at resolutions and time scales compatible with processes suchas grounding line dynamics for Antarctica ice shelves and calving front dynamics for Greenland marine-terminatingglaciers. The simulations rely on the Ice Sheet System Model (ISSM) and show the impact of higher-orderice flow dynamics and coupling feedbacks between ice flow and RSL. We quantify the exact impact of ESA andGIA inclusion on grounding line evolution for large ice shelves such as the Ronne and Ross ice shelves, as well asthe Agasea Embayment ice streams, and demonstate how offline vs online RSL simulations diverge in the long run,and the consequences for predictions of sea-level rise.This work was performed at the California Institute of Technology's Jet Propulsion Laboratory undera contract with the National Aeronautics and Space Administration's Cryosphere Science Program.

Manycast routing, modulation level and spectrum assignment over elastic optical networks

NASA Astrophysics Data System (ADS)

Luo, Xiao; Zhao, Yang; Chen, Xue; Wang, Lei; Zhang, Min; Zhang, Jie; Ji, Yuefeng; Wang, Huitao; Wang, Taili

2017-07-01

Manycast is a point to multi-point transmission framework that requires a subset of destination nodes successfully reached. It is particularly applicable for dealing with large amounts of data simultaneously in bandwidth-hungry, dynamic and cloud-based applications. As rapid increasing of traffics in these applications, the elastic optical networks (EONs) may be relied on to achieve high throughput manycast. In terms of finer spectrum granularity, the EONs could reach flexible accessing to network spectrum and efficient providing exact spectrum resource to demands. In this paper, we focus on the manycast routing, modulation level and spectrum assignment (MA-RMLSA) problem in EONs. Both EONs planning with static manycast traffic and EONs provisioning with dynamic manycast traffic are investigated. An integer linear programming (ILP) model is formulated to derive MA-RMLSA problem in static manycast scenario. Then corresponding heuristic algorithm called manycast routing, modulation level and spectrum assignment genetic algorithm (MA-RMLSA-GA) is proposed to adapt for both static and dynamic manycast scenarios. The MA-RMLSA-GA optimizes MA-RMLSA problem in destination nodes selection, routing light-tree constitution, modulation level allocation and spectrum resource assignment jointly, to achieve an effective improvement in network performance. Simulation results reveal that MA-RMLSA strategies offered by MA-RMLSA-GA have slightly disparity from the optimal solutions provided by ILP model in static scenario. Moreover, the results demonstrate that MA-RMLSA-GA realizes a highly efficient MA-RMLSA strategy with the lowest blocking probability in dynamic scenario compared with benchmark algorithms.

Scheduling Capacitated One-Way Vehicles on Paths with Deadlines

NASA Astrophysics Data System (ADS)

Uchida, Jun; Karuno, Yoshiyuki; Nagamochi, Hiroshi

In this paper, we deal with a scheduling problem of minimizing the number of employed vehicles on paths. Let G=(V,E) be a path with a set V={vi|i=1,2,...,n} of vertices and a set E={{vi,vi+1}|i=1,2,...,n-1} of edges. Vehicles with capacity b are initially situated at v1. There is a job i at each vertex vi∈V, which has its own handling time hi and deadline di. With each edge {vi,vi+1}∈E, a travel time wi,i+1 is associated. Each job is processed by exactly one vehicle, and the number of jobs processed by a vehicle does not exceed the capacity b. A routing of a vehicle is called one-way if the vehicle visits every edge {vi,vi+1} exactly once (i.e., it simply moves from v1 to vn on G). Any vehicle is assumed to follow the one-way routing constraint. The problem asks to find a schedule that minimizes the number of one-way vehicles, meeting the deadline and capacity constraints. A greedy heuristic is proposed, which repeats a dynamic programming procedure for a single one-way vehicle problem of maximizing the number of non-tardy jobs. We show that the greedy heuristic runs in O(n3) time, and the approximation ratio is at most ln b+1.

40 CFR 82.122 - Certification, recordkeeping, and notice requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... following address: Labeling Program Manager, Stratospheric Protection Division, Office of Atmospheric... (CONTINUED) AIR PROGRAMS (CONTINUED) PROTECTION OF STRATOSPHERIC OZONE The Labeling of Products Using Ozone... following information: (i) The exact location of documents verifying calendar year 1990 usage and the 95...

40 CFR 82.122 - Certification, recordkeeping, and notice requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... following address: Labeling Program Manager, Stratospheric Protection Division, Office of Atmospheric... (CONTINUED) AIR PROGRAMS (CONTINUED) PROTECTION OF STRATOSPHERIC OZONE The Labeling of Products Using Ozone... following information: (i) The exact location of documents verifying calendar year 1990 usage and the 95...

40 CFR 82.122 - Certification, recordkeeping, and notice requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... following address: Labeling Program Manager, Stratospheric Protection Division, Office of Atmospheric... (CONTINUED) AIR PROGRAMS (CONTINUED) PROTECTION OF STRATOSPHERIC OZONE The Labeling of Products Using Ozone... following information: (i) The exact location of documents verifying calendar year 1990 usage and the 95...

Applying dynamic Bayesian networks to perturbed gene expression data.

PubMed

Dojer, Norbert; Gambin, Anna; Mizera, Andrzej; Wilczyński, Bartek; Tiuryn, Jerzy

2006-05-08

A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

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

NASA Astrophysics Data System (ADS)

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.

Exact lower and upper bounds on stationary moments in stochastic biochemical systems

NASA Astrophysics Data System (ADS)

Ghusinga, Khem Raj; Vargas-Garcia, Cesar A.; Lamperski, Andrew; Singh, Abhyudai

2017-08-01

In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to find exact lower and upper bounds on stationary moments for a given arbitrary system of biochemical reactions. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints that are compactly represented through the positive semidefiniteness of moment matrices. Our analysis shows that solving moment equations at steady state in conjunction with constraints on moment matrices provides exact lower and upper bounds on the moments. These results are illustrated by three different examples—the commonly used logistic growth model, stochastic gene expression with auto-regulation and an activator-repressor gene network motif. Interestingly, in all cases the accuracy of the bounds is shown to improve as moment equations are expanded to include higher-order moments. Our results provide avenues for development of approximation methods that provide explicit bounds on moments for nonlinear stochastic systems that are otherwise analytically intractable.

Extending the Applicability of Exact Nuclear Overhauser Enhancements to Large Proteins and RNA.

PubMed

Nichols, Parker; Born, Alexandra; Henen, Morkos; Strotz, Dean; Chi, Celestine N; Güntert, Peter; Vögeli, Beat Rolf

2018-06-08

Distance-dependent NOEs are one of the most popular and important experimental restraints for calculating NMR structures. Despite this, they are mostly employed as semi-quantitative upper distance bounds, which discards a wealth of information that is encoded in the cross-relaxation rate constant. Information that is lost includes exact distances between protons and dynamics that occur on the sub-millisecond time-scale. Our recently introduced exact measurement of the NOE (eNOE) requires little additional experimental effort relative to other NMR observables. So far, we have used eNOEs to calculate multi-state ensembles of proteins up to ~150 residues. Here, we briefly revisit the eNOE methodology and present two new directions for the use of eNOEs: Applications to large proteins and RNA. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Non-equilibrium dynamics from RPMD and CMD.

PubMed

Welsch, Ralph; Song, Kai; Shi, Qiang; Althorpe, Stuart C; Miller, Thomas F

2016-11-28

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t 4 ) and O(t 1 ), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t 5 ) and O(t 2 ), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

[The province of East Prussia and "euthanasia" during national socialism: the SS-"Aktion Lange" and "Aktion T4"].

PubMed

Topp, Sascha; Fuchs, Petra; Hohendorf, Gerrit; Richter, Paul; Rotzoll, Maike

2008-01-01

During World War II, psychiatric patients hospitalized in asylums in Eastern Prussia became victims of two separate killing programmes: first, by the SS-special command Lange, second by the centrally (in Berlin) organized "euthanasia"-"Aktion T4". By an analysis of the patient files of the victims, the present paper shows that the historical actors responsible for the killings were communicating with each other. It is now also possible to reconstruct the exact dynamic in time and space of the killings. A comparative analysis of the selection criteria within the total population of the asylums documents that in both programs, the responsible historical actors included physicians and provincial administrative personnel; it further shows that under the conditions of war, only patients who were able to contribute to the asylum work and economy, and were behaviourally adapted could survive.

Optimisation algorithms for ECG data compression.

PubMed

Haugland, D; Heber, J G; Husøy, J H

1997-07-01

The use of exact optimisation algorithms for compressing digital electrocardiograms (ECGs) is demonstrated. As opposed to traditional time-domain methods, which use heuristics to select a small subset of representative signal samples, the problem of selecting the subset is formulated in rigorous mathematical terms. This approach makes it possible to derive algorithms guaranteeing the smallest possible reconstruction error when a bounded selection of signal samples is interpolated. The proposed model resembles well-known network models and is solved by a cubic dynamic programming algorithm. When applied to standard test problems, the algorithm produces a compressed representation for which the distortion is about one-half of that obtained by traditional time-domain compression techniques at reasonable compression ratios. This illustrates that, in terms of the accuracy of decoded signals, existing time-domain heuristics for ECG compression may be far from what is theoretically achievable. The paper is an attempt to bridge this gap.

Conformal dynamics of precursors to fracture

NASA Astrophysics Data System (ADS)

Barra, F.; Herrera, M.; Procaccia, I.

2003-09-01

An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and the stability of a circular cavity under biaxial stress, including the effects of surface stress.

Dynamics of Robertson–Walker spacetimes with diffusion

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

Alho, A., E-mail: aalho@math.ist.utl.pt; Calogero, S., E-mail: calogero@chalmers.se; Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt

2015-03-15

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.

Geometry and dynamics in the fractional discrete Fourier transform.

PubMed

Wolf, Kurt Bernardo; Krötzsch, Guillermo

2007-03-01

The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.

Analytical study of the critical behavior of the nonlinear pendulum

NASA Astrophysics Data System (ADS)

Lima, F. M. S.

2010-11-01

The dynamics of a simple pendulum consisting of a small bob and a massless rigid rod has three possible regimes depending on its total energy E: Oscillatory (when E is not enough for the pendulum to reach the top position), "perpetual ascent" when E is exactly the energy needed to reach the top, and nonoscillatory for greater energies. In the latter regime, the pendulum rotates periodically without velocity inversions. In contrast to the oscillatory regime, for which an exact analytic solution is known, the other two regimes are usually studied by solving the equation of motion numerically. By applying conservation of energy, I derive exact analytical solutions to both the perpetual ascent and nonoscillatory regimes and an exact expression for the pendulum period in the nonoscillatory regime. Based on Cromer's approximation for the large-angle pendulum period, I find a simple approximate expression for the decrease of the period with the initial velocity in the nonoscillatory regime, valid near the critical velocity. This expression is used to study the critical slowing down, which is observed near the transition between the oscillatory and nonoscillatory regimes.

Density-dependent resistance of the gypsy moth, Lymantria dispar, to its nucleopolyhedrovirus

Treesearch

James R. Reilly; Ann E. Hajek

2007-01-01

The processes controlling disease resistance can strongly influence the population dynamics of insect outbreaks. Evidence that disease resistance is density-dependent is accumulating, but the exact form of this relationship is highly variable from species to species.

A three-dimensional autonomous nonlinear dynamical system modelling equatorial ocean flows

NASA Astrophysics Data System (ADS)

Ionescu-Kruse, Delia

2018-04-01

We investigate a nonlinear three-dimensional model for equatorial flows, finding exact solutions that capture the most relevant geophysical features: depth-dependent currents, poleward or equatorial surface drift and a vertical mixture of upward and downward motions.

The molecular dynamics of adsorption and dissociation of O{sub 2} on Pt(553)

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

Jacobse, Leon, E-mail: l.jacobse@chem.leidenuniv.nl; Dunnen, Angela den; Juurlink, Ludo B. F.

2015-07-07

Molecular adsorption and dissociation of O{sub 2} on the stepped Pt(553) surface have been investigated using supersonic molecular beam techniques and temperature programmed desorption. The initial and coverage-dependent sticking probability was determined with the King and Wells technique for various combinations of incident kinetic energy, surface temperature, incident angle, and surface coverage. A comparison with similar data for Pt(533) and Pt(110)(1 × 2) shows quantitatively the same high step-induced sticking at low incident energies compared to Pt(111). The enhancement is therefore insensitive to the exact arrangement of atoms forming surface corrugation. We consider energy transfer and electronic effects to explainmore » the enhanced sticking. On the other hand, dissociation dynamics at higher incident kinetic energies are strongly dependent on step type. The Pt(553) and Pt(533) surfaces are more reactive than Pt(111), but the (100) step shows higher sticking than the (110) step. We relate this difference to a variation in the effective lowering of the barrier to dissociation from molecularly adsorbed states into atomic states. Our findings are in line with results from experimental desorption studies and theoretical studies of atomic binding energies. We discuss the influence of the different step types on sticking and dissociation dynamics with a one-dimensional potential energy surface.« less

Interlaced coarse-graining for the dynamical cluster approximation

NASA Astrophysics Data System (ADS)

Haehner, Urs; Staar, Peter; Jiang, Mi; Maier, Thomas; Schulthess, Thomas

The negative sign problem remains a challenging limiting factor in quantum Monte Carlo simulations of strongly correlated fermionic many-body systems. The dynamical cluster approximation (DCA) makes this problem less severe by coarse-graining the momentum space to map the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. We show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which with increasing cluster size converge to the results obtained using the standard coarse-graining. In addition, the new coarse-graining reduces the severity of the fermionic sign problem. Therefore, it enables calculations on much larger clusters and can allow the evaluation of the exact infinite cluster size result via finite size scaling. To demonstrate this, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the DCA+ algorithm permits the determination of the superconducting Tc on cluster sizes, for which the results can be fitted with the Kosterlitz-Thouless scaling law. This research used resources of the Oak Ridge Leadership Computing Facility (OLCF) awarded by the INCITE program, and of the Swiss National Supercomputing Center. OLCF is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.

Estimating the hemodynamic impact of interventional treatments of aneurysms: numerical simulation with experimental validation: technical case report.

PubMed

Acevedo-Bolton, Gabriel; Jou, Liang-Der; Dispensa, Bradley P; Lawton, Michael T; Higashida, Randall T; Martin, Alastair J; Young, William L; Saloner, David

2006-08-01

The goal of this study was to use phase-contrast magnetic resonance imaging and computational fluid dynamics to estimate the hemodynamic outcome that might result from different interventional options for treating a patient with a giant fusiform aneurysm. We followed a group of patients with giant intracranial aneurysms who have no clear surgical options. One patient demonstrated dramatic aneurysm growth and was selected for further analysis. The aneurysm geometry and input and output flow conditions were measured with contrast-enhanced magnetic resonance angiography and phase-contrast magnetic resonance imaging. The data was imported into a computational fluid dynamics program and the velocity fields and wall shear stress distributions were calculated for the presenting physiological condition and for cases in which the opposing vertebral arteries were either occluded or opened. These models were validated with in vitro flow experiments using a geometrically exact silicone flow phantom. Simulation indicated that altering the flow ratio in the two vertebrals would deflect the main blood jet into the aneurysm belly, and that this would likely reduce the extent of the region of low wall shear stress in the growth zone. Computational fluid dynamics flow simulations in a complex patient-specific aneurysm geometry were validated by in vivo and in vitro phase-contrast magnetic resonance imaging, and were shown to be useful in modeling the likely hemodynamic impact of interventional treatment of the aneurysm.

A Windows application for computing standardized mortality ratios and standardized incidence ratios in cohort studies based on calculation of exact person-years at risk.

PubMed

Geiss, Karla; Meyer, Martin

2013-09-01

Standardized mortality ratios and standardized incidence ratios are widely used in cohort studies to compare mortality or incidence in a study population to that in the general population on a age-time-specific basis, but their computation is not included in standard statistical software packages. Here we present a user-friendly Microsoft Windows program for computing standardized mortality ratios and standardized incidence ratios based on calculation of exact person-years at risk stratified by sex, age and calendar time. The program offers flexible import of different file formats for input data and easy handling of general population reference rate tables, such as mortality or incidence tables exported from cancer registry databases. The application of the program is illustrated with two examples using empirical data from the Bavarian Cancer Registry. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Selecting the Final Model — Joinpoint Help System 4.4.0.0

Cancer.gov

Why doesn't the joinpoint program give me the best possible fit? I can see other models with more joinpoints that would fit better. Exactly how does the program decide which tests to perform and which joinpoint model is the final model?

Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

NASA Astrophysics Data System (ADS)

Demina, Maria V.

2018-05-01

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing-van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing-van der Pol system are constructed.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Exact short-time height distribution for the flat Kardar-Parisi-Zhang interface

NASA Astrophysics Data System (ADS)

Smith, Naftali R.; Meerson, Baruch

2018-05-01

We determine the exact short-time distribution -lnPf(" close=")H ,t )">H ,t =Sf(H )/√{t } of the one-point height H =h (x =0 ,t ) of an evolving 1 +1 Kardar-Parisi-Zhang (KPZ) interface for flat initial condition. This is achieved by combining (i) the optimal fluctuation method, (ii) a time-reversal symmetry of the KPZ equation in 1 +1 dimension, and (iii) the recently determined exact short-time height distribution -lnPst(H ) of the latter, one encounters two branches: an analytic and a nonanalytic. The analytic branch is nonphysical beyond a critical value of H where a second-order dynamical phase transition occurs. Here we show that, remarkably, it is the analytic branch of Sst(H ) which determines the large-deviation function Sf(H ) of the flat interface via a simple mapping Sf(H )=2-3 /2SstLigand reorganization and activation energies in nonadiabatic electron transfer reactions

NASA Astrophysics Data System (ADS)

Zhu, Jianjun; Wang, Jianji; Stell, George

2006-10-01

The activation energy and ligand reorganization energy for nonadiabatic electron transfer reactions in chemical and biological systems are investigated in this paper. The free energy surfaces and the activation energy are derived exactly in the general case in which the ligand vibration frequencies are not equal. The activation energy is derived by free energy minimization at the transition state. Our formulation leads to the Marcus-Hush [J. Chem. Phys. 24, 979 (1956); 98, 7170 (1994); 28, 962 (1958)] results in the equal-frequency limit and also generalizes the Marcus-Sumi [J. Chem. Phys. 84, 4894 (1986)] model in the context of studying the solvent dynamic effect on electron transfer reactions. It is found that when the ligand vibration frequencies are different, the activation energy derived from the Marcus-Hush formula deviates by 5%-10% from the exact value. If the reduced reorganization energy approximation is introduced in the Marcus-Hush formula, the result is almost exact.

Spontaneous light emission by atomic hydrogen: Fermi's golden rule without cheating

NASA Astrophysics Data System (ADS)

Debierre, V.; Durt, T.; Nicolet, A.; Zolla, F.

2015-10-01

Focusing on the 2 p- 1 s transition in atomic hydrogen, we investigate through first order perturbation theory the time evolution of the survival probability of an electron initially taken to be in the excited (2 p) state. We examine both the results yielded by the standard dipole approximation for the coupling between the atom and the electromagnetic field - for which we propose a cutoff-independent regularisation - and those yielded by the exact coupling function. In both cases, Fermi's golden rule is shown to be an excellent approximation for the system at hand: we found its maximal deviation from the exact behaviour of the system to be of order 10-8 /10-7. Our treatment also yields a rigorous prescription for the choice of the optimal cutoff frequency in the dipole approximation. With our cutoff, the predictions of the dipole approximation are almost indistinguishable at all times from the exact dynamics of the system.

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

NASA Astrophysics Data System (ADS)

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.

Hairpin exact coherent states in channel flow

NASA Astrophysics Data System (ADS)

Graham, Michael; Shekar, Ashwin

2017-11-01

Questions remain over the role of hairpin vortices in fully developed turbulent flows. Studies have shown that hairpins play a role in the dynamics away from the wall but the question still persists if they play any part in (near wall) fully developed turbulent dynamics. In addition, the robustness of the hairpin vortex regeneration mechanism is still under investigation. Recent studies have shown the existence of nonlinear traveling wave solutions to the Navier-Stokes equations, also known as exact coherent states (ECS), that capture many aspects of near-wall turbulent structures. Previously discovered ECS in channel flow have a quasi-streamwise vortex structure, with no indication of hairpin formation. Here we present a family of traveling wave solutions for channel flow that displays hairpin vortices. They have a streamwise vortex-streak structure near the wall with a spatially localized hairpin head near the channel centerline, attached to and sustained by the near wall structures. This family of solutions emerges through a transcritical bifurcation from a branch of traveling wave solutions with y and z reflectional symmetry. We also look into the instabilities that lead to the development of hairpins also explore its connection to turbulent dynamics.

Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.

PubMed

Diakonos, F K; Katsimiga, G C; Maintas, X N; Tsagkarakis, C E

2015-02-01

We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass (m(H)) to the gauge-field mass (m(A)). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum," for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

NASA Astrophysics Data System (ADS)

Yalouz, S.; Falvo, C.; Pouthier, V.

2017-06-01

Based on the operatorial formulation of perturbation theory, the dynamical properties of a Frenkel exciton coupled with a thermal phonon bath on a star graph are studied. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud, whereas the phonons are dressed by virtual excitonic transitions. Special attention is paid to the description of the coherence of a qubit state initially located on the central node of the graph. Within the nonadiabatic weak coupling limit, it is shown that several timescales govern the coherence dynamics. In the short time limit, the coherence behaves as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place, this decoherence being enhanced by the size of the graph and by temperature. However, the coherence does not vanish in the long time limit. Instead, it exhibits incomplete revivals that occur periodically at specific revival times and it shows almost exact recurrences that take place at particular super-revival times, a singular behavior that has been corroborated by performing exact quantum calculations.

Dynamics of a modified Hindmarsh-Rose neural model with random perturbations: Moment analysis and firing activities

NASA Astrophysics Data System (ADS)

Mondal, Argha; Upadhyay, Ranjit Kumar

2017-11-01

In this paper, an attempt has been made to understand the activity of mean membrane voltage and subsidiary system variables with moment equations (i.e., mean, variance and covariance's) under noisy environment. We consider a biophysically plausible modified Hindmarsh-Rose (H-R) neural system injected by an applied current exhibiting spiking-bursting phenomenon. The effects of predominant parameters on the dynamical behavior of a modified H-R system are investigated. Numerically, it exhibits period-doubling, period halving bifurcation and chaos phenomena. Further, a nonlinear system has been analyzed for the first and second order moments with additive stochastic perturbations. It has been solved using fourth order Runge-Kutta method and noisy systems by Euler's scheme. It has been demonstrated that the firing properties of neurons to evoke an action potential in a certain parameter space of the large exact systems can be estimated using an approximated model. Strong stimulation can cause a change in increase or decrease of the firing patterns. Corresponding to a fixed set of parameter values, the firing behavior and dynamical differences of the collective variables of a large, exact and approximated systems are investigated.

At the end of a moving string

NASA Astrophysics Data System (ADS)

Hanna, James; Santangelo, Christian

2012-11-01

We address a basic problem in the dynamics of flexible bodies: the propagation of a shape along a string and its reflection at a free boundary. Although the string equations - inertia balancing stress in an inextensible curve - are quite old, the only exact solutions known for non-trivial geometries are traveling waves with spatially uniform stress. Suitable for closed ``lariats,'' these solutions are incompatible with a free end, where the stress must vanish. It is impossible to drag an open, flexible, curved string along its tangents. This is reflected in the unwrapping motion of a string or chain as it is pulled around an object, and has strong implications for slender structures in passive locomotion, whether industrial cables or the ribbons of rhythmic gymnastics. We consider planar dynamics restricted to time-independent, but spatially varying, stress. We find a new exact solution at a distance ~t4/3 from the free end; continuation to the end requires introduction of a secular error into the positions and velocities and a singularity in acceleration ~t-2/3 at the end, which appears to have a physical basis. This work is an early step towards understanding the dynamics of a wide class of industrial and natural thin-object systems.

Water dynamics: Gliding and trudging

NASA Astrophysics Data System (ADS)

Itoh, Yoshimitsu; Aida, Takuzo

2017-10-01

Water is increasingly recognized as being of paramount importance in biological processes, yet its exact role remains difficult to elucidate. Now, the motion of water molecules within and around a synthetic peptide-amphiphile nanofibre has been precisely determined, showing significant differences between its core and surface.

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP. Part 2; Coupled Versus Uncoupled Integration

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Ibrahim, Omar M.; Abdallah, Ayman A.; Sullivan, Timothy L.

1993-01-01

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

Attitude control with realization of linear error dynamics

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Bach, Ralph E.

1993-01-01

An attitude control law is derived to realize linear unforced error dynamics with the attitude error defined in terms of rotation group algebra (rather than vector algebra). Euler parameters are used in the rotational dynamics model because they are globally nonsingular, but only the minimal three Euler parameters are used in the error dynamics model because they have no nonlinear mathematical constraints to prevent the realization of linear error dynamics. The control law is singular only when the attitude error angle is exactly pi rad about any eigenaxis, and a simple intuitive modification at the singularity allows the control law to be used globally. The forced error dynamics are nonlinear but stable. Numerical simulation tests show that the control law performs robustly for both initial attitude acquisition and attitude control.

A new approach for describing glass transition kinetics.

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

Vasin, N. M.; Shchelkachev, M. G.; Vinokur, V. M.

2010-04-01

We use a functional integral technique generalizing the Keldysh diagram technique to describe glass transition kinetics. We show that the Keldysh functional approach takes the dynamical determinant arising in the glass dynamics into account exactly and generalizes the traditional approach based on using the supersymmetric dynamic generating functional method. In contrast to the supersymmetric method, this approach allows avoiding additional Grassmannian fields and tracking the violation of the fluctuation-dissipation theorem explicitly. We use this method to describe the dynamics of an Edwards-Anderson soft spin-glass-type model near the paramagnet-glass transition. We show that a Vogel-Fulcher-type dynamics arises in the fluctuation regionmore » only if the fluctuation-dissipation theorem is violated in the process of dynamical renormalization of the Keldysh action in the replica space.« less

Few-body quark dynamics for doubly heavy baryons and tetraquarks

NASA Astrophysics Data System (ADS)

Richard, Jean-Marc; Valcarce, Alfredo; Vijande, Javier

2018-03-01

We discuss the adequate treatment of the three- and four-body dynamics for the quark model picture of double-charm baryons and tetraquarks. We stress that the variational and Born-Oppenheimer approximations give energies very close to the exact ones, while the diquark approximation might be somewhat misleading. The Hall-Post inequalities also provide very useful lower bounds that exclude the possibility of stable tetraquarks for some mass ratios and some color wave functions.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

NASA Astrophysics Data System (ADS)

Lacasa, Lucas

2014-09-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein-Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments.

Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution.

PubMed

Orr, Lindsay; Hernández de la Peña, Lisandro; Roy, Pierre-Nicholas

2017-06-07

A derivation of quantum statistical mechanics based on the concept of a Feynman path centroid is presented for the case of generalized density operators using the projected density operator formalism of Blinov and Roy [J. Chem. Phys. 115, 7822-7831 (2001)]. The resulting centroid densities, centroid symbols, and centroid correlation functions are formulated and analyzed in the context of the canonical equilibrium picture of Jang and Voth [J. Chem. Phys. 111, 2357-2370 (1999)]. The case where the density operator projects onto a particular energy eigenstate of the system is discussed, and it is shown that one can extract microcanonical dynamical information from double Kubo transformed correlation functions. It is also shown that the proposed projection operator approach can be used to formally connect the centroid and Wigner phase-space distributions in the zero reciprocal temperature β limit. A Centroid Molecular Dynamics (CMD) approximation to the state-projected exact quantum dynamics is proposed and proven to be exact in the harmonic limit. The state projected CMD method is also tested numerically for a quartic oscillator and a double-well potential and found to be more accurate than canonical CMD. In the case of a ground state projection, this method can resolve tunnelling splittings of the double well problem in the higher barrier regime where canonical CMD fails. Finally, the state-projected CMD framework is cast in a path integral form.

Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution

NASA Astrophysics Data System (ADS)

Orr, Lindsay; Hernández de la Peña, Lisandro; Roy, Pierre-Nicholas

2017-06-01

A derivation of quantum statistical mechanics based on the concept of a Feynman path centroid is presented for the case of generalized density operators using the projected density operator formalism of Blinov and Roy [J. Chem. Phys. 115, 7822-7831 (2001)]. The resulting centroid densities, centroid symbols, and centroid correlation functions are formulated and analyzed in the context of the canonical equilibrium picture of Jang and Voth [J. Chem. Phys. 111, 2357-2370 (1999)]. The case where the density operator projects onto a particular energy eigenstate of the system is discussed, and it is shown that one can extract microcanonical dynamical information from double Kubo transformed correlation functions. It is also shown that the proposed projection operator approach can be used to formally connect the centroid and Wigner phase-space distributions in the zero reciprocal temperature β limit. A Centroid Molecular Dynamics (CMD) approximation to the state-projected exact quantum dynamics is proposed and proven to be exact in the harmonic limit. The state projected CMD method is also tested numerically for a quartic oscillator and a double-well potential and found to be more accurate than canonical CMD. In the case of a ground state projection, this method can resolve tunnelling splittings of the double well problem in the higher barrier regime where canonical CMD fails. Finally, the state-projected CMD framework is cast in a path integral form.

Oscillatory phase dynamics in neural entrainment underpin illusory percepts of time.

PubMed

Herrmann, Björn; Henry, Molly J; Grigutsch, Maren; Obleser, Jonas

2013-10-02

Neural oscillatory dynamics are a candidate mechanism to steer perception of time and temporal rate change. While oscillator models of time perception are strongly supported by behavioral evidence, a direct link to neural oscillations and oscillatory entrainment has not yet been provided. In addition, it has thus far remained unaddressed how context-induced illusory percepts of time are coded for in oscillator models of time perception. To investigate these questions, we used magnetoencephalography and examined the neural oscillatory dynamics that underpin pitch-induced illusory percepts of temporal rate change. Human participants listened to frequency-modulated sounds that varied over time in both modulation rate and pitch, and judged the direction of rate change (decrease vs increase). Our results demonstrate distinct neural mechanisms of rate perception: Modulation rate changes directly affected listeners' rate percept as well as the exact frequency of the neural oscillation. However, pitch-induced illusory rate changes were unrelated to the exact frequency of the neural responses. The rate change illusion was instead linked to changes in neural phase patterns, which allowed for single-trial decoding of percepts. That is, illusory underestimations or overestimations of perceived rate change were tightly coupled to increased intertrial phase coherence and changes in cerebro-acoustic phase lag. The results provide insight on how illusory percepts of time are coded for by neural oscillatory dynamics.

Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.

PubMed

Ma, Li-Yuan; Zhu, Zuo-Nong

2014-09-01

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.

COMPRESSIBLE FLOW, ENTRAINMENT, AND MEGAPLUME

EPA Science Inventory

It is generally believed that low Mach number, i.e., low-velocity, flow may be assumed to be incompressible flow. Under steady-state conditions, an exact equation of continuity may then be used to show that such flow is non-divergent. However, a rigorous, compressible fluid-dynam...

Thinking in Orienteering.

ERIC Educational Resources Information Center

Johansen, Bjorn Tore

1997-01-01

A think-aloud technique, in which 20 orienteers verbalized their exact thoughts during orienteering, was used to examine the phenomenon of cognition during orienteering. Results indicate that orienteering is experienced as a task to be accomplished, a physical movement, and a dynamic process, and that thinking involves attuning perceptions to…

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes

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

Ouyang, Wenjun; Dou, Wenjie; Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu

2015-02-28

We investigate the incorporation of the surface-leaking (SL) algorithm into Tully’s fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easinessmore » of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence)« less

Fractal attractors in economic growth models with random pollution externalities

NASA Astrophysics Data System (ADS)

La Torre, Davide; Marsiglio, Simone; Privileggi, Fabio

2018-05-01

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a two-dimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley's fern as the attractor of the log-linearized optimal dynamical system.

Emergent user behavior on Twitter modelled by a stochastic differential equation.

PubMed

Mollgaard, Anders; Mathiesen, Joachim

2015-01-01

Data from the social-media site, Twitter, is used to study the fluctuations in tweet rates of brand names. The tweet rates are the result of a strongly correlated user behavior, which leads to bursty collective dynamics with a characteristic 1/f noise. Here we use the aggregated "user interest" in a brand name to model collective human dynamics by a stochastic differential equation with multiplicative noise. The model is supported by a detailed analysis of the tweet rate fluctuations and it reproduces both the exact bursty dynamics found in the data and the 1/f noise.

Quantum versus classical hyperfine-induced dynamics in a quantum dota)

NASA Astrophysics Data System (ADS)

Coish, W. A.; Loss, Daniel; Yuzbashyan, E. A.; Altshuler, B. L.

2007-04-01

In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t <τc, after which they differ markedly.

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

PubMed

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

Emergent User Behavior on Twitter Modelled by a Stochastic Differential Equation

PubMed Central

Mollgaard, Anders; Mathiesen, Joachim

2015-01-01

Data from the social-media site, Twitter, is used to study the fluctuations in tweet rates of brand names. The tweet rates are the result of a strongly correlated user behavior, which leads to bursty collective dynamics with a characteristic 1/f noise. Here we use the aggregated "user interest" in a brand name to model collective human dynamics by a stochastic differential equation with multiplicative noise. The model is supported by a detailed analysis of the tweet rate fluctuations and it reproduces both the exact bursty dynamics found in the data and the 1/f noise. PMID:25955783

Accurate Sloshing Modes Modeling: A New Analytical Solution and its Consequences on Control

NASA Astrophysics Data System (ADS)

Gonidou, Luc-Olivier; Desmariaux, Jean

2014-06-01

This study addresses the issue of sloshing modes modeling for GNC analyses purposes. On European launchers, equivalent mechanical systems are commonly used for modeling sloshing effects on launcher dynamics. The representativeness of such a methodology is discussed here. First an exact analytical formulation of the launcher dynamics fitted with sloshing modes is proposed and discrepancies with equivalent mechanical system approach are emphasized. Then preliminary comparative GNC analyses are performed using the different models of dynamics in order to evaluate the impact of the aforementioned discrepancies from GNC standpoint. Special attention is paid to system stability.

Income dynamics with a stationary double Pareto distribution.

PubMed

Toda, Alexis Akira

2011-04-01

Once controlled for the trend, the distribution of personal income appears to be double Pareto, a distribution that obeys the power law exactly in both the upper and the lower tails. I propose a model of income dynamics with a stationary distribution that is consistent with this fact. Using US male wage data for 1970-1993, I estimate the power law exponent in two ways--(i) from each cross section, assuming that the distribution has converged to the stationary distribution, and (ii) from a panel directly estimating the parameters of the income dynamics model--and obtain the same value of 8.4.

Inclusion of transverse shear deformation in exact buckling and vibration analysis of composite plate assemblies

NASA Technical Reports Server (NTRS)

Anderson, Melvin S.; Kennedy, David

1992-01-01

The problem considered is the development of the necessary plate stiffnesses for use in a general purpose program for buckling and vibration of composite plate assemblies. The required stiffnesses are for the assumption of sinusoidal response along the plate length with transverse shear included. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D matrices which leads to a differential equation of tenth order.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Saakian, David B.; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Turbulence regeneration in pipe flow at moderate Reynolds numbers.

PubMed

Hof, Björn; van Doorne, Casimir W H; Westerweel, Jerry; Nieuwstadt, Frans T M

2005-11-18

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.

Bounding filter - A simple solution to lack of exact a priori statistics.

NASA Technical Reports Server (NTRS)

Nahi, N. E.; Weiss, I. M.

1972-01-01

Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

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

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

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

NASA Astrophysics Data System (ADS)

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.

Exact probability distribution functions for Parrondo's games.

PubMed

Zadourian, Rubina; Saakian, David B; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

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

PubMed

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.

Digit replacement: A generic map for nonlinear dynamical systems.

PubMed

García-Morales, Vladimir

2016-09-01

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

Quasibound states in a triple Gaussian potential

NASA Astrophysics Data System (ADS)

Reichl, L. E.; Porter, Max D.

2018-04-01

We derive the transmission probabilities and delay times, and identify quasibound state structures in an open quantum system consisting of three Gaussian potential energy peaks, a system whose classical scattering dynamics we show to be chaotic. Such open quantum systems can serve as models for nanoscale quantum devices and their wave dynamics are similar to electromagnetic wave dynamics in optical microcavities. We use a quantum web to determine energy regimes for which the system exhibits the quantum manifestations of chaos, and we show that the classical scattering dynamics contains a significant amount of chaos. We also derive an exact expression for the non-Hermitian Hamiltonian whose eigenvalues give quasibound state energies and lifetimes of the system.

Automated Simultaneous Assembly of Multistage Testlets for a High-Stakes Licensing Examination

ERIC Educational Resources Information Center

Breithaupt, Krista; Hare, Donovan R.

2007-01-01

Many challenges exist for high-stakes testing programs offering continuous computerized administration. The automated assembly of test questions to exactly meet content and other requirements, provide uniformity, and control item exposure can be modeled and solved by mixed-integer programming (MIP) methods. A case study of the computerized…

Lecturers' Attitudes on Electronically Supported Pre-Lecturing Material for Intensive Programs: A Case Study

ERIC Educational Resources Information Center

Kozaris, Ioannis; Varella, Evangelia A.

2010-01-01

In 2006 and 2008, two large trans-national residential summer schools on conservation science were organized as intensive programs. Learners were not only second/third cycle students in both exact sciences and humanities, but further practicing restorers; consequently their educational background, and even their way of approaching scientific…

Impact of Poison Prevention Education on the Knowledge and Behaviors of Seniors

ERIC Educational Resources Information Center

Jones, Paul R.; Sheppard, Monique A.; Snowden, Cecelia B.; Miller, Ted R.; Nelkin, Valerie S.; Nguyen, Denise D.; Tominack, Ivy; Dunlap, Hallie Chillag

2010-01-01

Background: Unintentional poisoning is an important public health issue that exacts a heavy toll on our nation's seniors. However, relatively few empirical studies have examined the efficacy of poison prevention education programs on this cohort. Purpose: This study assessed the impact of a poison education program on the knowledge, perceptions,…

Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian

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

Bello-Rivas, Juan M.; Elber, Ron; Department of Chemistry, University of Texas at Austin, Austin, Texas 78712

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 themore » 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.« less

Anisotropic nonequilibrium hydrodynamic attractor

NASA Astrophysics Data System (ADS)

Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.

2018-02-01

We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.

Optimal control of hydroelectric facilities

NASA Astrophysics Data System (ADS)

Zhao, Guangzhi

This thesis considers a simple yet realistic model of pump-assisted hydroelectric facilities operating in a market with time-varying but deterministic power prices. Both deterministic and stochastic water inflows are considered. The fluid mechanical and engineering details of the facility are described by a model containing several parameters. We present a dynamic programming algorithm for optimizing either the total energy produced or the total cash generated by these plants. The algorithm allows us to give the optimal control strategy as a function of time and to see how this strategy, and the associated plant value, varies with water inflow and electricity price. We investigate various cases. For a single pumped storage facility experiencing deterministic power prices and water inflows, we investigate the varying behaviour for an oversimplified constant turbine- and pump-efficiency model with simple reservoir geometries. We then generalize this simple model to include more realistic turbine efficiencies, situations with more complicated reservoir geometry, and the introduction of dissipative switching costs between various control states. We find many results which reinforce our physical intuition about this complicated system as well as results which initially challenge, though later deepen, this intuition. One major lesson of this work is that the optimal control strategy does not differ much between two differing objectives of maximizing energy production and maximizing its cash value. We then turn our attention to the case of stochastic water inflows. We present a stochastic dynamic programming algorithm which can find an on-average optimal control in the face of this randomness. As the operator of a facility must be more cautious when inflows are random, the randomness destroys facility value. Following this insight we quantify exactly how much a perfect hydrological inflow forecast would be worth to a dam operator. In our final chapter we discuss the challenging problem of optimizing a sequence of two hydro dams sharing the same river system. The complexity of this problem is magnified and we just scratch its surface here. The thesis concludes with suggestions for future work in this fertile area. Keywords: dynamic programming, hydroelectric facility, optimization, optimal control, switching cost, turbine efficiency.

Nonequilibrium quantum field dynamics from the two-particle-irreducible effective action

NASA Astrophysics Data System (ADS)

Laurie, Nathan S.

The two-particle-irreducible effective action offers a powerful approach to the study of quantum field dynamics far from equilibrium. Recent and upcoming heavy ion collision experiments motivate the study of such nonequilibrium dynamics in an expanding space-time background. For the O(N) model I derive exact, causal evolution equations for the statistical and spectral functions in a longitudinally expanding system. It is followed by an investigation into how the expansion affects the prospect of the system reaching equilibrium. Results are obtained in 1+1 dimensions at next-to- leading order in loop- and 1/N-expansions of the 2PI effective action. I focus on the evolution of the statistical function from highly nonequilibrium initial conditions, presenting a detailed analysis of early, intermediate and late-time dynamics. It is found that dynamics at very early times is attracted by a nonthermal fixed point of the mean field equations, after which interactions attempt to drive the system to equilibrium. The competition between the interactions and the expansion is eventually won by the expansion, with so-called freeze-out emerging naturally in this description. In order to investigate the convergence of the 2PI-1/N expansion in the 0(N) model, I compare results obtained numerically in 1+1 dimensions at leading, next- to-leading and next-to-next-to-leading order in 1/N. Convergence with increasing N, and also with decreasing coupling are discussed. A comparison is also made in the classical statistical field theory limit, where exact numerical results are available. I focus on early-time dynamics and quasi-particle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling strength.

Mechanism for subgap optical conductivity in honeycomb Kitaev materials

NASA Astrophysics Data System (ADS)

Bolens, Adrien; Katsura, Hosho; Ogata, Masao; Miyashita, Seiji

2018-04-01

Motivated by recent terahertz absorption measurements in α -RuCl3 , we develop a theory for the electromagnetic absorption of materials described by the Kitaev model on the honeycomb lattice. We derive a mechanism for the polarization operator at second order in the nearest-neighbor hopping Hamiltonian. Using the exact results of the Kitaev honeycomb model, we then calculate the polarization dynamical correlation function corresponding to electric dipole transitions in addition to the spin dynamical correlation function corresponding to magnetic dipole transitions.

Fluid dynamics of out of equilibrium boost invariant plasmas

NASA Astrophysics Data System (ADS)

Blaizot, Jean-Paul; Yan, Li

2018-05-01

By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.

Dynamics of atom-field entanglement for Tavis-Cummings models

NASA Astrophysics Data System (ADS)

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.

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

NASA Technical Reports Server (NTRS)

Sidwell, K.

1976-01-01

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

User manual for BUNVIS-RG: An exact buckling and vibration program for lattice structures, with repetitive geometry and substructuring options

NASA Technical Reports Server (NTRS)

Anderson, M. S.; Warnaar, D. B.; Ling, B. J. AEHERSTROM, C. l. afkennedy, d

1986-01-01

A computer program is described which is especially suited for making vibration and buckling calculations for prestressed lattice structures that might be used for space application. Structures having repetitive geometry are treated in a very efficient manner. Detailed instructions for data input are given along with several example problems illustrating the use and capability of the program.

Dynamic programming methods for concurrent design and dynamic allocation of vehicles embedded in a system-of-systems

NASA Astrophysics Data System (ADS)

Nusawardhana

2007-12-01

Recent developments indicate a changing perspective on how systems or vehicles should be designed. Such transition comes from the way decision makers in defense related agencies address complex problems. Complex problems are now often posed in terms of the capabilities desired, rather than in terms of requirements for a single systems. As a result, the way to provide a set of capabilities is through a collection of several individual, independent systems. This collection of individual independent systems is often referred to as a "System of Systems'' (SoS). Because of the independent nature of the constituent systems in an SoS, approaches to design an SoS, and more specifically, approaches to design a new system as a member of an SoS, will likely be different than the traditional design approaches for complex, monolithic (meaning the constituent parts have no ability for independent operation) systems. Because a system of system evolves over time, this simultaneous system design and resource allocation problem should be investigated in a dynamic context. Such dynamic optimization problems are similar to conventional control problems. However, this research considers problems which not only seek optimizing policies but also seek the proper system or vehicle to operate under these policies. This thesis presents a framework and a set of analytical tools to solve a class of SoS problems that involves the simultaneous design of a new system and allocation of the new system along with existing systems. Such a class of problems belongs to the problems of concurrent design and control of a new systems with solutions consisting of both optimal system design and optimal control strategy. Rigorous mathematical arguments show that the proposed framework solves the concurrent design and control problems. Many results exist for dynamic optimization problems of linear systems. In contrary, results on optimal nonlinear dynamic optimization problems are rare. The proposed framework is equipped with the set of analytical tools to solve several cases of nonlinear optimal control problems: continuous- and discrete-time nonlinear problems with applications on both optimal regulation and tracking. These tools are useful when mathematical descriptions of dynamic systems are available. In the absence of such a mathematical model, it is often necessary to derive a solution based on computer simulation. For this case, a set of parameterized decision may constitute a solution. This thesis presents a method to adjust these parameters based on the principle of stochastic approximation simultaneous perturbation using continuous measurements. The set of tools developed here mostly employs the methods of exact dynamic programming. However, due to the complexity of SoS problems, this research also develops suboptimal solution approaches, collectively recognized as approximate dynamic programming solutions, for large scale problems. The thesis presents, explores, and solves problems from an airline industry, in which a new aircraft is to be designed and allocated along with an existing fleet of aircraft. Because the life cycle of an aircraft is on the order of 10 to 20 years, this problem is to be addressed dynamically so that the new aircraft design is the best design for the fleet over a given time horizon.

Cockpit management and Specific Behavioral Objectives (SBOs)

NASA Technical Reports Server (NTRS)

Mudge, R. W.

1987-01-01

One of the primary tools used to accomplish the task of effective training is the specific behavioral objective (SBO). An SBO is simply a statement which specifically identifies a small segment of the final behavior sought, and a little more. The key word is specific. The company pinpoints exactly what it is it wants the pilot to do after completing training, and what it should evaluate from the point of view of both the program and the pilot. It tells the junior crewmember exactly, specifically, what he should monitor and support insofar as the management function is concerned. It gives greater meaning to the term second in command. And finally, it tells the supervisory pilot exactly what he should observe, evaluate, and instruct, insofar as the management function is concerned.

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

NASA Astrophysics Data System (ADS)

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 such as intermittent hibernating dynamics.

Analysis of the single-vehicle cyclic inventory routing problem

NASA Astrophysics Data System (ADS)

Aghezzaf, El-Houssaine; Zhong, Yiqing; Raa, Birger; Mateo, Manel

2012-11-01

The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general, the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP.

Classicalization by phase space measurements

NASA Astrophysics Data System (ADS)

Bolaños, Marduk

2018-05-01

This article provides an illustration of the measurement approach to the quantum–classical transition suitable for beginning graduate students. As an example, we apply this framework to a quantum system with a general quadratic Hamiltonian, and obtain the exact solution of the dynamics for an arbitrary measurement strength using phase space methods.

SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

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

Ungun, B; Stanford University School of Medicine, Stanford, CA; Fu, A

2016-06-15

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction,more » we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.« less

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

NASA Astrophysics Data System (ADS)

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.

Perimetry update.

PubMed

Leydhecker, W

1983-06-01

The possible applications of computer-assisted static perimetry are examined after five years of personal controlled studies of different types of computerized perimeters. The common advantage of all computer-assisted perimeters is the elimination of the influence of the perimetrist on the results. However, some perimeters are fully computer-assisted and some are only partially so. Even after complete elimination of the perimetrist's influence, some physiological and psychological influences remain due to the patient and will cause fluctuations of the results. In perimeters, the density of the grid and the adaptive strategy of exact threshold measurement are important in obtaining reproducible results. A compromise between duration of the test and exactness has to be found. The most acceptable compromise seems to be an uneven distribution of stimuli, which form a denser grid in areas of special interest and a wider grid in areas less likely to be involved, combined with exact threshold measurements only in suspicious areas. Multiple stimulus presentation is not adequate. High sensitivity of screening is not a great advantage, unless combined with a high specificity. We have shown that using the same stimulus luminosity for center and periphery (a nonadaptive strategy) produces nonspecific results. Only an adaptive strategy can result in high sensitivity and specificity. Adaptive strategy means that the luminosity of the stimulus is adapted to the individual threshold curve of the visual field. In addition, the exact individual thresholds are bracketed by small up and down steps of variation in luminosity. In some cases, scanning programs with two levels of adaptation can be sufficient. The user of modern perimeters must understand such terms as: asb, dB, presentation time, and diameter of stimuli. Projection of stimuli is preferred to light emitting diodes or glass fiber optics. The programs (software) of the modern instruments are of the greatest importance, because the clinical experience that the perimetrist had to acquire in previous manual perimetry is incorporated in these programs. In the Octopus perimeter a delta program is available that differentiates patient fluctuations that may be insignificant from directed significant alterations of the field which might require alteration of therapy. The programs are listed for different computer-assisted perimeters, and their choice is described. The costs of the perimeters are also given. Many controlled clinical studies are quoted briefly where they are useful for understanding the discussion. A brief chapter deals with the reliability of the perimetric test.(ABSTRACT TRUNCATED AT 400 WORDS)

User's guide to the UTIL-ODRC tape processing program. [for the Orbital Data Reduction Center

NASA Technical Reports Server (NTRS)

Juba, S. M. (Principal Investigator)

1981-01-01

The UTIL-ODRC computer compatible tape processing program, its input/output requirements, and its interface with the EXEC 8 operating system are described. It is a multipurpose orbital data reduction center (ODRC) tape processing program enabling the user to create either exact duplicate tapes and/or tapes in SINDA/HISTRY format. Input data elements for PRAMPT/FLOPLT and/or BATCH PLOT programs, a temperature summary, and a printed summary can also be produced.

Exact solution for the quench dynamics of a nested integrable system

NASA Astrophysics Data System (ADS)

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.

Applicability of transfer tensor method for open quantum system dynamics.

PubMed

Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas

2017-12-21

Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.

Teacher-Leader Degree Designed as a Vehicle for Career Fulfillment

ERIC Educational Resources Information Center

Rebora, Anthony

2012-01-01

Programs in teacher leadership have emerged as a growing number of teachers look to advance their careers and stay in the classroom. Exactly how many teacher-leadership degree programs exist is difficult to determine since no organization tracks them separately from other master's offerings in educational leadership. But a review of U.S. education…

The School Librarian as Program Administrator: Just-in-Time Librarianship

ERIC Educational Resources Information Center

Yates, Steven D.

2011-01-01

By applying just-in-time philosophy to today's school libraries, librarians can fulfill the role of program administrator by continuing to provide the resources students and faculty deserve, exactly at their individual points of need. Just-in-time librarianship is a mindset that could prove unsettling for some school librarians. The main facets of…

TheatreLink: Wired to Make Plays Together at a Distance

ERIC Educational Resources Information Center

Shookhoff, David

2004-01-01

Now entering its eighth year, TheatreLink, Manhattan Theater Club's Internet-based distance-learning project remains the most exciting and most challenging initiative. MTC's Education Program had existed for seven years (since 1989 to be exact) before it started TheatreLink. During that early period MTC created an array of programs, all of them…

The Luminous Convolution Model-The light side of dark matter

NASA Astrophysics Data System (ADS)

Cisneros, Sophia; Oblath, Noah; Formaggio, Joe; Goedecke, George; Chester, David; Ott, Richard; Ashley, Aaron; Rodriguez, Adrianna

2014-03-01

We present a heuristic model for predicting the rotation curves of spiral galaxies. The Luminous Convolution Model (LCM) utilizes Lorentz-type transformations of very small changes in the photon's frequencies from curved space-times to construct a dynamic mass model of galaxies. These frequency changes are derived using the exact solution to the exterior Kerr wave equation, as opposed to a linearized treatment. The LCM Lorentz-type transformations map between the emitter and the receiver rotating galactic frames, and then to the associated flat frames in each galaxy where the photons are emitted and received. This treatment necessarily rests upon estimates of the luminous matter in both the emitter and the receiver galaxies. The LCM is tested on a sample of 22 randomly chosen galaxies, represented in 33 different data sets. LCM fits are compared to the Navarro, Frenk & White (NFW) Dark Matter Model and to the Modified Newtonian Dynamics (MOND) model when possible. The high degree of sensitivity of the LCM to the initial assumption of a luminous mass to light ratios (M/L), of the given galaxy, is demonstrated. We demonstrate that the LCM is successful across a wide range of spiral galaxies for predicting the observed rotation curves. Through the generous support of the MIT Dr. Martin Luther King Jr. Fellowship program.

Dynamical properties of dissipative XYZ Heisenberg lattices

NASA Astrophysics Data System (ADS)

Rota, R.; Minganti, F.; Biella, A.; Ciuti, C.

2018-04-01

We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the behavior of individual homodyne quantum trajectories, which reveal the nature of the transition.

Inclusive heavy flavor hadroproduction in NLO QCD: The exact analytic result

NASA Astrophysics Data System (ADS)

Czakon, M.; Mitov, A.

2010-01-01

We present the first exact analytic result for all partonic channels contributing to the total cross section for the production of a pair of heavy flavors in hadronic collisions in NLO QCD. Our calculation is a step in the derivation of the top quark pair production cross section at NNLO in QCD, which is a cornerstone of the precision LHC program. Our results uncover the analytical structures behind observables with heavy flavors at higher orders. They also reveal surprising and non-trivial implications for kinematics close to partonic threshold.

Inclusion of transverse shear deformation in the exact buckling and vibration analysis of composite plate assemblies

NASA Technical Reports Server (NTRS)

Anderson, Melvin S.; Kennedy, David

1993-01-01

The problem considered is the development of the necessary plate stiffnesses for use in the general purpose program VICONOPT for buckling and vibration of composite plate assemblies. The required stiffnesses include the effects of transverse shear deformation and are for sinusoidal response along the plate length as required in VICONOPT. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D stiffness matrices which leads to an ordinary differential equation of tenth order.

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

PubMed

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.

Ligand reorganization and activation energies in nonadiabatic electron transfer reactions

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

Zhu Jianjun; Wang Jianji; Stell, George

2006-10-28

The activation energy and ligand reorganization energy for nonadiabatic electron transfer reactions in chemical and biological systems are investigated in this paper. The free energy surfaces and the activation energy are derived exactly in the general case in which the ligand vibration frequencies are not equal. The activation energy is derived by free energy minimization at the transition state. Our formulation leads to the Marcus-Hush [J. Chem. Phys. 24, 979 (1956); 98, 7170 (1994); 28, 962 (1958)] results in the equal-frequency limit and also generalizes the Marcus-Sumi [J. Chem. Phys. 84, 4894 (1986)] model in the context of studying themore » solvent dynamic effect on electron transfer reactions. It is found that when the ligand vibration frequencies are different, the activation energy derived from the Marcus-Hush formula deviates by 5%-10% from the exact value. If the reduced reorganization energy approximation is introduced in the Marcus-Hush formula, the result is almost exact.« less

Rainfall-runoff response informed by exact solutions of Boussinesq equation on hillslopes

NASA Astrophysics Data System (ADS)

Bartlett, M. S., Jr.; Porporato, A. M.

2017-12-01

The Boussinesq equation offers a powerful approach forunderstanding the flow dynamics of unconfined aquifers. Though this nonlinear equation allows for concise representation of both soil and geomorphological controls on groundwater flow, it has only been solved exactly for a limited number of initial and boundary conditions. These solutions do not include source/sink terms (evapotranspiration, recharge, and seepage to bedrock) and are typically limited to horizontal aquifers. Here we present a class of exact solutions that are general to sloping aquifers and a time varying source/sink term. By incorporating the source/sink term, they may describe aquifers with both time varying recharge over seasonal or weekly time scales, as well as a loss of water from seepage to the bedrock interface, which is a common feature in hillslopes. These new solutions shed light on the hysteretic relationship between streamflow and groundwater and the behavior of the hydrograph recession curves, thus providing a robust basis for deriving a runoff curves for the partition of rainfall into infiltration and runoff.

Memory-efficient RNA energy landscape exploration

PubMed Central

Mann, Martin; Kucharík, Marcel; Flamm, Christoph; Wolfinger, Michael T.

2014-01-01

Motivation: Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the landscape enable the study of larger systems; however, they are still restricted by huge memory requirements of exact approaches. Results: We present a highly parallelizable local enumeration scheme that enables the computation of exact macro-state transition models with highly reduced memory requirements. The approach is evaluated on RNA secondary structure landscapes using a gradient basin definition for macro-states. Furthermore, we demonstrate the need for exact transition models by comparing two barrier-based approaches, and perform a detailed investigation of gradient basins in RNA energy landscapes. Availability and implementation: Source code is part of the C++ Energy Landscape Library available at http://www.bioinf.uni-freiburg.de/Software/. Contact: mmann@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:24833804

Dynamics of polymers: A mean-field theory

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

Fredrickson, Glenn H.; Materials Research Laboratory, University of California, Santa Barbara, California 93106; Department of Materials, University of California, Santa Barbara, California 93106

2014-02-28

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamicsmore » involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.« less

Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide

NASA Astrophysics Data System (ADS)

Fang, Yao-Lung L.; Ciccarello, Francesco; Baranger, Harold U.

2018-04-01

We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to show the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.

Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2013-04-01

In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar-Parisi-Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-ichi; Seideman, Tamar; Stener, Mauro

2004-01-01

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.

Dynamic regime of coherent population trapping and optimization of frequency modulation parameters in atomic clocks.

PubMed

Yudin, V I; Taichenachev, A V; Basalaev, M Yu; Kovalenko, D V

2017-02-06

We theoretically investigate the dynamic regime of coherent population trapping (CPT) in the presence of frequency modulation (FM). We have formulated the criteria for quasi-stationary (adiabatic) and dynamic (non-adiabatic) responses of atomic system driven by this FM. Using the density matrix formalism for Λ system, the error signal is exactly calculated and optimized. It is shown that the optimal FM parameters correspond to the dynamic regime of atomic-field interaction, which significantly differs from conventional description of CPT resonances in the frame of quasi-stationary approach (under small modulation frequency). Obtained theoretical results are in good qualitative agreement with different experiments. Also we have found CPT-analogue of Pound-Driver-Hall regime of frequency stabilization.

Ecological communities with Lotka-Volterra dynamics

NASA Astrophysics Data System (ADS)

Bunin, Guy

2017-04-01

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

Ecological communities with Lotka-Volterra dynamics.

PubMed

Bunin, Guy

2017-04-01

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

NASA Astrophysics Data System (ADS)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

What can we learn from the dynamics of entanglement and quantum discord in the Tavis-Cummings model?

NASA Astrophysics Data System (ADS)

Restrepo, Juliana; Rodriguez, Boris A.

We revisit the problem of the dynamics of quantum correlations in the exact Tavis-Cummings model. We show that many of the dynamical features of quantum discord attributed to dissipation are already present in the exact framework and are due to the well known non-linearities in the model and to the choice of initial conditions. Through a comprehensive analysis, supported by explicit analytical calculations, we find that the dynamics of entanglement and quantum discord are far from being trivial or intuitive. In this context, we find states that are indistinguishable from the point of view of entanglement and distinguishable from the point of view of quantum discord, states where the two quantifiers give opposite information and states where they give roughly the same information about correlations at a certain time. Depending on the initial conditions, this model exhibits a fascinating range of phenomena that can be used for experimental purposes such as: Robust states against change of manifold or dissipation, tunable entanglement states and states with a counterintuitive sudden birth as the number of photons increase. We furthermore propose an experiment called quantum discord gates where discord is zero or non-zero depending on the number of photons. This work was supported by the Vicerrectoria de Investigacion of the Universidad Antonio Narino, Colombia under Project Number 20141031 and by the Departamento Administrativo de Ciencia, Tecnologia e Innovacion (COLCIENCIAS) of Colombia under Grant Number.

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions.

PubMed

Salis, Howard; Kaznessis, Yiannis

2005-02-01

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Quantum synchronization of many coupled atoms for an ultranarrow linewidth laser

NASA Astrophysics Data System (ADS)

He, Peiru; Xu, Minghui; Tieri, David; Zhu, Bihui; Rey, Ana Maria; Hazzard, Kaden; Holland, Murray

2014-05-01

We theoretically investigate the effect of quantum synchronization on many coupled two-level atoms acting as high quality oscillators. We show that quantum synchronization - the spontaneous alignment of the phase (of the two-level superposition) between different atoms - provides a potential approach to produce robust atomic coherences and coherent light with ultranarrow linewidth and extreme phase stability. The atoms may be coupled either through their direct dipole-dipole interactions or, as in a superradiant laser, through an optical cavity. We develop a variety of analytic and computational approaches for this problem, including exact open quantum system methods for small systems, semiclassical theories, and approaches that make use of the permutation symmetry of identically coupled ensembles. We investigate the first and second order coherence properties of both the optical and atomic degrees of freedom. We study synchronization in both the steady-state, as well as during the dynamically applied pulse sequences of Rabi and Ramsey interferometry. This work was supported by the DARPA QuASAR program, the NSF, and NIST.

A Software Upgrade of the NASA Aeroheating Code "MINIVER"

NASA Technical Reports Server (NTRS)

Louderback, Pierce Mathew

2013-01-01

Computational Fluid Dynamics (CFD) is a powerful and versatile tool simulating fluid and thermal environments of launch and re-entry vehicles alike. Where it excels in power and accuracy, however, it lacks in speed. An alternative tool for this purpose is known as MINIVER, an aeroheating code widely used by NASA and within the aerospace industry. Capable of providing swift, reasonably accurate approximations of the fluid and thermal environment of launch vehicles, MINIVER is used where time is of the essence and accuracy need not be exact. However, MINIVER is an old, aging tool: running on a user-unfriendly, legacy command-line interface, it is difficult for it to keep pace with more modem software tools. Florida Institute of Technology was tasked with the construction of a new Graphical User Interface (GUI) that implemented the legacy version's capabilities and enhanced them with new tools and utilities. This thesis provides background to the legacy version of the program, the progression and final version of a modem user interface, and benchmarks to demonstrate its usefulness.

On the r-dynamic chromatic number of the corronation by complete graph

NASA Astrophysics Data System (ADS)

Indah Kristiana, Arika; Imam Utoyo, M.; Dafik

2018-04-01

In this paper we will study the r-dynamic chromatic number of the coronation by complete graph. A proper k-coloring of graph G such that the neighbors of any vertex v receive at least min{r, d(v)} different colors. The r-dynamic chromatic number, χ r (G) is the minimum k such that graph G has an r-dynamic k-coloring. We will obtain lower bound of the r-dynamic chromatic number of {χ }r({K}nȯ H), and {χ }r(Hȯ {K}m) We also study the exact value of the r-dynamic chromatic number of {χ }r({K}nȯ {S}m),{χ }r({K}nȯ {F}m),{χ }r({S}nȯ {K}m),{χ }r({F}nȯ {K}m) and {χ }r({K}nȯ {K}m) for m, n > 3.

Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field

NASA Astrophysics Data System (ADS)

Zhang, Ruili; Wang, Yulei; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa

2018-02-01

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. The numerical simulation of relativistic dynamics is often multi-scale and requires accurate long-term numerical simulations. Therefore, explicit symplectic algorithms are much more preferable than non-symplectic methods and implicit symplectic algorithms. In this paper, we employ the proper time and express the Hamiltonian as the sum of exactly solvable terms and product-separable terms in space-time coordinates. Then, we give the explicit symplectic algorithms based on the generating functions of orders 2 and 3 for relativistic dynamics of a charged particle. The methodology is not new, which has been applied to non-relativistic dynamics of charged particles, but the algorithm for relativistic dynamics has much significance in practical simulations, such as the secular simulation of runaway electrons in tokamaks.

Approximate and exact numerical integration of the gas dynamic equations

NASA Technical Reports Server (NTRS)

Lewis, T. S.; Sirovich, L.

1979-01-01

A highly accurate approximation and a rapidly convergent numerical procedure are developed for two dimensional steady supersonic flow over an airfoil. Examples are given for a symmetric airfoil over a range of Mach numbers. Several interesting features are found in the calculation of the tail shock and the flow behind the airfoil.

Monotonic Derivative Correction for Calculation of Supersonic Flows

ERIC Educational Resources Information Center

Bulat, Pavel V.; Volkov, Konstantin N.

2016-01-01

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.

PubMed

Li, Qi; Duan, Qiu-yuan; Zhang, Jian-bing

2014-01-01

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

Alternative to the traditional discount method of wholesaler purchasing.

PubMed

Lee, G F; Bair, J N; Piz, J W

1982-07-01

A program of purchasing drugs from wholesalers at the wholesaler's exact invoice cost plus a percentage is described and compared with the traditional method of average wholesale price (AWP) less a discount. The comparison was conducted by the pharmacy department of a 310-bed, teaching hospital that awarded a one-year contract to a wholesaler offering its items at the exact cost plus a pre-established percentage. Data collected from monthly wholesaler computer printouts gave the following information on each product: (1) list price per item, (2) actual cost to pharmacy per item, (3) percentage discount from AWP, and (4) quantity ordered. The net percentage discount from AWP for 12 months was calculated and compared to the former (traditional) discount rate. The net discount from AWP was 15.6% for purchases made by the hospital during the first 12 months of the program. When compared with the smaller discount the hospital traditionally received, the new program saved the hospital $5758 on annual purchases of $136,419. The actual dollar savings to an institution that changes from a traditional discount program to a cost-plus-percentage program depends on: (1) the negotiated percentage added to wholesaler cost, (2) the discount from AWP that the institution was previously receiving, and (3) the volume of wholesale purchases.

Topics in Diffusion Limited Reaction Processes

NASA Astrophysics Data System (ADS)

Lin, Jian-Cheng

We study, both theoretically and numerically, the macroscopic particle concentration in a class of simple diffusion-limited reactions: one species coagulation A + A to A, reversible coagulation A + A rightleftharpoons A, A + A to A with particle input, A + A rightleftharpoons A with particle input, single species annihilation A + A to inert, and two species annihilation A + B to inert. The main interest is in the asymptotic behavior of the particle concentration. We review the standard mean-field theory, mass-reaction kinetics and the associated nonlinear rate and diffusion-reaction equations. Theoretically we study the concentration using several closure schemes for truncating the infinite hierarchy of the kinetic equations for the joint density functions. Our goal is to evaluate the quality of some nonsystematic approximations by comparison with exact solutions. It is found that these approximations are very good at capturing the asymptotic behavior of the particle concentrations in the irreversible reactions, while they fail to predict the far-from-equilibrium dynamic phase transition in the one dimensional reversible coagulation reaction predicted by exact results. Numerically we use Monte Carlo simulation to study concentrations in the single species reversible coagulation process. In one dimension the numerical results are in excellent agreement with the exact analytic results. In two dimensions, our simulation data in the transient states suggest an interesting scaling for the deviation of the concentration from its equilibrium value, delta C(t) ~ exp( -beta(C_0)t^{alpha(C_0) }), where alpha(C_0) and beta(C_0) are functions of the initial concentration C_0. However, it seems unlikely to be able to answer the question of the existence of a dynamic phase transition in two dimensions by Monte Carlo simulation within a reasonable CPU time due to the long persistence of the transient states. In an appendix we solve exactly an annihilation-related percolation problem.

Exact results for Schrödinger cats in driven-dissipative systems and their feedback control

NASA Astrophysics Data System (ADS)

Minganti, Fabrizio; Bartolo, Nicola; Lolli, Jared; Casteels, Wim; Ciuti, Cristiano

2016-05-01

In quantum optics, photonic Schrödinger cats are superpositions of two coherent states with opposite phases and with a significant number of photons. Recently, these states have been observed in the transient dynamics of driven-dissipative resonators subject to engineered two-photon processes. Here we present an exact analytical solution of the steady-state density matrix for this class of systems, including one-photon losses, which are considered detrimental for the achievement of cat states. We demonstrate that the unique steady state is a statistical mixture of two cat-like states with opposite parity, in spite of significant one-photon losses. The transient dynamics to the steady state depends dramatically on the initial state and can pass through a metastable regime lasting orders of magnitudes longer than the photon lifetime. By considering individual quantum trajectories in photon-counting configuration, we find that the system intermittently jumps between two cats. Finally, we propose and study a feedback protocol based on this behaviour to generate a pure cat-like steady state.

Blip decomposition of the path integral: exponential acceleration of real-time calculations on quantum dissipative systems.

PubMed

Makri, Nancy

2014-10-07

The real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, it is shown that the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term and thus can be summed by an inexpensive iterative procedure. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the "fully incoherent limit" zero-blip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.

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

PubMed

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.

An approach of the exact linearization techniques to analysis of population dynamics of the mosquito Aedes aegypti.

PubMed

Dos Reis, Célia A; Florentino, Helenice de O; Cólon, Diego; Rosa, Suélia R Fleury; Cantane, Daniela R

2018-05-01

Dengue fever, chikungunya and zika are caused by different viruses and mainly transmitted by Aedes aegypti mosquitoes. These diseases have received special attention of public health officials due to the large number of infected people in tropical and subtropical countries and the possible sequels that those diseases can cause. In severe cases, the infection can have devastating effects, affecting the central nervous system, muscles, brain and respiratory system, often resulting in death. Vaccines against these diseases are still under development and, therefore, current studies are focused on the treatment of diseases and vector (mosquito) control. This work focuses on this last topic, and presents the analysis of a mathematical model describing the population dynamics of Aedes aegypti, as well as present the design of a control law for the mosquito population (vector control) via exact linearization techniques and optimal control. This control strategy optimizes the use of resources for vector control, and focuses on the aquatic stage of the mosquito life. Theoretical and computational results are also presented. Copyright © 2017 Elsevier Inc. All rights reserved.

Nonstationary magnetosonic wave dynamics in plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2013-08-01

In a Lagrangian fluid approach, an explicit method has been presented previously to obtain an exact nonstationary magnetosonic-type wave solution in compressible magnetized plasmas of arbitrary resistivity showing competition among hydrodynamic convection, magnetic field diffusion, and dispersion [Chakrabarti et al., Phys. Rev. Lett. 106, 145003 (2011)]. The purpose of the present work is twofold: it serves (i) to describe the physical and mathematical background of the involved magnetosonic wave dynamics in more detail, as proposed by our original Letter, and (ii) to present an alternative approach, which utilizes the Lagrangian mass variable as a new spatial coordinate [Schamel, Phys. Rep. 392, 279 (2004)]. The obtained exact nonlinear wave solutions confirm the correctness of our previous results, indicating a collapse of the magnetic field irrespective of the presence of dispersion and resistivity. The mean plasma density, on the other hand, is less singular, showing collapse only when dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas, and they are expected to be of special importance in the astrophysical context of magnetic star formation.

Quantum dynamical framework for Brownian heat engines

NASA Astrophysics Data System (ADS)

Agarwal, G. S.; Chaturvedi, S.

2013-07-01

We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.

Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors

NASA Astrophysics Data System (ADS)

Pietroni, Massimo

2018-06-01

Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and the nonperturbative sectors. Then, we show that the dynamics in the deep multistreaming regime is governed by attractors. In the case of simple initial conditions, these attractors coincide with the asymptotic configurations of the adhesion model, but in general they may differ. These results are applied to a cosmological setting, and an algorithm to build the attractor solution starting from the Zel'dovich approximation is developed. Finally, this algorithm is applied to the search of `haloes' and the results are compared with those obtained from the exact dynamical equations.

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

NASA Astrophysics Data System (ADS)

Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu

2015-04-01

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

Differential invariants in nonclassical models of hydrodynamics

NASA Astrophysics Data System (ADS)

Bublik, Vasily V.

2017-10-01

In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with analytical methods makes it possible to make the results of mathematical modeling more accurate and reliable.

Estimating and circumventing the effects of perturbing and swapping inventory plot locations

Treesearch

Ronald E. McRoberts; Geoffrey R. Holden; Mark D. Nelson; Greg C. Liknes; Warren K. Moser; Andrew J. Lister; Susan L. King; Elizabeth B. LaPoint; John W. Coulston; W. Brad Smith; Gregory A. Reams

2005-01-01

The Forest Inventory and Analysis (FIA) program of the USDA Forest Service reports data and information about the Nation's forest resources. Increasingly, users request that FIA data and information be reported and distributed in a geospatial context, and they request access to exact plot locations for their own analyses. However, the FIA program is constrained by...

Hybrid Nested Partitions and Math Programming Framework for Large-scale Combinatorial Optimization

DTIC Science & Technology

2010-03-31

optimization problems: 1) exact algorithms and 2) metaheuristic algorithms . This project will integrate concepts from these two technologies to develop...optimal solutions within an acceptable amount of computation time, and 2) metaheuristic algorithms such as genetic algorithms , tabu search, and the...integer programming decomposition approaches, such as Dantzig Wolfe decomposition and Lagrangian relaxation, and metaheuristics such as the Nested

AN ION CORRELATION PROGRAM FOR DECONVOLUTING COMPOSITE MASS SPECTRA ACQUIRED USING A DIRECT SURFACE IONIZATION SOURCE INTERFACED TO A TIME-OF-FLIGHT MASS SPECTROMETER

EPA Science Inventory

The rapid sampling provided by the DART in ambient air will allow rapid delineation of areas of dispersed chemicals after natural or man-made disasters. Exact masses and RIAs of dimer, precursor, and product ions measured by the oa-TOFMS entered dinto the Ion Correlation Program...

Competing for the Virtual Student

ERIC Educational Resources Information Center

Waters, John K.

2011-01-01

Most K-12 school districts know that they are losing children who are going to other programs to get their needs met, and they know that they are going to have to offer some kind of online program to meet those needs if they are going to survive. K-12 districts have not exactly been sitting on the online-learning sidelines. In fact, by pioneering…

Activated aging dynamics and effective trap model description in the random energy model

NASA Astrophysics Data System (ADS)

Baity-Jesi, M.; Biroli, G.; Cammarota, C.

2018-01-01

We study the out-of-equilibrium aging dynamics of the random energy model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.

Functional determinants, index theorems, and exact quantum black hole entropy

NASA Astrophysics Data System (ADS)

Murthy, Sameer; Reys, Valentin

2015-12-01

The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

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

NASA Astrophysics Data System (ADS)

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.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

A Lifting-Surface Program for Contrarotating Propellers

DTIC Science & Technology

1989-04-01

computer program for a set the force and induced flow field could be determined . of CR propellers has been developed based on a modi- The variations of...and their methods. To determine the forces and induced Nelson’s lifting life programs use the same approach, flow field, they applied lifting-line...Velocimetry (LDV). The propeller set, designed wake should be exactly the same as the hub geometry, to operate in uniform flow , was tested in the DTRC The

Phase diagram and quench dynamics of the cluster-XY spin chain

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

Time-resolved spectroscopy at surfaces and adsorbate dynamics:insights from a model-system approach

NASA Astrophysics Data System (ADS)

Boström, Emil; Mikkelsen, Anders; Verdozzi, Claudio

We introduce a finite-system, model description of the initial stages of femtosecond laser induced desorption at surfaces. Using the exact many-body time evolution and also results from a novel time-dependent DFT description for electron-nuclear systems, we analyse the competition between several surface-response mechanisms and electronic correlations in the transient and longer time dynamics under the influence of dipole-coupled fields. Our model allows us to explore how coherent multiple-pulse protocols impact desorption in a variety of prototypical experiments.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Dynamic characteristics of specialty composite structures with embedded damping layers

NASA Technical Reports Server (NTRS)

Saravanos, D. A.; Chamis, C. C.

1993-01-01

Damping mechanics for simulating the damped dynamic characteristics in specialty composite structures with compliant interlaminar damping layers are presented. Finite-element based mechanics incorporating a discrete layer (or layer-wise) laminate damping theory are utilized to represent general laminate configurations in terms of lay-up and fiber orientation angles, cross-sectional thickness, shape, and boundary conditions. Evaluations of the method with exact solutions and experimental data illustrate the accuracy of the method. Additional applications investigate the potential for significant damping enhancement in angle-ply composite laminates with cocured interlaminar damping layers.

Interpolation Method Needed for Numerical Uncertainty Analysis of Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Groves, Curtis; Ilie, Marcel; Schallhorn, Paul

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors in an unstructured grid, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors. Nomenclature

A Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.

Phase diagram and quench dynamics of the cluster-XY spin chain.

PubMed

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Satellite recovery - Attitude dynamics of the targets

NASA Technical Reports Server (NTRS)

Cochran, J. E., Jr.; Lahr, B. S.

1986-01-01

The problems of categorizing and modeling the attitude dynamics of uncontrolled artificial earth satellites which may be targets in recovery attempts are addressed. Methods of classification presented are based on satellite rotational kinetic energy, rotational angular momentum and orbit and on the type of control present prior to the benign failure of the control system. The use of approximate analytical solutions and 'exact' numerical solutions to the equations governing satellite attitude motions to predict uncontrolled attitude motion is considered. Analytical and numerical results are presented for the evolution of satellite attitude motions after active control termination.

Better Than Counting: Density Profiles from Force Sampling

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-05-01

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here, we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian dynamics, and molecular dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard counting method, reducing therefore the computation time.

Semiclassical modelling of finite-pulse effects on non-adiabatic photodynamics via initial condition filtering: The predissociation of NaI as a test case

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

Martínez-Mesa, Aliezer; Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm; Saalfrank, Peter

2015-05-21

Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the “curse of dimensionality” encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influencemore » of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0{sup +}) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given.« less

Creation of quasi-Dirac points in the Floquet band structure of bilayer graphene.

PubMed

Cheung, W M; Chan, K S

2017-06-01

We study the Floquet quasi-energy band structure of bilayer graphene when it is illuminated by two laser lights with frequencies [Formula: see text] and [Formula: see text] using Floquet theory. We focus on the dynamical gap formed by the conduction band with Floquet index  =  -1 and the valence band with Floquet index  =  +1 to understand how Dirac points can be formed. It is found that the dynamical gap does not have rotation symmetry in the momentum space, and quasi-Dirac points, where the conduction and valence bands almost touch, can be created when the dynamical gap closes along some directions with suitably chosen radiation parameters. We derive analytical expressions for the direction dependence of the dynamical gaps using Lowdin perturbation theory to gain a better understanding of the formation of quasi-Dirac points. When both radiations are circularly polarized, the gap can be exactly zero along some directions, when only the first and second order perturbations are considered. Higher order perturbations can open a very small gap in this case. When both radiations are linearly polarized, the gap can be exactly zero up to the fourth order perturbation and more than one quasi-Dirac point is formed. We also study the electron velocity around a dynamical gap and show that the magnitude of the velocity drops to values close to zero when the k vector is near to the gap minimum. The direction of the velocity also changes around the gap minimum, and when the gap is larger in value the change in the velocity direction is more gradual. The warping effect does not affect the formation of a Dirac point along the k x axis, while it prevents its formation when there is phase shift between the two radiations.

Adaptive hybrid simulations for multiscale stochastic reaction networks

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

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

Lessons on electronic decoherence in molecules from exact modeling

NASA Astrophysics Data System (ADS)

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.

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

Venus EPIC Model Spinup Results

NASA Astrophysics Data System (ADS)

Dowling, Timothy E.; Herrnstein, A.

2006-09-01

We describe the new Venus EPIC model, including its hybrid isentropic/terrain-following vertical coordinate, and explore how topography affects atmospheric spinup from rest. We force the model with the Newtonian cooling used by Lee, Lewis, and Read (2005, Adv. Space Res. 36, 2142-2145) to generate a substantial superrotation in a Venus model without topography, achieving approximately half the desired wind speed. With topography, the Eliassen-Palm flux divergence, a diagnostic tool that maps where eddies have a net effect on the zonal wind, is more steady in time and strongly enhanced at high latitudes in the northern hemisphere by the presence of Ishtar Terra, compared to the case of no topography. In general, the mountains cause the model to achieve a dynamical steady state in a matter of years rather than decades, the northern polar jet to be weaker than its southern counterpart, and the overall magnitude of superrotation to be weaker. Since adding mountains has moved the model superrotation farther below the target, the next step will be to employ more realistic forcing, with attention paid to exactly how the mountains shape the eddy structure, which in turn drives the model's superrotation. This research is funded by the NSF Planetary Astronomy Program and the NASA Planetary Atmospheres Program.

Legal and definitional issues affecting the identification and education of adults with specific learning disabilities in adult education programs.

PubMed

Taymans, Juliana M

2012-01-01

Although the exact prevalence is not determined, a noticeable subset of individuals who enroll in adult education and training programs have either diagnosed or undiagnosed specific learning disabilities (SLD). Understanding SLD is important basic information for adult educators to inform program policies as well as determine effective instructional practices. This article discusses the development of definitions of SLD and current agreement on the nature of SLD relevant to working with adults. It concludes with implications for adult education programs.

Solving large-scale fixed cost integer linear programming models for grid-based location problems with heuristic techniques

NASA Astrophysics Data System (ADS)

Noor-E-Alam, Md.; Doucette, John

2015-08-01

Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.

A Novel Implementation of Efficient Algorithms for Quantum Circuit Synthesis

NASA Astrophysics Data System (ADS)

Zeller, Luke

In this project, we design and develop a computer program to effectively approximate arbitrary quantum gates using the discrete set of Clifford Gates together with the T gate (π/8 gate). Employing recent results from Mosca et. al. and Giles and Selinger, we implement a decomposition scheme that outputs a sequence of Clifford, T, and Tt gates that approximate the input to within a specified error range ɛ. Specifically, the given gate is first rounded to an element of Z[1/2, i] with a precision determined by ɛ, and then exact synthesis is employed to produce the resulting gate. It is known that this procedure is optimal in approximating an arbitrary single qubit gate. Our program, written in Matlab and Python, can complete both approximate and exact synthesis of qubits. It can be used to assist in the experimental implementation of an arbitrary fault-tolerant single qubit gate, for which direct implementation isn't feasible.

Punctuated equilibrium and shock waves in molecular models of biological evolution.

PubMed

Saakian, David B; Ghazaryan, Makar H; Hu, Chin-Kun

2014-08-01

We consider the dynamics in infinite population evolution models with a general symmetric fitness landscape. We find shock waves, i.e., discontinuous transitions in the mean fitness, in evolution dynamics even with smooth fitness landscapes, which means that the search for the optimal evolution trajectory is more complicated. These shock waves appear in the case of positive epistasis and can be used to represent punctuated equilibria in biological evolution during long geological time scales. We find exact analytical solutions for discontinuous dynamics at the large-genome-length limit and derive optimal mutation rates for a fixed fitness landscape to send the population from the initial configuration to some final configuration in the fastest way.

Novel Dynamic Framed-Slotted ALOHA Using Litmus Slots in RFID Systems

NASA Astrophysics Data System (ADS)

Yim, Soon-Bin; Park, Jongho; Lee, Tae-Jin

Dynamic Framed Slotted ALOHA (DFSA) is one of the most popular protocols to resolve tag collisions in RFID systems. In DFSA, it is widely known that the optimal performance is achieved when the frame size is equal to the number of tags. So, a reader dynamically adjusts the next frame size according to the current number of tags. Thus it is important to estimate the number of tags exactly. In this paper, we propose a novel tag estimation and identification method using litmus (test) slots for DFSA. We compare the performance of the proposed method with those of existing methods by analysis. We conduct simulations and show that our scheme improves the speed of tag identification.

Dynamical spin structure factors of α-RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-03-01

Honeycomb-lattice magnet α-RuCl3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.

Free energy landscape theory of glass transition

NASA Astrophysics Data System (ADS)

Odagaki, Takashi

2010-03-01

I first present a free energy landscape (FEL) description of statistical mechanics, which is an exact reformulation of statistical mechanics and can be applied to non-equilibrium systems. Then, I discuss thermodynamic and dynamic properties of the vitrification process on the basis of the FEL formalism. I show that thermodynamic and dynamic anomalies at the glass transition, including the cooling rate dependence, can be understood in a unified manner which has not been achieved by any other theories of the glass transition. Namely, I show that the vitrification is a transition from annealed to quenched averages in the FEL and that the fast beta, the JG and the slow alpha relaxations are attributed to stochastic dynamics within a basin of FEL, jumping motion among locally connected basins and diffusive dynamics over barriers of the FEL.

Time correlation functions of simple liquids: A new insight on the underlying dynamical processes

NASA Astrophysics Data System (ADS)

Garberoglio, Giovanni; Vallauri, Renzo; Bafile, Ubaldo

2018-05-01

Extensive molecular dynamics simulations of liquid sodium have been carried out to evaluate correlation functions of several dynamical quantities. We report the results of a novel analysis of the longitudinal and transverse correlation functions obtained by evaluating directly their self- and distinct contributions at different wavevectors k. It is easily recognized that the self-contribution remains close to its k → 0 limit, which turns out to be exactly the autocorrelation function of the single particle velocity. The wavevector dependence of the longitudinal and transverse spectra and their self- and distinct parts is also presented. By making use of the decomposition of the velocity autocorrelation spectrum in terms of longitudinal and transverse parts, our analysis is able to recognize the effect of different dynamical processes in different frequency ranges.

Mean-field theory of active electrolytes: Dynamic adsorption and overscreening

NASA Astrophysics Data System (ADS)

Frydel, Derek; Podgornik, Rudolf

2018-05-01

We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.

Numerical investigation of exact coherent structures in turbulent small-aspect-ratio Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Krygier, Michael; Crowley, Christopher J.; Schatz, Michael F.; Grigoriev, Roman O.

2017-11-01

As suggested by recent theoretical and experimental studies, fluid turbulence can be described as a walk between neighborhoods of unstable nonchaotic solutions of the Navier-Stokes equation known as exact coherent structures (ECS). Finding ECS in an experimentally-accessible setting is the first step toward rigorous testing of the dynamical role of ECS in 3D turbulence. We found several ECS (both relative periodic orbits and relative equilibria) in a weakly turbulent regime of small-aspect-ratio Taylor-Couette flow with counter-rotating cylinders. This talk will discuss how the geometry of these solutions guides the evolution of turbulent flow in the simulations. This work is supported by the Army Research Office (Contract # W911NF-15-1-0471).

Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence

NASA Astrophysics Data System (ADS)

Andrés, N.; Galtier, S.; Sahraoui, F.

2018-01-01

We derive an exact law for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamic turbulence, without the assumption of isotropy. The Hall current is shown to introduce new flux and source terms that act at the small scales (comparable or smaller than the ion skin depth) to significantly impact the turbulence dynamics. The law provides an accurate means to estimate the energy cascade rate over a broad range of scales covering the magnetohydrodynamic inertial range and the sub-ion dispersive range in 3D numerical simulations and in in situ spacecraft observations of compressible turbulence. This work is particularly relevant to astrophysical flows in which small-scale density fluctuations cannot be ignored such as the solar wind, planetary magnetospheres, and the interstellar medium.

A New Class of Almost Ricci Solitons and Their Physical Interpretation

PubMed Central

2016-01-01

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u, μ, p, α, η, σ ij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems. PMID:28044145

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

Recovery time in quantum dynamics of wave packets

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

Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru

2017-01-15

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of themore » system is established. The recovery time is the longest for the maximal excitation level.« less

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

Prakash, S. Arun; Malathi, V.; Mani Rajan, M. S., E-mail: senthilmanirajanofc@gmail.com

We obtain the bright similariton solutions for generalized inhomogeneous nonlinear Schrödinger equation (GINLSE) which governs the pulse propagation in a tapered graded index diffraction decreasing waveguide (DDW). The exact solutions have been worked out by employing similarity transformations which involve the mapping of the GINLSE to standard NLSE for the certain conditions of the parameters. By making use of the exact analytical solutions, we have investigated the dynamical behavior of optical similariton pairs and have suggested the methods to control them as they propagate through DDW. Moreover, pulse width of similariton is controlled through various profiles. These results are helpfulmore » to understand the similaritons in DDW and can be potentially useful for future experiments in optical communications which involve optical amplifiers and long-haul telecommunication networks.« less

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

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

Vianna, Reinaldo O.; Departamento de Fisica, ICEX, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31270-901 Belo Horizonte, Minas Gerais; Doherty, Andrew C.

2006-11-15

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Infrared dynamics of cold atoms on hot graphene membranes

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri N.; Clougherty, Dennis P.

2016-06-01

We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact nonperturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.

Ramp and periodic dynamics across non-Ising critical points

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Sen, Arnab; Sengupta, K.

2018-01-01

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3 or Z4 symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L ≤24 using exact diagonalization (ED), of the excitation density D , the wave function overlap F , and the excess energy Q at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which D and Q show Kibble-Zurek scaling. We find, based on numerical analysis with L ≤24 , that such scaling is consistent with that expected from critical exponents of the q -state Potts universality class with q =3 ,4 . For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D ,Q →0 and |F |→1 . We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

Cultural and Social Interpretation of Chinese Addressing Strategies

ERIC Educational Resources Information Center

Yin, Yahui

2010-01-01

This paper examines the influence of Chinese cultural factors on the addressing terms, together with the history of their use, the social dynamics involved in their use. Through the examination of exact terms, the author demonstrates to the reader, the deeply rooted cultural factors behind it and different ways that these terms can be used,…

Advancing dendrochronological studies of fire in the United States

Treesearch

Grant L. Harley; Christopher H. Baisan; Peter M. Brown; Donald A. Falk; William T. Flatley; Henri D. Grissino-Mayer; Amy Hessl; Emily K. Heyerdahl; Margot W. Kaye; Charles W. Lafon; Ellis Q. Margolis; R. Stockton Maxwell; Adam T. Naito; William J. Platt; Monica T. Rother; Thomas Saladyga; Rosemary L. Sherriff; Lauren A. Stachowiak; Michael C. Stambaugh; Elaine Kennedy Sutherland; Alan H. Taylor

2018-01-01

Dendroecology is the science that dates tree rings to their exact calendar year of formation to study processes that influence forest ecology (e.g., Speer 2010 [1], Amoroso et al., 2017 [2]). Reconstruction of past fire regimes is a core application of dendroecology, linking fire history to population dynamics and climate effects on tree growth and survivorship. Since...

Dynamics of test particles in thin-shell wormhole spacetimes

NASA Astrophysics Data System (ADS)

Diemer, Valeria; Smolarek, Elena

2013-09-01

Geodesic motion in traversable Schwarzschild and Kerr thin-shell wormholes constructed by the cut-and-paste method introduced by Visser (1989 Nucl. Phys. B 328 203; 1995 Wormholes: from Einstein to Hawking (Woodbury, MN: American Institute of Physics)) is studied. The orbits are calculated exactly in terms of elliptic functions and visualized with the help of embedding diagrams.

A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Yu; Cao, Jianshu

2018-01-01

We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.

Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality.

PubMed

Forti, Mauro; Nistri, Paolo; Quincampoix, Marc

2006-11-01

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: (1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; (2) for convex QP problems, the same result as in (1) holds; moreover, the singleton belongs to the set of global minimizers; and (3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

Introducing difference recurrence relations for faster semi-global alignment of long sequences.

PubMed

Suzuki, Hajime; Kasahara, Masahiro

2018-02-19

The read length of single-molecule DNA sequencers is reaching 1 Mb. Popular alignment software tools widely used for analyzing such long reads often take advantage of single-instruction multiple-data (SIMD) operations to accelerate calculation of dynamic programming (DP) matrices in the Smith-Waterman-Gotoh (SWG) algorithm with a fixed alignment start position at the origin. Nonetheless, 16-bit or 32-bit integers are necessary for storing the values in a DP matrix when sequences to be aligned are long; this situation hampers the use of the full SIMD width of modern processors. We proposed a faster semi-global alignment algorithm, "difference recurrence relations," that runs more rapidly than the state-of-the-art algorithm by a factor of 2.1. Instead of calculating and storing all the values in a DP matrix directly, our algorithm computes and stores mainly the differences between the values of adjacent cells in the matrix. Although the SWG algorithm and our algorithm can output exactly the same result, our algorithm mainly involves 8-bit integer operations, enabling us to exploit the full width of SIMD operations (e.g., 32) on modern processors. We also developed a library, libgaba, so that developers can easily integrate our algorithm into alignment programs. Our novel algorithm and optimized library implementation will facilitate accelerating nucleotide long-read analysis algorithms that use pairwise alignment stages. The library is implemented in the C programming language and available at https://github.com/ocxtal/libgaba .

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

NASA Astrophysics Data System (ADS)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Dynamics in multiple-well Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Nigro, M.; Capuzzi, P.; Cataldo, H. M.; Jezek, D. M.

2018-01-01

We study the dynamics of three-dimensional weakly linked Bose-Einstein condensates using a multimode model with an effective interaction parameter. The system is confined by a ring-shaped four-well trapping potential. By constructing a two-mode Hamiltonian in a reduced highly symmetric phase space, we examine the periodic orbits and calculate their time periods both in the self-trapping and Josephson regimes. The dynamics in the vicinity of the reduced phase space is investigated by means of a Floquet multiplier analysis, finding regions of different linear stability and analyzing their implications on the exact dynamics. The numerical exploration in an extended region of the phase space demonstrates that two-mode tools can also be useful for performing a partition of the space in different regimes. Comparisons with Gross-Pitaevskii simulations confirm these findings and emphasize the importance of properly determining the effective on-site interaction parameter governing the multimode dynamics.

Interaction quench dynamics in the Kondo model in the presence of a local magnetic field.

PubMed

Heyl, M; Kehrein, S

2010-09-01

In this work we investigate the quench dynamics in the Kondo model on the Toulouse line in the presence of a local magnetic field. It is shown that this setup can be realized by either applying the local magnetic field directly or by preparing the system in a macroscopically spin-polarized initial state. In the latter case, the magnetic field results from a subtlety in applying the bosonization technique where terms that are usually referred to as finite-size corrections become important in the present non-equilibrium setting. The transient dynamics are studied by analyzing exact analytical results for the local spin dynamics. The timescale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.

Ab Initio and Monte Carlo Approaches For the MagnetocaloricEffect in Co- and In-Doped Ni-Mn-Ga Heusler Alloys

NASA Astrophysics Data System (ADS)

Sokolovskiy, Vladimir; Grünebohm, Anna; Buchelnikov, Vasiliy; Entel, Peter

2014-09-01

This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

Self-balancing dynamic scheduling of electrical energy for energy-intensive enterprises

NASA Astrophysics Data System (ADS)

Gao, Yunlong; Gao, Feng; Zhai, Qiaozhu; Guan, Xiaohong

2013-06-01

Balancing production and consumption with self-generation capacity in energy-intensive enterprises has huge economic and environmental benefits. However, balancing production and consumption with self-generation capacity is a challenging task since the energy production and consumption must be balanced in real time with the criteria specified by power grid. In this article, a mathematical model for minimising the production cost with exactly realisable energy delivery schedule is formulated. And a dynamic programming (DP)-based self-balancing dynamic scheduling algorithm is developed to obtain the complete solution set for such a multiple optimal solutions problem. For each stage, a set of conditions are established to determine whether a feasible control trajectory exists. The state space under these conditions is partitioned into subsets and each subset is viewed as an aggregate state, the cost-to-go function is then expressed as a function of initial and terminal generation levels of each stage and is proved to be a staircase function with finite steps. This avoids the calculation of the cost-to-go of every state to resolve the issue of dimensionality in DP algorithm. In the backward sweep process of the algorithm, an optimal policy is determined to maximise the realisability of energy delivery schedule across the entire time horizon. And then in the forward sweep process, the feasible region of the optimal policy with the initial and terminal state at each stage is identified. Different feasible control trajectories can be identified based on the region; therefore, optimising for the feasible control trajectory is performed based on the region with economic and reliability objectives taken into account.

General connected and reconnected fields in plasmas

NASA Astrophysics Data System (ADS)

Mahajan, Swadesh M.; Asenjo, Felipe A.

2018-02-01

For plasma dynamics, more encompassing than the magnetohydrodynamical (MHD) approximation, the foundational concepts of "magnetic reconnection" may require deep revisions because, in the larger dynamics, magnetic field is no longer connected to the fluid lines; it is replaced by more general fields (one for each plasma specie) that are weighted combination of the electromagnetic and the thermal-vortical fields. We study the two-fluid plasma dynamics plasma expressed in two different sets of variables: the two-fluid (2F) description in terms of individual fluid velocities, and the one-fluid (1F) variables comprising the plasma bulk motion and plasma current. In the 2F description, a Connection Theorem is readily established; we show that, for each specie, there exists a Generalized (Magnetofluid/Electro-Vortic) field that is frozen-in the fluid and consequently remains, forever, connected to the flow. This field is an expression of the unification of the electromagnetic, and fluid forces (kinematic and thermal) for each specie. Since the magnetic field, by itself, is not connected in the first place, its reconnection is never forbidden and does not require any external agency (like resistivity). In fact, a magnetic field reconnection (local destruction) must be interpreted simply as a consequence of the preservation of the dynamical structure of the unified field. In the 1F plasma description, however, it is shown that there is no exact physically meaningful Connection Theorem; a general and exact field does not exist, which remains connected to the bulk plasma flow. It is also shown that the helicity conservation and the existence of a Connected field follow from the same dynamical structure; the dynamics must be expressible as an ideal Ohm's law with a physical velocity. This new perspective, emerging from the analysis of the post MHD physics, must force us to reexamine the meaning as well as our understanding of magnetic reconnection.

Nonperturbative stochastic method for driven spin-boson model

NASA Astrophysics Data System (ADS)

Orth, Peter P.; Imambekov, Adilet; Le Hur, Karyn

2013-01-01

We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that describes a two-level system interacting with a bosonic bath of harmonic oscillators. This model is archetypal for investigating dissipation in quantum systems, and tunable experimental realizations exist in mesoscopic and cold-atom systems. It finds abundant applications in physics ranging from the study of decoherence in quantum computing and quantum optics to extended dynamical mean-field theory. Starting from the real-time Feynman-Vernon path integral, we derive an exact stochastic Schrödinger equation that allows us to compute the full spin density matrix and spin-spin correlation functions beyond weak coupling. We greatly extend our earlier work [P. P. Orth, A. Imambekov, and K. Le Hur, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.032118 82, 032118 (2010)] by fleshing out the core concepts of the method and by presenting a number of interesting applications. Methodologically, we present an analogy between the dissipative dynamics of a quantum spin and that of a classical spin in a random magnetic field. This analogy is used to recover the well-known noninteracting-blip approximation in the weak-coupling limit. We explain in detail how to compute spin-spin autocorrelation functions. As interesting applications of our method, we explore the non-Markovian effects of the initial spin-bath preparation on the dynamics of the coherence σx(t) and of σz(t) under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of σz(t) without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at nonzero bias and different temperatures.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Exact event-driven implementation for recurrent networks of stochastic perfect integrate-and-fire neurons.

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Comparative DMFT study of the eg-orbital Hubbard model in thin films

NASA Astrophysics Data System (ADS)

Rüegg, Andreas; Hung, Hsiang-Hsuan; Gull, Emanuel; Fiete, Gregory A.

2014-02-01

Heterostructures of transition-metal oxides have emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization-based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin-film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

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

NASA Astrophysics Data System (ADS)

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.

A Path Algorithm for Constrained Estimation

PubMed Central

Zhou, Hua; Lange, Kenneth

2013-01-01

Many least-square problems involve affine equality and inequality constraints. Although there are a variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current article proposes a new path-following algorithm for quadratic programming that replaces hard constraints by what are called exact penalties. Similar penalties arise in l1 regularization in model selection. In the regularization setting, penalties encapsulate prior knowledge, and penalized parameter estimates represent a trade-off between the observed data and the prior knowledge. Classical penalty methods of optimization, such as the quadratic penalty method, solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties!are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path-following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in Lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the Lasso and generalized Lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well-chosen examples illustrate the mechanics and potential of path following. This article has supplementary materials available online. PMID:24039382

PRN 83-3: Label Improvement Program - Storage and Disposal Label Statements

EPA Pesticide Factsheets

This Notice is to inform all registrants that the label of all pesticide products must include updated storage and disposal statements. No application for amended registration is required if you use the exact wording contained in this Notice.

Exact and Heuristic Minimization of the Average Path Length in Decision Diagrams

DTIC Science & Technology

2005-01-01

34$&%’ (*) &+#-,./&%1023 ’+/4%! 5637& 158+#&9 1 SHINOBU NAGAYAMA∗ , ALAN ...reviewers for constructive comments. REFERENCES [1] Ashar , P. and Malik, S. (1995). Fast functional simulation using branching programs, ICCAD’95, 408–412. [2

Neutron Scattering in Chemistry: Experiments, Models and Statistical Description of Physical Phenomena

NASA Astrophysics Data System (ADS)

Ramirez Cuesta, Timmy

Incoherent inelastic neutron scattering spectroscopy is a very powerful technique that requires the use of ab-initio models to interpret the experimental data. Albeit not exact the information obtained from the models gives very valuable insight into the dynamics of atoms in solids and molecules, that, in turn, provides unique access to the vibrational density of states. It is extremely sensitive to hydrogen since the neutron cross section of hydrogen is the largest of all chemical elements. Hydrogen, being the lightest element highlights quantum effects more pronounced than the rest of the elements.In the case of non-crystalline or disordered materials, the models provide partial information and only a reduced sampling of possible configurations can be done at the present. With very large computing power, as exascale computing will provide, a new opportunity arises to study these systems and introduce a description of statistical configurations including energetics and dynamics characterization of configurational entropy. As part of the ICE-MAN project, we are developing the tools to manage the workflows, visualize and analyze the results. To use state of the art computational methods and most neutron scattering that using atomistic models for interpretation of experimental data This work is supported by the Laboratory Directed Research and Development (LDRD 8237) program of the UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy.

Ferrofluid patterns in a radial magnetic field: linear stability, nonlinear dynamics, and exact solutions.

PubMed

Oliveira, Rafael M; Miranda, José A; Leandro, Eduardo S G

2008-01-01

The response of a ferrofluid droplet to a radial magnetic field is investigated, when the droplet is confined in a Hele-Shaw cell. We study how the stability properties of the interface and the shape of the emerging patterns react to the action of the magnetic field. At early linear stages, it is found that the radial field is destabilizing and determines the growth of fingering structures at the interface. In the weakly nonlinear regime, we have verified that the magnetic field favors the formation of peaked patterned structures that tend to become sharper and sharper as the magnitude of the magnetic effects is increased. A more detailed account of the pattern morphology is provided by the determination of nontrivial exact stationary solutions for the problem with finite surface tension. These solutions are obtained analytically and reveal the development of interesting polygon-shaped and starfishlike patterns. For sufficiently large applied fields or magnetic susceptibilities, pinch-off phenomena are detected, tending to occur near the fingertips. We have found that the morphological features obtained from the exact solutions are consistent with our linear and weakly nonlinear predictions. By contrasting the exact solutions for ferrofluids under radial field with those obtained for rotating Hele-Shaw flows with ordinary nonmagnetic fluids, we deduce that they coincide in the limit of very small susceptibilities.

Block clustering based on difference of convex functions (DC) programming and DC algorithms.

PubMed

Le, Hoai Minh; Le Thi, Hoai An; Dinh, Tao Pham; Huynh, Van Ngai

2013-10-01

We investigate difference of convex functions (DC) programming and the DC algorithm (DCA) to solve the block clustering problem in the continuous framework, which traditionally requires solving a hard combinatorial optimization problem. DC reformulation techniques and exact penalty in DC programming are developed to build an appropriate equivalent DC program of the block clustering problem. They lead to an elegant and explicit DCA scheme for the resulting DC program. Computational experiments show the robustness and efficiency of the proposed algorithm and its superiority over standard algorithms such as two-mode K-means, two-mode fuzzy clustering, and block classification EM.

The effect of sampling techniques used in the multiconfigurational Ehrenfest method

NASA Astrophysics Data System (ADS)

Symonds, C.; Kattirtzi, J. A.; Shalashilin, D. V.

2018-05-01

In this paper, we compare and contrast basis set sampling techniques recently developed for use in the ab initio multiple cloning method, a direct dynamics extension to the multiconfigurational Ehrenfest approach, used recently for the quantum simulation of ultrafast photochemistry. We demonstrate that simultaneous use of basis set cloning and basis function trains can produce results which are converged to the exact quantum result. To demonstrate this, we employ these sampling methods in simulations of quantum dynamics in the spin boson model with a broad range of parameters and compare the results to accurate benchmarks.

U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

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

Zheltukhin, A. A.; Fysikum, AlbaNova, Stockholm University, 106 91 Stockholm; NORDITA, Roslagstullsbacken 23, 106 91 Stockholm

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

On a class of integrals of Legendre polynomials with complicated arguments--with applications in electrostatics and biomolecular modeling.

PubMed

Yu, Yi-Kuo

2003-08-15

The exact analytical result for a class of integrals involving (associated) Legendre polynomials of complicated argument is presented. The method employed can in principle be generalized to integrals involving other special functions. This class of integrals also proves useful in the electrostatic problems in which dielectric spheres are involved, which is of importance in modeling the dynamics of biological macromolecules. In fact, with this solution, a more robust foundation is laid for the Generalized Born method in modeling the dynamics of biomolecules. c2003 Elsevier B.V. All rights reserved.

Random walk in degree space and the time-dependent Watts-Strogatz model

NASA Astrophysics Data System (ADS)

Casa Grande, H. L.; Cotacallapa, M.; Hase, M. O.

2017-01-01

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

Random walk in degree space and the time-dependent Watts-Strogatz model.

PubMed

Casa Grande, H L; Cotacallapa, M; Hase, M O

2017-01-01

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

The Quantum Phase-Dynamical Properties of the Squeezed Vacuum State Intensity-Couple Interacting with the Atom

NASA Technical Reports Server (NTRS)

Fan, An-Fu; Sun, Nian-Chun; Zhou, Xin

1996-01-01

The Phase-dynamical properties of the squeezed vacuum state intensity-couple interacting with the two-level atom in an ideal cavity are studied using the Hermitian phase operator formalism. Exact general expressions for the phase distribution and the associated expectation value and variance of the phase operator have been derived. we have also obtained the analytic results of the phase variance for two special cases-weakly and strongly squeezed vacuum. The results calculated numerically show that squeezing has a significant effect on the phase properties of squeezed vacuum.

Robust inverse kinematics using damped least squares with dynamic weighting

NASA Technical Reports Server (NTRS)

Schinstock, D. E.; Faddis, T. N.; Greenway, R. B.

1994-01-01

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Relativistic Newtonian Dynamics under a central force

NASA Astrophysics Data System (ADS)

Friedman, Yaakov

2016-10-01

Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Clock Hypothesis, an explicit description of this influence is derived. We present a new relativity model by incorporating the influence of the potential energy on spacetime in Newton's dynamics for motion under a central force. This model extends the model used by Friedman and Steiner (EPL, 113 (2016) 39001) to obtain the exact precession of Mercury without curving spacetime. We also present a solution of this model for a hydrogen-like atom, which explains the reason for a probabilistic description.

A Fluid Dynamic Approach to the Dust-Acoustic Soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2002-12-01

The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.

The effect of sampling techniques used in the multiconfigurational Ehrenfest method.

PubMed

Symonds, C; Kattirtzi, J A; Shalashilin, D V

2018-05-14

In this paper, we compare and contrast basis set sampling techniques recently developed for use in the ab initio multiple cloning method, a direct dynamics extension to the multiconfigurational Ehrenfest approach, used recently for the quantum simulation of ultrafast photochemistry. We demonstrate that simultaneous use of basis set cloning and basis function trains can produce results which are converged to the exact quantum result. To demonstrate this, we employ these sampling methods in simulations of quantum dynamics in the spin boson model with a broad range of parameters and compare the results to accurate benchmarks.

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

NASA Astrophysics Data System (ADS)

Mallayya, Krishnanand; Rigol, Marcos

2018-02-01

We implement numerical linked cluster expansions (NLCEs) to study dynamics of lattice systems following quantum quenches, and focus on a hard-core boson model in one-dimensional lattices. We find that, in the nonintegrable regime and within the accessible times, local observables exhibit exponential relaxation. We determine the relaxation rate as one departs from the integrable point and show that it scales quadratically with the strength of the integrability breaking perturbation. We compare the NLCE results with those from exact diagonalization calculations on finite chains with periodic boundary conditions, and show that NLCEs are far more accurate.

Voltage Quench Dynamics of a Kondo System.

PubMed

Antipov, Andrey E; Dong, Qiaoyuan; Gull, Emanuel

2016-01-22

We examine the dynamics of a correlated quantum dot in the mixed valence regime. We perform numerically exact calculations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibration times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. The time-dependent current saturation temperature connects the equilibrium Kondo temperature to a substantially increased value at voltages outside of the linear response. These signatures are directly observable by experiments in the time domain.

Traveling waves in actin dynamics and cell motility

PubMed Central

Allard, Jun; Mogilner, Alex

2012-01-01

Much of current understanding of cell motility arose from studying steady treadmilling of actin arrays. Recently, there have been a growing number of observations of a more complex, non-steady, actin behavior, including self-organized waves. It is becoming clear that these waves result from activation and inhibition feedbacks in actin dynamics acting on different scales, but the exact molecular nature of these feedbacks and respective roles of biomechanics and biochemistry are still unclear. Here, we review recent advances achieved in experimental and theoretical studies of actin waves and discuss mechanisms and physiological significance of wavy protrusions. PMID:22985541

Fractional dynamics using an ensemble of classical trajectories

NASA Astrophysics Data System (ADS)

Sun, Zhaopeng; Dong, Hao; Zheng, Yujun

2018-01-01

A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function (F11) to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of index α is investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective.

Dynamic states of a unidirectional ring of chen oscillators

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

Carvalho, Ana; Pinto, Carla M.A.

2015-03-10

We study curious dynamical patterns appearing in a network of a unidirectional ring of Chen oscillators coupled to a ‘buffer’ cell. The network has Z{sub 3} exact symmetry group. We simulate the coupled cell systems associated to the two networks and obtain steady-states, rotating waves, quasiperiodic behavior, and chaos. The different patterns appear to arise through a sequence of Hopf, period-doubling and period-halving bifurcations. The network architecture appears to explain some patterns, whereas the properties of the chaotic oscillator may explain others. We use XPPAUT and MATLAB to compute numerically the relevant states.

The free and forced vibrations of structures using the finite dynamic element method. Ph.D. Thesis, Aug. 1991 Final Report

NASA Technical Reports Server (NTRS)

Fergusson, Neil J.

1992-01-01

In addition to an extensive review of the literature on exact and corrective displacement based methods of vibration analysis, a few theorems are proven concerning the various structural matrices involved in such analyses. In particular, the consistent mass matrix and the quasi-static mass matrix are shown to be equivalent, in the sense that the terms in their respective Taylor expansions are proportional to one another, and that they both lead to the same dynamic stiffness matrix when used with the appropriate stiffness matrix.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Helicity in dynamic atmospheric processes

NASA Astrophysics Data System (ADS)

Kurgansky, M. V.

2017-03-01

An overview on the helicity of the velocity field and the role played by this concept in modern research in the field of geophysical fluid dynamics and dynamic meteorology is given. Different (both previously known in the literature and first presented) formulations of the equation of helicity balance in atmospheric motions (including those with allowance for effects of air compressibility and Earth's rotation) are brought together. Equations and relationships are given which are valid in different approximations accepted in dynamic meteorology: Boussinesq approximation, quasi-static approximation, and quasi-geostrophic approximation. Emphasis is placed on the analysis of helicity budget in large-scale quasi-geostrophic systems of motion; a formula for the helicity flux across the upper boundary of the nonlinear Ekman boundary layer is given, and this flux is shown to be exactly compensated for by the helicity destruction inside the Ekman boundary layer.

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

NASA Astrophysics Data System (ADS)

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.

Universality in survivor distributions: Characterizing the winners of competitive dynamics

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2015-11-01

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept—the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

Non-Markovian dynamics of single- and two-qubit systems interacting with Gaussian and non-Gaussian fluctuating transverse environments

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

Rossi, Matteo A. C., E-mail: matteo.rossi@unimi.it; Paris, Matteo G. A., E-mail: matteo.paris@fisica.unimi.it; CNISM, Unità Milano Statale, I-20133 Milano

2016-01-14

We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where themore » two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.« less

Evaluation of MOSTAS computer code for predicting dynamic loads in two bladed wind turbines

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Janetzke, D. C.; Sullivan, T. L.

1979-01-01

Calculated dynamic blade loads were compared with measured loads over a range of yaw stiffnesses of the DOE/NASA Mod-O wind turbine to evaluate the performance of two versions of the MOSTAS computer code. The first version uses a time-averaged coefficient approximation in conjunction with a multi-blade coordinate transformation for two bladed rotors to solve the equations of motion by standard eigenanalysis. The second version accounts for periodic coefficients while solving the equations by a time history integration. A hypothetical three-degree of freedom dynamic model was investigated. The exact equations of motion of this model were solved using the Floquet-Lipunov method. The equations with time-averaged coefficients were solved by standard eigenanalysis.

Classical and quantum dynamics of a kicked relativistic particle in a box

NASA Astrophysics Data System (ADS)

Yusupov, J. R.; Otajanov, D. M.; Eshniyazov, V. E.; Matrasulov, D. U.

2018-03-01

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.

Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.

1991-01-01

The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Trivial dynamics in discrete-time systems: carrying simplex and translation arcs

NASA Astrophysics Data System (ADS)

Niu, Lei; Ruiz-Herrera, Alfonso

2018-06-01

In this paper we show that the dynamical behavior in (first octant) of the classical Kolmogorov systems of competitive type admitting a carrying simplex can be sometimes determined completely by the number of fixed points on the boundary and the local behavior around them. Roughly speaking, T has trivial dynamics (i.e. the omega limit set of any orbit is a connected set contained in the set of fixed points) provided T has exactly four hyperbolic nontrivial fixed points in with local attractors on the carrying simplex and local repellers on the carrying simplex; and there exists a unique hyperbolic fixed point in Int. Our results are applied to some classical models including the Leslie–Gower models, Atkinson-Allen systems and Ricker maps.

Experimental search for Exact Coherent Structures in turbulent small aspect ratio Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Crowley, Christopher J.; Krygier, Michael; Grigoriev, Roman O.; Schatz, Michael F.

2017-11-01

Recent theoretical and experimental work suggests that the dynamics of turbulent flows are guided by unstable nonchaotic solutions to the Navier-Stokes equations. These solutions, known as exact coherent structures (ECS), play a key role in a fundamentally deterministic description of turbulence. In order to quantitatively demonstrate that actual turbulence in 3D flows is guided by ECS, high resolution, 3D-3C experimental measurements of the velocity need to be compared to solutions from direct numerical simulation of the Navier-Stokes equations. In this talk, we will present experimental measurements of fully time resolved, velocity measurements in a volume of turbulence in a counter-rotating, small aspect ratio Taylor-Couette flow. This work is supported by the Army Research Office (Contract # W911NF-16-1-0281).

Unlocking higher harmonics in atomic force microscopy with gentle interactions.

PubMed

Santos, Sergio; Barcons, Victor; Font, Josep; Verdaguer, Albert

2014-01-01

In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.

A Gaussian theory for fluctuations in simple liquids.

PubMed

Krüger, Matthias; Dean, David S

2017-04-07

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Controlling rogue waves in inhomogeneous Bose-Einstein condensates.

PubMed

Loomba, Shally; Kaur, Harleen; Gupta, Rama; Kumar, C N; Raju, Thokala Soloman

2014-05-01

We present the exact rogue wave solutions of the quasi-one-dimensional inhomogeneous Gross-Pitaevskii equation by using similarity transformation. Then, by employing the exact analytical solutions we have studied the controllable behavior of rogue waves in the Bose-Einstein condensates context for the experimentally relevant systems. Additionally, we have also investigated the nonlinear tunneling of rogue waves through a conventional hyperbolic barrier and periodic barrier. We have found that, for the conventional nonlinearity barrier case, rogue waves are localized in space and time and get amplified near the barrier, while for the dispersion barrier case rogue waves are localized in space and propagating in time and their amplitude is reduced at the barrier location. In the case of the periodic barrier, the interesting dynamical features of rogue waves are obtained and analyzed analytically.

On the structure of the master equation for a two-level system coupled to a thermal bath

NASA Astrophysics Data System (ADS)

de Vega, Inés

2015-04-01

We derive a master equation from the exact stochastic Liouville-von-Neumann (SLN) equation (Stockburger and Grabert 2002 Phys. Rev. Lett. 88 170407). The latter depends on two correlated noises and describes exactly the dynamics of an oscillator (which can be either harmonic or present an anharmonicity) coupled to an environment at thermal equilibrium. The newly derived master equation is obtained by performing analytically the average over different noise trajectories. It is found to have a complex hierarchical structure that might be helpful to explain the convergence problems occurring when performing numerically the stochastic average of trajectories given by the SLN equation (Koch et al 2008 Phys. Rev. Lett. 100 230402, Koch 2010 PhD thesis Fakultät Mathematik und Naturwissenschaften der Technischen Universitat Dresden).

A Gaussian theory for fluctuations in simple liquids

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Dean, David S.

2017-04-01

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions).

PubMed

Bulanov, Sergei V; Esirkepov, Timur Zh; Kando, Masaki; Koga, James K; Bulanov, Stepan S

2011-11-01

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions)

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

Bulanov, Sergei V.; Esirkepov, Timur Zh.; Kando, Masaki

2011-11-15

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to themore » nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.« less

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

Derrida, B.; Nadal, J.P.

It is possible to construct diluted asymmetric models of neural networks for which the dynamics can be calculated exactly. The authors test several learning schemes, in particular, models for which the values of the synapses remain bounded and depend on the history. Our analytical results on the relative efficiencies of the various learning schemes are qualitatively similar to the corresponding ones obtained numerically on fully connected symmetric networks.

Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data

NASA Astrophysics Data System (ADS)

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.

The giant acoustic atom - a single quantum system with a deterministic time delay

NASA Astrophysics Data System (ADS)

Guo, Lingzhen; Grimsmo, Arne; Frisk Kockum, Anton; Pletyukhov, Mikhail; Johansson, Göran

2017-04-01

We investigate the quantum dynamics of a single transmon qubit coupled to surface acoustic waves (SAWs) via two distant connection points. Since the acoustic speed is five orders of magnitude slower than the speed of light, the travelling time between the two connection points needs to be taken into account. Therefore, we treat the transmon qubit as a giant atom with a deterministic time delay. We find that the spontaneous emission of the system, formed by the giant atom and the SAWs between its connection points, initially follows a polynomial decay law instead of an exponential one, as would be the case for a small atom. We obtain exact analytical results for the scattering properties of the giant atom up to two-phonon processes by using a diagrammatic approach. The time delay gives rise to novel features in the reflection, transmission, power spectra, and second-order correlation functions of the system. Furthermore, we find the short-time dynamics of the giant atom for arbitrary drive strength by a numerically exact method for open quantum systems with a finite-time-delay feedback loop. L. G. acknowledges financial support from Carl-Zeiss Stiftung (0563-2.8/508/2).

Modified stochastic fragmentation of an interval as an ageing process

NASA Astrophysics Data System (ADS)

Fortin, Jean-Yves

2018-02-01

We study a stochastic model based on modified fragmentation of a finite interval. The mechanism consists of cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve the interval length. This leads to a set of segments of random sizes, with the accumulation of small fragments near the origin. This model is an example of record dynamics, with the presence of ‘quakes’ and slow dynamics. The fragment size distribution is a universal inverse power law with logarithmic corrections. The exact distribution for the fragment number as function of time is simply related to the unsigned Stirling numbers of the first kind. Two-time correlation functions are defined, and computed exactly. They satisfy scaling relations, and exhibit aging phenomena. In particular, the probability that the same number of fragments is found at two different times t>s is asymptotically equal to [4πlog(s)]-1/2 when s\\gg 1 and the ratio t/s is fixed, in agreement with the numerical simulations. The same process with a reset impedes the aging phenomenon-beyond a typical time scale defined by the reset parameter.

Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

NASA Astrophysics Data System (ADS)

Kandrup, H.

1981-02-01

Assume that the evolution of a system is determined by an N-particle Liouville equation. Suppose, moreover, that the particles which compose the system interact via a long range force like gravity so that the system will be spatially inhomogeneous. In this case, the mean force acting upon a test particle does not vanish, so that one wishes to isolate a self-consistent mean field and distinguish its "systematic" effects from the effects of "fluctuations." This is done here. The time-dependent projection operator formalism of Willis and Picard is used to obtain an exact equation for the time evolution of an appropriately defined one-particle probability density. If one implements the assumption that the "fluctuation" time scale is much shorter than both the relaxation and dynamical time scales, this exact equation can be approximated as a closed Markovian equation. In the limiting case of spatial homogeneity, one recovers precisely the standard Landau equation, which is customarily derived by a stochastic binary-encounter argument. This equation is contrasted with the standard heuristic equation for a mean field theory, as formulated for a Newtonian r-1 gravitational potential in stellar dynamics.

Finite-size effects in the dynamics of few bosons in a ring potential

NASA Astrophysics Data System (ADS)

Eriksson, G.; Bengtsson, J.; Karabulut, E. Ö.; Kavoulakis, G. M.; Reimann, S. M.

2018-02-01

We study the temporal evolution of a small number N of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schrödinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a ‘decay’ of the density variation, and the third is associated with periodic ‘collapses’ and ‘revivals’ of the density variations, with a factor of \\sqrt{N} separating each of them. The last two timescales tend to infinity in the appropriate limit of large N, in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.

Millisecond accuracy video display using OpenGL under Linux.

PubMed

Stewart, Neil

2006-02-01

To measure people's reaction times to the nearest millisecond, it is necessary to know exactly when a stimulus is displayed. This article describes how to display stimuli with millisecond accuracy on a normal CRT monitor, using a PC running Linux. A simple C program is presented to illustrate how this may be done within X Windows using the OpenGL rendering system. A test of this system is reported that demonstrates that stimuli may be consistently displayed with millisecond accuracy. An algorithm is presented that allows the exact time of stimulus presentation to be deduced, even if there are relatively large errors in measuring the display time.

Van Kampen Colimits as Bicolimits in Span

NASA Astrophysics Data System (ADS)

Heindel, Tobias; Sobociński, Paweł

The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics, data type theory and rewriting. We show that these properties can be understood as a single universal property in the associated bicategory of spans. To this end, we first provide a general notion of Van Kampen cocone that specialises to the above colimits. The main result states that Van Kampen cocones can be characterised as exactly those diagrams in ℂ that induce bicolimit diagrams in the bicategory of spans mathcal{S}pan_{mathbb{C}}, provided that ℂ has pullbacks and enough colimits.

Versatile and declarative dynamic programming using pair algebras.

PubMed

Steffen, Peter; Giegerich, Robert

2005-09-12

Dynamic programming is a widely used programming technique in bioinformatics. In sharp contrast to the simplicity of textbook examples, implementing a dynamic programming algorithm for a novel and non-trivial application is a tedious and error prone task. The algebraic dynamic programming approach seeks to alleviate this situation by clearly separating the dynamic programming recurrences and scoring schemes. Based on this programming style, we introduce a generic product operation of scoring schemes. This leads to a remarkable variety of applications, allowing us to achieve optimizations under multiple objective functions, alternative solutions and backtracing, holistic search space analysis, ambiguity checking, and more, without additional programming effort. We demonstrate the method on several applications for RNA secondary structure prediction. The product operation as introduced here adds a significant amount of flexibility to dynamic programming. It provides a versatile testbed for the development of new algorithmic ideas, which can immediately be put to practice.

Determining linear vibration frequencies of a ferromagnetic shell

NASA Astrophysics Data System (ADS)

Bagdoev, A. G.; Vardanyan, A. V.; Vardanyan, S. V.; Kukudzhanov, V. N.

2007-10-01

The problems of determining the roots of dispersion equations for free bending vibrations of thin magnetoelastic plates and shells are of both theoretical and practical interest, in particular, in studying vibrations of metallic structures used in controlled thermonuclear reactors. These problems were solved on the basis of the Kirchhoff hypothesis in [1-5]. In [6], an exact spatial approach to determining the vibration frequencies of thin plates was suggested, and it was shown that it completely agrees with the solution obtained according to the Kirchhoff hypothesis. In [7-9], this exact approach was used to solve the problem on vibrations of thin magnetoelastic plates, and it was shown by cumbersome calculations that the solutions obtained according to the exact theory and the Kirchhoff hypothesis differ substantially except in a single case. In [10], the equations of the dynamic theory of elasticity in the axisymmetric problem are given. In [11], the equations for the vibration frequencies of thin ferromagnetic plates with arbitrary conductivity were obtained in the exact statement. In [12], the Kirchhoff hypothesis was used to obtain dispersion relations for a magnetoelastic thin shell. In [5, 13-16], the relations for the Maxwell tensor and the ponderomotive force for magnetics were presented. In [17], the dispersion relations for thin ferromagnetic plates in the transverse field in the spatial statement were studied analytically and numerically. In the present paper, on the basis of the exact approach, we study free bending vibrations of a thin ferromagnetic cylindrical shell. We obtain the exact dispersion equation in the form of a sixth-order determinant, which can be solved numerically in the case of a magnetoelastic thin shell. The numerical results are presented in tables and compared with the results obtained by the Kirchhoff hypothesis. We show a large number of differences in the results, even for the least frequency.

Adaption of a corrector module to the IMP dynamics program

NASA Technical Reports Server (NTRS)

1972-01-01

The corrector module of the RAEIOS program and the IMP dynamics computer program were combined to achieve a date-fitting capability with the more general spacecraft dynamics models of the IMP program. The IMP dynamics program presents models of spacecraft dynamics for satellites with long, flexible booms. The properties of the corrector are discussed and a description is presented of the performance criteria and search logic for parameter estimation. A description is also given of the modifications made to add the corrector to the IMP program. This includes subroutine descriptions, common definitions, definition of input, and a description of output.