Collapse of the soap-film bridge - Quasistatic description

NASA Technical Reports Server (NTRS)

Cryer, Steven A.; Steen, Paul H.

1992-01-01

Observations of the collapse of a soap-film bridge from a connected to a disconnected state are recorded. The equilibrium framework for this nonequilibrium event is classical. Experiments confirm predictions of stable and unstable equilibria. A quasistatic description is introduced for the dynamic states to extend the static theory. It is found to adequately describe the collapse trajectory while the bridge is still connected.

Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2 X X model

NASA Astrophysics Data System (ADS)

Giorgi, Gian Luca; Galve, Fernando; Zambrini, Roberta

2015-08-01

Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the ground state of the XX model, which exhibits different phases; we find that the different phases have different abilities to redundantly acquire classical information about the system, the "ferromagnetic phase" being the only one able to complete quantum Darwinism. At the same time we relate this ability to how non-Markovian the system dynamics is, based on the interpretation that non-Markovian dynamics is associated with backflow of information from environment to system, thus spoiling the information transfer needed for Darwinism. Finally, we explore mixing of bath registers by allowing a small interaction among them, finding that this spoils the stored information as previously found in the literature.

Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems

NASA Technical Reports Server (NTRS)

Fields, Chris

1989-01-01

Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countably many quasistable states has at least the computational power of a universal Turing machine. Such an analysis assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine.

Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems

NASA Technical Reports Server (NTRS)

Fields, Chris

1989-01-01

Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countablely many quasistable states has at least the computational power of a universal Turing machine. Such an analyses assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine.

Thermodynamics of a time-dependent and dissipative oval billiard: A heat transfer and billiard approach.

PubMed

Leonel, Edson D; Galia, Marcus Vinícius Camillo; Barreiro, Luiz Antonio; Oliveira, Diego F M

2016-12-01

We study some statistical properties for the behavior of the average squared velocity-hence the temperature-for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the particles with the boundary of the billiard are inelastic, leading the average squared velocity to reach a steady-state dynamics for large enough time. The description of the stationary state is made by using two different approaches: (i) heat transfer motivated by the Fourier law and (ii) billiard dynamics using either numerical simulations and theoretical description.

On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

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

Lee, Sang-Bong

1993-09-01

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaoticmore » nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.« less

Proliferation of Observables and Measurement in Quantum-Classical Hybrids

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2012-01-01

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). Hybrids consist in coupled classical (CL) and quantum mechanical (QM) objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM-CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and nonsignaling. Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

Electrical control of spin dynamics in finite one-dimensional systems

NASA Astrophysics Data System (ADS)

Pertsova, A.; Stamenova, M.; Sanvito, S.

2011-10-01

We investigate the possibility of the electrical control of spin transfer in monoatomic chains incorporating spin impurities. Our theoretical framework is the mixed quantum-classical (Ehrenfest) description of the spin dynamics, in the spirit of the s-d model, where the itinerant electrons are described by a tight-binding model while localized spins are treated classically. Our main focus is on the dynamical exchange interaction between two well-separated spins. This can be quantified by the transfer of excitations in the form of transverse spin oscillations. We systematically study the effect of an electrostatic gate bias Vg on the interconnecting channel and we map out the long-range dynamical spin transfer as a function of Vg. We identify regions of Vg giving rise to significant amplification of the spin transmission at low frequencies and relate this to the electronic structure of the channel.

Impact of Beads and Drops on a Repellent Solid Surface: A Unified Description

NASA Astrophysics Data System (ADS)

Arora, S.; Fromental, J.-M.; Mora, S.; Phou, Ty; Ramos, L.; Ligoure, C.

2018-04-01

We investigate freely expanding sheets formed by ultrasoft gel beads, and liquid and viscoelastic drops, produced by the impact of the bead or drop on a silicon wafer covered with a thin layer of liquid nitrogen that suppresses viscous dissipation thanks to an inverse Leidenfrost effect. Our experiments show a unified behavior for the impact dynamics that holds for solids, liquids, and viscoelastic fluids and that we rationalize by properly taking into account elastocapillary effects. In this framework, the classical impact dynamics of solids and liquids, as far as viscous dissipation is negligible, appears as the asymptotic limits of a universal theoretical description. A novel material-dependent characteristic velocity that includes both capillary and bulk elasticity emerges from this unified description of the physics of impact.

Parsimonious description for predicting high-dimensional dynamics

PubMed Central

Hirata, Yoshito; Takeuchi, Tomoya; Horai, Shunsuke; Suzuki, Hideyuki; Aihara, Kazuyuki

2015-01-01

When we observe a system, we often cannot observe all its variables and may have some of its limited measurements. Under such a circumstance, delay coordinates, vectors made of successive measurements, are useful to reconstruct the states of the whole system. Although the method of delay coordinates is theoretically supported for high-dimensional dynamical systems, practically there is a limitation because the calculation for higher-dimensional delay coordinates becomes more expensive. Here, we propose a parsimonious description of virtually infinite-dimensional delay coordinates by evaluating their distances with exponentially decaying weights. This description enables us to predict the future values of the measurements faster because we can reuse the calculated distances, and more accurately because the description naturally reduces the bias of the classical delay coordinates toward the stable directions. We demonstrate the proposed method with toy models of the atmosphere and real datasets related to renewable energy. PMID:26510518

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

On the fly quantum dynamics of electronic and nuclear wave packets

NASA Astrophysics Data System (ADS)

Komarova, Ksenia G.; Remacle, F.; Levine, R. D.

2018-05-01

Multielectronic states quantum dynamics on a grid is described in a manner motivated by on the fly classical trajectory computations. Non stationary electronic states are prepared by a few cycle laser pulse. The nuclei respond and begin moving. We solve the time dependent Schrödinger equation for the electronic and nuclear dynamics for excitation from the ground electronic state. A satisfactory accuracy is possible using a localized description on a discrete grid. This enables computing on the fly for both the nuclear and electronic dynamics including non-adiabatic couplings. Attosecond dynamics in LiH is used as an example.

Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2017-02-01

The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of description of physical phenomena. In general there are no reasons to expect that properties of ontic states are approachable through our measurements. There is a gap between ontic and epistemic descriptions, cf. also with 't Hooft [49,50] and G G. Groessing et al. [51]. In general the presence of such a gap also implies unapproachability of the probabilistic ontic states, i.e., probability distributions on the space of ontic states. De Broglie [28] called such probability distributions hidden probabilities and distinguished them sharply from probability distributions of measurements outcomes, see also Lochak [29]. (The latter distributions are described by the quantum formalism.)This ontic-epistemic approach based on the combination of two descriptive levels for natural phenomena is closely related to the old Bild conception which was originated in the works of Hertz. Later it was heavily explored by Schrödinger in the quantum domain, see, e.g., [8,11] for detailed analysis. According to Hertz one cannot expect to construct a complete theoretical model based explicitly on observable quantities. The complete theoretical model can contain quantities which are unapproachable for external measurement inspection. For example, Hertz by trying to create a mechanical model for Maxwell's electromagnetism invented hidden masses. The main distinguishing property of a theoretical model (in contrast to an observational model) is the continuity of description, i.e., the absence of gaps in description. From this viewpoint, the quantum mechanical description is not continuous: there is a gap between premeasurement dynamics and the measurement outcome. QM cannot say anything what happens in the process of measurement, this is the well known measurement problem of QM [32], cf. [52,53]. Continuity of description is closely related to causality. However, here we cannot go in more detail, see [8,11].The important question is about interrelation between two levels of description, ontic-epistemic (or theoretical-observational). In the introduction we have already cited Schrödinger who emphasized the possible complexity of this interrelation. In particular, in general there is no reason to expect a straightforward coupling of the form, cf. [9,10]:

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

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

Khrennikov, Andrei

2010-08-15

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical randommore » fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.« less

The dynamics of stock exchange based on the formalism of weak continuous quantum measurement

NASA Astrophysics Data System (ADS)

Melnyk, S.; Tuluzov, I.

2010-07-01

The problem of measurement in economic models and the possibility of their quantum-mechanical description are considered. It is revealed that the apparent paradox of such a description is associated with a priori requirement of conformity of the model to all the alternatives of free choice of the observer. The measurement of the state of a trader on a stock exchange is formally defined as his responses to the proposals of sale at a fixed price. It is shown that an analogue of Bell's inequalities for this measurement model is violated at the most general assumptions related to the strategy of the trader and requires a quantum-mechanical description of the dynamics of his condition. In the framework of the theory of weak continuous quantum measurements, the equation of stock price dynamics and the quantum-mechanical generalization of the F. Black and M. Scholes model for pricing options are obtained. The fundamental distinctions between the obtained model and the classical one are discussed.

Seed Dispersal Near and Far: Patterns Across Temperate and Tropical Forests

Treesearch

James S. Clark; Miles Silman; Ruth Kern; Eric Macklin; Janneke HilleRisLambers

1999-01-01

Dispersal affects community dynamics and vegetation response to global change. Understanding these effects requires descriptions of dispersal at local and regional scales and statistical models that permit estimation. Classical models of dispersal describe local or long-distance dispersal, but not both. The lack of statistical methods means that models have rarely been...

Stability of Dynamical Systems with Discontinuous Motions:

NASA Astrophysics Data System (ADS)

Michel, Anthony N.; Hou, Ling

In this paper we present a stability theory for discontinuous dynamical systems (DDS): continuous-time systems whose motions are not necessarily continuous with respect to time. We show that this theory is not only applicable in the analysis of DDS, but also in the analysis of continuous dynamical systems (continuous-time systems whose motions are continuous with respect to time), discrete-time dynamical systems (systems whose motions are defined at discrete points in time) and hybrid dynamical systems (HDS) (systems whose descriptions involve simultaneously continuous-time and discrete-time). We show that the stability results for DDS are in general less conservative than the corresponding well-known classical Lyapunov results for continuous dynamical systems and discrete-time dynamical systems. Although the DDS stability results are applicable to general dynamical systems defined on metric spaces (divorced from any kind of description by differential equations, or any other kinds of equations), we confine ourselves to finite-dimensional dynamical systems defined by ordinary differential equations and difference equations, to make this paper as widely accessible as possible. We present only sample results, namely, results for uniform asymptotic stability in the large.

A Classical Phase Space Framework For the Description of Supercooled Liquids and an Apparent Universal Viscosity Collapse

NASA Astrophysics Data System (ADS)

Weingartner, Nicholas; Pueblo, Chris; Nogueira, Flavio; Kelton, Kenneth; Nussinov, Zohar

A fundamental understanding of the phenomenology of the metastable supercooled liquid state remains elusive. Two of the most pressing questions in this field are how to describe the temperature dependence of the viscosity, and determine whether or not the dynamical behaviors are universal. To address these questions, we have devised a simple first-principles classical phase space description of supercooled liquids that (along with a complementary quantum approach) predicts a unique functional form for the viscosity which relies on only a single parameter. We tested this form for 45 liquids of all types and fragilities, and have demonstrated that it provides a statistically significant fit to all liquids. Additionally, by scaling the viscosity of all studied liquids using the single parameter, we have observed a complete collapse of the data of all 45 liquids to a single scaling curve over 16 decades, suggesting an underlying universality in the dynamics of supercooled liquids. In this talk I will outline the basic approach of our model, as well as demonstrate the quality of the model performance and collapse of the data.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

A New Dynamic 3D Virtual Methodology for Teaching the Mechanics of Atrial Septation as Seen in the Human Heart

ERIC Educational Resources Information Center

Schleich, Jean-Marc; Dillenseger, Jean-Louis; Houyel, Lucile; Almange, Claude; Anderson, Robert H.

2009-01-01

Learning embryology remains difficult, since it requires understanding of many complex phenomena. The temporal evolution of developmental events has classically been illustrated using cartoons, which create difficulty in linking spatial and temporal aspects, such correlation being the keystone of descriptive embryology. We synthesized the…

A structural and theoretical study of the alkylammonium nitrates forefather: Liquid methylammonium nitrate

NASA Astrophysics Data System (ADS)

Gontrani, Lorenzo; Caminiti, Ruggero; Salma, Umme; Campetella, Marco

2017-09-01

We present here a structural and vibrational analysis of melted methylammonium nitrate, the simplest compound of the family of alkylammonium nitrates. The static and dynamical features calculated were endorsed by comparing the experimental X-ray data with the theoretical ones. A reliable description cannot be obtained with classical molecular dynamics owing to polarization effects. Contrariwise, the structure factor and the vibrational frequencies obtained from ab initio molecular dynamics trajectories are in very good agreement with the experiment. A careful analysis has provided additional information on the complex hydrogen bonding network that exists in this liquid.

Quantum dynamical simulations of local field enhancement in metal nanoparticles.

PubMed

Negre, Christian F A; Perassi, Eduardo M; Coronado, Eduardo A; Sánchez, Cristián G

2013-03-27

Field enhancements (Γ) around small Ag nanoparticles (NPs) are calculated using a quantum dynamical simulation formalism and the results are compared with electrodynamic simulations using the discrete dipole approximation (DDA) in order to address the important issue of the intrinsic atomistic structure of NPs. Quite remarkably, in both quantum and classical approaches the highest values of Γ are located in the same regions around single NPs. However, by introducing a complete atomistic description of the metallic NPs in optical simulations, a different pattern of the Γ distribution is obtained. Knowing the correct pattern of the Γ distribution around NPs is crucial for understanding the spectroscopic features of molecules inside hot spots. The enhancement produced by surface plasmon coupling is studied by using both approaches in NP dimers for different inter-particle distances. The results show that the trend of the variation of Γ versus inter-particle distance is different for classical and quantum simulations. This difference is explained in terms of a charge transfer mechanism that cannot be obtained with classical electrodynamics. Finally, time dependent distribution of the enhancement factor is simulated by introducing a time dependent field perturbation into the Hamiltonian, allowing an assessment of the localized surface plasmon resonance quantum dynamics.

Realistic finite temperature simulations of magnetic systems using quantum statistics

NASA Astrophysics Data System (ADS)

Bergqvist, Lars; Bergman, Anders

2018-01-01

We have performed realistic atomistic simulations at finite temperatures using Monte Carlo and atomistic spin dynamics simulations incorporating quantum (Bose-Einstein) statistics. The description is much improved at low temperatures compared to classical (Boltzmann) statistics normally used in these kind of simulations, while at higher temperatures the classical statistics are recovered. This corrected low-temperature description is reflected in both magnetization and the magnetic specific heat, the latter allowing for improved modeling of the magnetic contribution to free energies. A central property in the method is the magnon density of states at finite temperatures, and we have compared several different implementations for obtaining it. The method has no restrictions regarding chemical and magnetic order of the considered materials. This is demonstrated by applying the method to elemental ferromagnetic systems, including Fe and Ni, as well as Fe-Co random alloys and the ferrimagnetic system GdFe3.

A discussion on turbine design for safe operation

NASA Astrophysics Data System (ADS)

Brekke, H.

2012-11-01

The paper gives a brief description of the hydraulic design of Francis and Pelton runners. The dynamic behaviour at part load has been a major problem for low head and medium head Francis turbines. The main reason for this has been inter blade separation and unstable swirl flow in the draft tube. A description is given on the hydraulic design of X-BLADE runners to obtain stable operation on the whole range of operation by reducing the cross flow. A classical theoretical analysis is also given on the dynamic hydraulic load on Pelton buckets. Several CFD analyses of this non stationary flow have been presented during the last decade, but the velocity distribution in the jets have not been correct. Experimental research work is presented on the complexity of this problem.

Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

NASA Astrophysics Data System (ADS)

Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen

2015-07-01

We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.

Femtosecond dynamics and laser control of charge transport in trans-polyacetylene.

PubMed

Franco, Ignacio; Shapiro, Moshe; Brumer, Paul

2008-06-28

The induction of dc electronic transport in rigid and flexible trans-polyacetylene oligomers according to the omega versus 2omega coherent control scenario is investigated using a quantum-classical mean field approximation. The approach involves running a large ensemble of mixed quantum-classical trajectories under the influence of omega+2omega laser fields and choosing the initial conditions by sampling the ground-state Wigner distribution function for the nuclei. The vibronic couplings are shown to change the mean single-particle spectrum, introduce ultrafast decoherence, and enhance intramolecular vibrational and electronic relaxation. Nevertheless, even in the presence of significant couplings, limited coherent control of the electronic dynamics is still viable, the most promising route involving the use of femtosecond pulses with a duration that is comparable to the electronic dephasing time. The simulations offer a realistic description of the behavior of a simple coherent control scenario in a complex system and provide a detailed account of the femtosecond photoinduced vibronic dynamics of a conjugated polymer.

Ab Initio Molecular Dynamics and Lattice Dynamics-Based Force Field for Modeling Hexagonal Boron Nitride in Mechanical and Interfacial Applications.

PubMed

Govind Rajan, Ananth; Strano, Michael S; Blankschtein, Daniel

2018-04-05

Hexagonal boron nitride (hBN) is an up-and-coming two-dimensional material, with applications in electronic devices, tribology, and separation membranes. Herein, we utilize density-functional-theory-based ab initio molecular dynamics (MD) simulations and lattice dynamics calculations to develop a classical force field (FF) for modeling hBN. The FF predicts the crystal structure, elastic constants, and phonon dispersion relation of hBN with good accuracy and exhibits remarkable agreement with the interlayer binding energy predicted by random phase approximation calculations. We demonstrate the importance of including Coulombic interactions but excluding 1-4 intrasheet interactions to obtain the correct phonon dispersion relation. We find that improper dihedrals do not modify the bulk mechanical properties and the extent of thermal vibrations in hBN, although they impact its flexural rigidity. Combining the FF with the accurate TIP4P/Ice water model yields excellent agreement with interaction energies predicted by quantum Monte Carlo calculations. Our FF should enable an accurate description of hBN interfaces in classical MD simulations.

Characterizing and modeling the dynamics of online popularity.

PubMed

Ratkiewicz, Jacob; Fortunato, Santo; Flammini, Alessandro; Menczer, Filippo; Vespignani, Alessandro

2010-10-08

Online popularity has an enormous impact on opinions, culture, policy, and profits. We provide a quantitative, large scale, temporal analysis of the dynamics of online content popularity in two massive model systems: the Wikipedia and an entire country's Web space. We find that the dynamics of popularity are characterized by bursts, displaying characteristic features of critical systems such as fat-tailed distributions of magnitude and interevent time. We propose a minimal model combining the classic preferential popularity increase mechanism with the occurrence of random popularity shifts due to exogenous factors. The model recovers the critical features observed in the empirical analysis of the systems analyzed here, highlighting the key factors needed in the description of popularity dynamics.

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Chemical reactivity and spectroscopy explored from QM/MM molecular dynamics simulations using the LIO code

NASA Astrophysics Data System (ADS)

Marcolongo, Juan P.; Zeida, Ari; Semelak, Jonathan A.; Foglia, Nicolás O.; Morzan, Uriel N.; Estrin, Dario A.; González Lebrero, Mariano C.; Scherlis, Damián A.

2018-03-01

In this work we present the current advances in the development and the applications of LIO, a lab-made code designed for density functional theory calculations in graphical processing units (GPU), that can be coupled with different classical molecular dynamics engines. This code has been thoroughly optimized to perform efficient molecular dynamics simulations at the QM/MM DFT level, allowing for an exhaustive sampling of the configurational space. Selected examples are presented for the description of chemical reactivity in terms of free energy profiles, and also for the computation of optical properties, such as vibrational and electronic spectra in solvent and protein environments.

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.

Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

NASA Astrophysics Data System (ADS)

Koslowski, Tim A.; Mercati, Flavio; Sloan, David

2018-03-01

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

Quantized Electromagnetic-Field Propagation in General Non-Local and Non-Stationary Dispersive and Absorbing Media

NASA Astrophysics Data System (ADS)

Jacobs, Verne

Dynamical descriptions for the propagation of quantized electromagnetic fields, in the presence of environmental interactions, are systematically and self-consistently developed in the complimentary Schrödinger and Heisenberg pictures. An open-systems (non-equilibrium) quantum-electrodynamics description is thereby provided for electromagnetic-field propagation in general non-local and non-stationary dispersive and absorbing optical media, including a fundamental microscopic treatment of decoherence and relaxation processes due to environmental collisional and electromagnetic interactions. Particular interest is centered on entangled states and other non-classical states of electromagnetic fields, which may be created by non-linear electromagnetic interactions and detected by the measurement of various electromagnetic-field correlation functions. Accordingly, we present dynamical descriptions based on general forms of electromagnetic-field correlation functions involving both the electric-field and the magnetic-field components of the electromagnetic field, which are treated on an equal footing. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.

Transport Phenomena of Water in Molecular Fluidic Channels

PubMed Central

Vo, Truong Quoc; Kim, BoHung

2016-01-01

In molecular-level fluidic transport, where the discrete characteristics of a molecular system are not negligible (in contrast to a continuum description), the response of the molecular water system might still be similar to the continuum description if the time and ensemble averages satisfy the ergodic hypothesis and the scale of the average is enough to recover the classical thermodynamic properties. However, even in such cases, the continuum description breaks down on the material interfaces. In short, molecular-level liquid flows exhibit substantially different physics from classical fluid transport theories because of (i) the interface/surface force field, (ii) thermal/velocity slip, (iii) the discreteness of fluid molecules at the interface and (iv) local viscosity. Therefore, in this study, we present the result of our investigations using molecular dynamics (MD) simulations with continuum-based energy equations and check the validity and limitations of the continuum hypothesis. Our study shows that when the continuum description is subjected to the proper treatment of the interface effects via modified boundary conditions, the so-called continuum-based modified-analytical solutions, they can adequately predict nanoscale fluid transport phenomena. The findings in this work have broad effects in overcoming current limitations in modeling/predicting the fluid behaviors of molecular fluidic devices. PMID:27650138

Atom transistor from the point of view of nonequilibrium dynamics

NASA Astrophysics Data System (ADS)

Zhang, Z.; Dunjko, V.; Olshanii, M.

2015-12-01

We analyze the atom field-effect transistor scheme (Stickney et al 2007 Phys. Rev. A 75 013608) using the standard tools of quantum and classical nonequlilibrium dynamics. We first study the correspondence between the quantum and the mean-field descriptions of this system by computing, both ab initio and by using their mean-field analogs, the deviations from the Eigenstate Thermalization Hypothesis, quantum fluctuations, and the density of states. We find that, as far as the quantities that interest us, the mean-field model can serve as a semi-classical emulator of the quantum system. Then, using the mean-field model, we interpret the point of maximal output signal in our transistor as the onset of ergodicity—the point where the system becomes, in principle, able to attain the thermal values of the former integrals of motion, albeit not being fully thermalized yet.

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

NASA Astrophysics Data System (ADS)

Graefe, E. M.; Korsch, H. J.; Rush, A.

2016-07-01

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and PT-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.

Protein flexibility in the light of structural alphabets

PubMed Central

Craveur, Pierrick; Joseph, Agnel P.; Esque, Jeremy; Narwani, Tarun J.; Noël, Floriane; Shinada, Nicolas; Goguet, Matthieu; Leonard, Sylvain; Poulain, Pierre; Bertrand, Olivier; Faure, Guilhem; Rebehmed, Joseph; Ghozlane, Amine; Swapna, Lakshmipuram S.; Bhaskara, Ramachandra M.; Barnoud, Jonathan; Téletchéa, Stéphane; Jallu, Vincent; Cerny, Jiri; Schneider, Bohdan; Etchebest, Catherine; Srinivasan, Narayanaswamy; Gelly, Jean-Christophe; de Brevern, Alexandre G.

2015-01-01

Protein structures are valuable tools to understand protein function. Nonetheless, proteins are often considered as rigid macromolecules while their structures exhibit specific flexibility, which is essential to complete their functions. Analyses of protein structures and dynamics are often performed with a simplified three-state description, i.e., the classical secondary structures. More precise and complete description of protein backbone conformation can be obtained using libraries of small protein fragments that are able to approximate every part of protein structures. These libraries, called structural alphabets (SAs), have been widely used in structure analysis field, from definition of ligand binding sites to superimposition of protein structures. SAs are also well suited to analyze the dynamics of protein structures. Here, we review innovative approaches that investigate protein flexibility based on SAs description. Coupled to various sources of experimental data (e.g., B-factor) and computational methodology (e.g., Molecular Dynamic simulation), SAs turn out to be powerful tools to analyze protein dynamics, e.g., to examine allosteric mechanisms in large set of structures in complexes, to identify order/disorder transition. SAs were also shown to be quite efficient to predict protein flexibility from amino-acid sequence. Finally, in this review, we exemplify the interest of SAs for studying flexibility with different cases of proteins implicated in pathologies and diseases. PMID:26075209

The Classical Theory of Light Colors: a Paradigm for Description of Particle Interactions

NASA Astrophysics Data System (ADS)

Mazilu, Nicolae; Agop, Maricel; Gatu, Irina; Iacob, Dan Dezideriu; Butuc, Irina; Ghizdovat, Vlad

2016-06-01

The color is an interaction property: of the interaction of light with matter. Classically speaking it is therefore akin to the forces. But while forces engendered the mechanical view of the world, the colors generated the optical view. One of the modern concepts of interaction between the fundamental particles of matter - the quantum chromodynamics - aims to fill the gap between mechanics and optics, in a specific description of strong interactions. We show here that this modern description of the particle interactions has ties with both the classical and quantum theories of light, regardless of the connection between forces and colors. In a word, the light is a universal model in the description of matter. The description involves classical Yang-Mills fields related to color.

Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase.

PubMed

Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele

2014-11-14

Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

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

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Quantum critical dynamics of the boson system in the Ginzburg-Landau model

NASA Astrophysics Data System (ADS)

Vasin, M. G.

2014-12-01

The quantum critical dynamics of the quantum phase transitions is considered. In the framework of the unified theory, based on the Keldysh technique, we consider the crossover from the classical to the quantum description of the boson many-body system dynamics close to the second order quantum phase transition. It is shown that in this case the upper critical space dimension of this model is dc+=2, therefore the quantum critical dynamics approach is useful in case of d<2. In the one-dimension system the phase coherence time does diverge at the quantum critical point, gc, and has the form of τ∝-ln∣g-gc∣/∣g-gc∣, the correlation radius diverges as rc∝∣g-gc∣(ν=0.6).

Classical investigation of long-range coherence in biological systems

NASA Astrophysics Data System (ADS)

Preto, Jordane

2016-12-01

Almost five decades ago, H. Fröhlich [H. Fröhlich, "Long-range coherence and energy storage in biological systems," Int. J. Quantum Chem. 2(5), 641-649 (1968)] reported, on a theoretical basis, that the excitation of quantum modes of vibration in contact with a thermal reservoir may lead to steady states, where under high enough rate of energy supply, only specific low-frequency modes of vibration are strongly excited. This nonlinear phenomenon was predicted to occur in biomolecular systems, which are known to exhibit complex vibrational spectral properties, especially in the terahertz frequency domain. However, since the effects of terahertz or lower-frequency modes are mainly classical at physiological temperatures, there are serious doubts that Fröhlich's quantum description can be applied to predict such a coherent behavior in a biological environment, as suggested by the author. In addition, a quantum formalism makes the phenomenon hard to investigate using realistic molecular dynamics simulations (MD) as they are usually based on the classical principles. In the current paper, we provide a general classical Hamiltonian description of a nonlinear open system composed of many degrees of freedom (biomolecular structure) excited by an external energy source. It is shown that a coherent behaviour similar to Fröhlich's effect is to be expected in the classical case for a given range of parameter values. Thus, the supplied energy is not completely thermalized but stored in a highly ordered fashion. The connection between our Hamiltonian description, carried out in the space of normal modes, and a more standard treatment in the physical space is emphasized in order to facilitate the prediction of the effect from MD simulations. It is shown how such a coherent phenomenon may induce long-range resonance effects that could be of critical importance at the biomolecular level. The present work is motivated by recent experimental evidences of long-lived excited low-frequency modes in protein structures, which were reported as a consequence of the Fröhlich's effect.

Hamiltonian description of closed configurations of the vacuum magnetic field

NASA Astrophysics Data System (ADS)

Skovoroda, A. A.

2015-05-01

Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.

Anharmonic quantum mechanical systems do not feature phase space trajectories

NASA Astrophysics Data System (ADS)

Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole

2018-07-01

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

Gravitational self-interactions of a degenerate quantum scalar field

NASA Astrophysics Data System (ADS)

Chakrabarty, Sankha S.; Enomoto, Seishi; Han, Yaqi; Sikivie, Pierre; Todarello, Elisa M.

2018-02-01

We develop a formalism to help calculate in quantum field theory the departures from the description of a system by classical field equations. We apply the formalism to a homogeneous condensate with attractive contact interactions and to a homogeneous self-gravitating condensate in critical expansion. In their classical descriptions, such condensates persist forever. We show that in their quantum description, parametric resonance causes quanta to jump in pairs out of the condensate into all modes with wave vector less than some critical value. We calculate, in each case, the time scale over which the homogeneous condensate is depleted and after which a classical description is invalid. We argue that the duration of classicality of inhomogeneous condensates is shorter than that of homogeneous condensates.

A surprisingly simple correlation between the classical and quantum structural networks in liquid water

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

Hamm, Peter; Fanourgakis, George S.; Xantheas, Sotiris S.

Nuclear quantum effects in liquid water have profound implications for several of its macroscopic properties related to structure, dynamics, spectroscopy and transport. Although several of water’s macroscopic properties can be reproduced by classical descriptions of the nuclei using potentials effectively parameterized for a narrow range of its phase diagram, a proper account of the nuclear quantum effects is required in order to ensure that the underlying molecular interactions are transferable across a wide temperature range covering different regions of that diagram. When performing an analysis of the hydrogen bonded structural networks in liquid water resulting from the classical (class.) andmore » quantum (q.m.) descriptions of the nuclei with the transferable, flexible, polarizable TTM3-F interaction potential, we found that the two results can be superimposed over the temperature range of T=270-350 K using a surprisingly simple, linear scaling of the two temperatures according to T(q.m.)=aT(class)- T , where a=1.2 and T=51 K. The linear scaling and constant shift of the temperature scale can be considered as a generalization of the previously reported temperature shifts (corresponding to structural changes and the melting T) induced by quantum effects in liquid water.« less

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

D’Arrigo, A., E-mail: antonio.darrigo@dmfci.unict.it; Dipartimento di Fisica e Astronomia, Università degli Studi Catania, Via Santa Sofia 64, 95123 Catania; Centro Siciliano di Fisica Nucleare e Struttura della Materia

We investigate the phenomenon of bipartite entanglement revivals under purely local operations in systems subject to local and independent classical noise sources. We explain this apparent paradox in the physical ensemble description of the system state by introducing the concept of “hidden” entanglement, which indicates the amount of entanglement that cannot be exploited due to the lack of classical information on the system. For this reason this part of entanglement can be recovered without the action of non-local operations or back-transfer process. For two noninteracting qubits under a low-frequency stochastic noise, we show that entanglement can be recovered by localmore » pulses only. We also discuss how hidden entanglement may provide new insights about entanglement revivals in non-Markovian dynamics.« less

Critical analysis of partial discharge dynamics in air filled spherical voids

NASA Astrophysics Data System (ADS)

Callender, G.; Golosnoy, I. O.; Rapisarda, P.; Lewin, P. L.

2018-03-01

In this paper partial discharge (PD) is investigated inside a spherical air filled void at atmospheric pressure using a drift diffusion model. Discharge dynamics consisted of an electron avalanche transitioning into positive streamer, in agreement with earlier work on dielectric barrier discharges. Different model configurations were utilised to test many of the concepts employed in semi-analytical PD activity models, which use simplistic descriptions of the discharge dynamics. The results showed that many of these concepts may be erroneous, with significant discrepancies between the canonical reasoning and the simulation results. For example, the residual electric field, the electric field after a discharge, is significantly lower than the estimates used by classical PD activity models in the literature.

Interaction and dynamics of ionic liquids based on choline and amino acid anions

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

Campetella, M.; Bodo, E., E-mail: enrico.bodo@uniroma1.it; Caminiti, R., E-mail: ruggero.caminiti@uniroma1.it

2015-06-21

The combination of amino acid anions with the choline cation gives origin to a new and potentially important class of organic ionic liquids that might represent a viable and bio-compatible alternative with respect to the traditional ones. We present here a detailed study of the bulk phase of the prototype system composed of the simplest amino acid (alanine) anion and the choline cation, based on ab initio and classical molecular dynamics. Theoretical findings have been validated by comparing with accurate experimental X-ray diffraction data and infrared spectra. We find that hydrogen bonding (HB) features in these systems are crucial inmore » establishing their local geometric structure. We have also found that these HBs once formed are persistent and that the proton resides exclusively on the choline cation. In addition, we show that a classical force field description for this particular ionic liquid can be accurately performed by using a slightly modified version of the generalized AMBER force field.« less

Interaction and dynamics of ionic liquids based on choline and amino acid anions

NASA Astrophysics Data System (ADS)

Campetella, M.; Bodo, E.; Caminiti, R.; Martino, A.; D'Apuzzo, F.; Lupi, S.; Gontrani, L.

2015-06-01

The combination of amino acid anions with the choline cation gives origin to a new and potentially important class of organic ionic liquids that might represent a viable and bio-compatible alternative with respect to the traditional ones. We present here a detailed study of the bulk phase of the prototype system composed of the simplest amino acid (alanine) anion and the choline cation, based on ab initio and classical molecular dynamics. Theoretical findings have been validated by comparing with accurate experimental X-ray diffraction data and infrared spectra. We find that hydrogen bonding (HB) features in these systems are crucial in establishing their local geometric structure. We have also found that these HBs once formed are persistent and that the proton resides exclusively on the choline cation. In addition, we show that a classical force field description for this particular ionic liquid can be accurately performed by using a slightly modified version of the generalized AMBER force field.

First experimental test of a trace formula for billiard systems showing mixed dynamics.

PubMed

Dembowski, C; Gräf, H D; Heine, A; Hesse, T; Rehfeld, H; Richter, A

2001-04-09

In general, trace formulas relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart. Here we report for the first time on a semiclassical description of microwave spectra taken from superconducting billiards of the Limaçon family showing mixed dynamics in terms of a generalized trace formula derived by Ullmo et al. [Phys. Rev. E 54, 136 (1996)]. This expression not only describes mixed-typed behavior but also the limiting cases of fully regular and fully chaotic systems and thus presents a continuous interpolation between the Berry-Tabor and Gutzwiller formulas.

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power

NASA Astrophysics Data System (ADS)

Bulgac, Aurel; Jin, Shi; Magierski, Piotr; Roche, Kenneth; Schunck, Nicolas; Stetcu, Ionel

2017-11-01

Two major recent developments in theory and computational resources created the favorable conditions for achieving a microscopic description of fission dynamics in classically allowed regions of the collective potential energy surface, almost eighty years after its discovery in 1939 by Hahn and Strassmann [1]. The first major development was in theory, the extension of the Time-Dependent Density Functional Theory (TDDFT) [2-5] to superfluid fermion systems [6]. The second development was in computing, the emergence of powerful enough supercomputers capable of solving the complex systems of equations describing the time evolution in three dimensions without any restrictions of hundreds of strongly interacting nucleons. Thus the conditions have been created to renounce phenomenological models and incomplete microscopic treatments with uncontrollable approximations and/or assumptions in the description of the complex dynamics of fission. Even though the available nuclear energy density functionals (NEDFs) are phenomenological still, their accuracy is improving steadily and the prospects of being able to perform calculations of the nuclear fission dynamics and to predict many properties of the fission fragments, otherwise not possible to extract from experiments.

Trajectory description of the quantum–classical transition for wave packet interference

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-08-15

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow themore » main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.« less

Classical and ab-initio simulations of hydrogen in the dissociating regime

NASA Astrophysics Data System (ADS)

Clerouin, Jean; Blottiau, Patrick; Bernard, Stephane; Dufreche, Jean-Francois

1999-11-01

Recent experiments on shock compressed hydrogen ( L. B. Da Silva, P. Cellires, G. W. Collins., et al., Physical Review Letters 78, 483-486 (1997).) have motivated a large number of theoretical studies to try to reproduce the experimental Hugoniot data. In spite of the simplicity of the hydrogen molecule, a precise description of its dissociation under pressure and temperature is still missing. Here, we compare three different approaches: the empirical Ross model (M. Ross, Physical Review B 58, 669-677 (1998).) which reproduces the experimental data, a classical molecular dynamics model, which allows for the computation of transport coefficients such as the viscosity footnote J. F. Dufreche and J. Clerouin, Physical Review E , submitted (1999). and ab initio simulations for a detailed description of the dissociation process. This comparison reveals that in the region [0.1 g/cm^3< ρ< 1g/cm^3, 2000K

A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling

DOE PAGES

Cotton, Stephen J.; Miller, William H.

2016-10-14

Previous work has shown how a symmetrical quasi-classical (SQC) windowing procedure can be used to quantize the initial and final electronic degrees of freedom in the Meyer-Miller (MM) classical vibronic (i.e, nuclear + electronic) Hamiltonian, and that the approach provides a very good description of electronically non-adiabatic processes within a standard classical molecular dynamics framework for a number of benchmark problems. This study explores application of the SQC/MM approach to the case of very weak non-adiabatic coupling between the electronic states, showing (as anticipated) how the standard SQC/MM approach used to date fails in this limit, and then devises amore » new SQC windowing scheme to deal with it. Finally, application of this new SQC model to a variety of realistic benchmark systems shows that the new model not only treats the weak coupling case extremely well, but it is also seen to describe the “normal” regime (of electronic transition probabilities ≳ 0.1) even more accurately than the previous “standard” model.« less

A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling

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

Cotton, Stephen J.; Miller, William H.

Previous work has shown how a symmetrical quasi-classical (SQC) windowing procedure can be used to quantize the initial and final electronic degrees of freedom in the Meyer-Miller (MM) classical vibronic (i.e, nuclear + electronic) Hamiltonian, and that the approach provides a very good description of electronically non-adiabatic processes within a standard classical molecular dynamics framework for a number of benchmark problems. This study explores application of the SQC/MM approach to the case of very weak non-adiabatic coupling between the electronic states, showing (as anticipated) how the standard SQC/MM approach used to date fails in this limit, and then devises amore » new SQC windowing scheme to deal with it. Finally, application of this new SQC model to a variety of realistic benchmark systems shows that the new model not only treats the weak coupling case extremely well, but it is also seen to describe the “normal” regime (of electronic transition probabilities ≳ 0.1) even more accurately than the previous “standard” model.« less

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.

PubMed

Graziani, F R; Bauer, J D; Murillo, M S

2014-09-01

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

Topological classification of the Goryachev integrable case in rigid body dynamics

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

Nikolaenko, S S

2016-01-31

A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in othermore » words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.« less

Crystallization by Particle Attachment in Synthetic, Biogenic, and Geologic Environments

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

De Yoreo, James J.; Gilbert, Pupa U.; Sommerdijk, Nico

Field and laboratory observations show that crystals commonly form by the addition and attachment of particles that range from multi-ion complexes to fully formed nanoparticles. These non-classical pathways to crystallization are diverse, in contrast to classical models that consider the addition of monomeric chemical species. We review progress toward understanding crystal growth by particle attachment processes and show that multiple pathways result from the interplay of free energy landscapes and reaction dynamics. Much remains unknown about the fundamental aspects; particularly the relationships between solution structure, interfacial forces, and particle motion. Developing a predictive description that connects molecular details to ensemblemore » behavior will require revisiting long-standing interpretations of crystal formation in synthetic systems and patterns of mineralization in natural environments.« less

Zubarev's Nonequilibrium Statistical Operator Method in the Generalized Statistics of Multiparticle Systems

NASA Astrophysics Data System (ADS)

Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.

2018-01-01

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.

Fractional Generalizations of Maxwell and Kelvin-Voigt Models for Biopolymer Characterization

PubMed Central

Jóźwiak, Bertrand; Orczykowska, Magdalena; Dziubiński, Marek

2015-01-01

The paper proposes a fractional generalization of the Maxwell and Kelvin-Voigt rheological models for a description of dynamic behavior of biopolymer materials. It was found that the rheological models of Maxwell-type do not work in the case of modeling of viscoelastic solids, and the model which significantly better describes the nature of changes in rheological properties of such media is the modified fractional Kelvin-Voigt model with two built-in springpots (MFKVM2). The proposed model was used to describe the experimental data from the oscillatory and creep tests of 3% (w/v) kuzu starch pastes, and to determine the values of their rheological parameters as a function of pasting time. These parameters provide a lot of additional information about structure and viscoelastic properties of the medium in comparison to the classical analysis of dynamic curves G’ and G” and shear creep compliance J(t). It allowed for a comprehensive description of a wide range of properties of kuzu starch pastes, depending on the conditions of pasting process. PMID:26599756

Alternative descriptions of wave and particle aspects of the harmonic oscillator

NASA Technical Reports Server (NTRS)

Schuch, Dieter

1993-01-01

The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.

Scalar field quantum cosmology: A Schrödinger picture

NASA Astrophysics Data System (ADS)

Vakili, Babak

2012-11-01

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.

Leading-order classical Lagrangians for the nonminimal standard-model extension

NASA Astrophysics Data System (ADS)

Reis, J. A. A. S.; Schreck, M.

2018-03-01

In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal standard-model extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the Lagrangian obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.

Eternal non-Markovianity: from random unitary to Markov chain realisations.

PubMed

Megier, Nina; Chruściński, Dariusz; Piilo, Jyrki; Strunz, Walter T

2017-07-25

The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple stochastic Schrödinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more general family of CPT maps, characterized by a point within a parameter triangle. Our results show how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master equation based on unitary transformations and projective measurements in an extended Hilbert space, guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) representation of the dynamics in an extended Hilbert space can be found, with a remarkable property: there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these results from non-CP-divisible to non-P-divisible dynamics.

A new bio-inspired, population-level approach to the socioeconomic evolution of dynamic spectrum access services

NASA Astrophysics Data System (ADS)

Horvath, Denis; Gazda, Juraj; Brutovsky, Branislav

Evolutionary species and quasispecies models provide the universal and flexible basis for a large-scale description of the dynamics of evolutionary systems, which can be built conceived as a constraint satisfaction dynamics. It represents a general framework to design and study many novel, technologically contemporary models and their variants. Here, we apply the classical quasispecies concept to model the emerging dynamic spectrum access (DSA) markets. The theory describes the mechanisms of mimetic transfer, competitive interactions between socioeconomic strata of the end-users, their perception of the utility and inter-operator switching in the variable technological environments of the operators offering the wireless spectrum services. The algorithmization and numerical modeling demonstrate the long-term evolutionary socioeconomic changes which reflect the end-user preferences and results of the majorization of their irrational decisions in the same manner as the prevailing tendencies which are embodied in the efficient market hypothesis.

Enhanced Molecular Dynamics Methods Applied to Drug Design Projects.

PubMed

Ziada, Sonia; Braka, Abdennour; Diharce, Julien; Aci-Sèche, Samia; Bonnet, Pascal

2018-01-01

Nobel Laureate Richard P. Feynman stated: "[…] everything that living things do can be understood in terms of jiggling and wiggling of atoms […]." The importance of computer simulations of macromolecules, which use classical mechanics principles to describe atom behavior, is widely acknowledged and nowadays, they are applied in many fields such as material sciences and drug discovery. With the increase of computing power, molecular dynamics simulations can be applied to understand biological mechanisms at realistic timescales. In this chapter, we share our computational experience providing a global view of two of the widely used enhanced molecular dynamics methods to study protein structure and dynamics through the description of their characteristics, limits and we provide some examples of their applications in drug design. We also discuss the appropriate choice of software and hardware. In a detailed practical procedure, we describe how to set up, run, and analyze two main molecular dynamics methods, the umbrella sampling (US) and the accelerated molecular dynamics (aMD) methods.

Atomic-Scale Lightning Rod Effect in Plasmonic Picocavities: A Classical View to a Quantum Effect.

PubMed

Urbieta, Mattin; Barbry, Marc; Zhang, Yao; Koval, Peter; Sánchez-Portal, Daniel; Zabala, Nerea; Aizpurua, Javier

2018-01-23

Plasmonic gaps are known to produce nanoscale localization and enhancement of optical fields, providing small effective mode volumes of about a few hundred nm 3 . Atomistic quantum calculations based on time-dependent density functional theory reveal the effect of subnanometric localization of electromagnetic fields due to the presence of atomic-scale features at the interfaces of plasmonic gaps. Using a classical model, we explain this as a nonresonant lightning rod effect at the atomic scale that produces an extra enhancement over that of the plasmonic background. The near-field distribution of atomic-scale hot spots around atomic features is robust against dynamical screening and spill-out effects and follows the potential landscape determined by the electron density around the atomic sites. A detailed comparison of the field distribution around atomic hot spots from full quantum atomistic calculations and from the local classical approach considering the geometrical profile of the atoms' electronic density validates the use of a classical framework to determine the effective mode volume in these extreme subnanometric optical cavities. This finding is of practical importance for the community of surface-enhanced molecular spectroscopy and quantum nanophotonics, as it provides an adequate description of the local electromagnetic fields around atomic-scale features with use of simplified classical methods.

Computation and Dynamics: Classical and Quantum

NASA Astrophysics Data System (ADS)

Kisil, Vladimir V.

2010-05-01

We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed quantum-classical dynamics we look for a full cost of computations on quantum computers with classical terminals.

Modeling of crack growth under mixed-mode loading by a molecular dynamics method and a linear fracture mechanics approach

NASA Astrophysics Data System (ADS)

Stepanova, L. V.

2017-12-01

Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is the Embedded Atom Method (EAM) potential. Plane specimens with an initial central crack are subjected to mixed-mode loadings. The simulation cell contains 400,000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide range of temperatures (from 0.1 K to 800 K) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields. The multi-parameter fracture criteria are based on the multi-parameter stress field description taking into account the higher order terms of the Williams series expansion of the crack tip fields.

Cold chemistry with cold molecules

NASA Astrophysics Data System (ADS)

Shagam, Yuval

Low temperature chemistry has been predicted to be dominated by quantum effects, such as shape resonances, where colliding particles exhibit wave-like behavior and tunnel through potential barriers. Observation of these quantum effects provides valuable insight into the microscopic mechanism that governs scattering processes. Our recent advances in the control of neutral supersonic molecular beams, namely merged beam experiments, have enabled continuous tuning of collision energies from the classical regime at room temperature down to 0.01 kelvin, where a quantum description of the dynamics is necessary. I will discuss our use of this technique to study how the dynamics change when molecules participate in collisions, demonstrating the crucial role the molecular quantum rotor plays. We have found that at low temperatures rotational state of the molecule can strongly affect collision dynamics considerably changing reaction rates, due to the different symmetries of the molecular wavefunction.

Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows

NASA Astrophysics Data System (ADS)

Minier, Jean-Pierre; Profeta, Christophe

2015-11-01

This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Zp=(xp,Up) and is represented by its PDF p (t ;yp,Vp) which is the solution of a kinetic PDF equation obtained through a flux closure based on the Furutsu-Novikov theorem. The second PDF formulation includes fluid variables into the particle state vector, for example, the fluid velocity seen by particles Zp=(xp,Up,Us) , and, consequently, handles an extended PDF p (t ;yp,Vp,Vs) which is the solution of a dynamic PDF equation. For high-Reynolds-number fluid flows, a typical formulation of the latter category relies on a Langevin model for the trajectories of the fluid seen or, conversely, on a Fokker-Planck equation for the extended PDF. In the present work, a new derivation of the kinetic PDF equation is worked out and new physical expressions of the dispersion tensors entering the kinetic PDF equation are obtained by starting from the extended PDF and integrating over the fluid seen. This demonstrates that, under the same assumption of a Gaussian colored noise and irrespective of the specific stochastic model chosen for the fluid seen, the kinetic PDF description is the marginal of a dynamic PDF one. However, a detailed analysis reveals that kinetic PDF models of particle dynamics in turbulent flows described by statistical correlations constitute incomplete stand-alone PDF descriptions and, moreover, that present kinetic-PDF equations are mathematically ill posed. This is shown to be the consequence of the non-Markovian characteristic of the stochastic process retained to describe the system and the use of an external colored noise. Furthermore, developments bring out that well-posed PDF descriptions are essentially due to a proper choice of the variables selected to describe physical systems and guidelines are formulated to emphasize the key role played by the notion of slow and fast variables.

Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

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

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de; Noh, Changsuk, E-mail: changsuk@kias.re.kr; Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogicalmore » introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.« less

Nonisothermal fluctuating hydrodynamics and Brownian motion

NASA Astrophysics Data System (ADS)

Falasco, G.; Kroy, K.

2016-03-01

The classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.

Contrasting liquid imbibition into uncoated versus pigment coated paper enables a description of imbibition into new-generation surface-filled paper.

PubMed

Liu, Guodong; Fu, Sijia; Lu, Zhaoqing; Zhang, Meiyun; Ridgway, Cathy; Gane, Patrick

2017-12-18

The transport of print fluids into paper is directly dependent on the imbibition characteristic of the paper including both the z-, x- and y-directions. As the measurement of free liquid imbibition into the paper thickness (z-direction) is difficult experimentally, due to the thin nature of paper, in this paper we resort to imbibition along the y-direction of paper to analyse and explore the possibility of understanding the mechanistic differences between wicking into uncoated unfilled paper versus that of controllable pigment-filled paper and paper coating. Considering the classical imbibition dynamic, the measured imbibition was characterised firstly with respect to [Formula: see text] and secondly with respect to linear t. It is shown that the wicking behaviour of uncoated unfilled paper follows neither the classical viscous drag balance model of Lucas-Washburn ([Formula: see text]) nor the more comprehensive inertia-included imbibition described by Bosanquet. However, by increasing the filler load into the surface layer of the paper, the imbibition dynamic is seen to revert to the Bosanquet model. Thus, when using highly filled papers, the imbibition dynamic for printing liquid shows a fast imbibition at the initial stages dominated by inertial plug flow, and then transits to the Lucas-Washburn viscosity-dominated imbibition component over longer time.

A quantum relaxation-time approximation for finite fermion systems

NASA Astrophysics Data System (ADS)

Reinhard, P.-G.; Suraud, E.

2015-03-01

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

Parity-time symmetry breaking in magnetic systems

DOE PAGES

Galda, Alexey; Vinokur, Valerii M.

2016-07-14

The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science, spanning the broadest wealth of research areas that range from quantum optics to living organisms. By focusing on nonequilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. Here, we reveal the spin-transfer torque-drivenmore » parity-time symmetry-breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. These findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.« less

Solution NMR structure of a designed metalloprotein and complementary molecular dynamics refinement.

PubMed

Calhoun, Jennifer R; Liu, Weixia; Spiegel, Katrin; Dal Peraro, Matteo; Klein, Michael L; Valentine, Kathleen G; Wand, A Joshua; DeGrado, William F

2008-02-01

We report the solution NMR structure of a designed dimetal-binding protein, di-Zn(II) DFsc, along with a secondary refinement step employing molecular dynamics techniques. Calculation of the initial NMR structural ensemble by standard methods led to distortions in the metal-ligand geometries at the active site. Unrestrained molecular dynamics using a nonbonded force field for the metal shell, followed by quantum mechanical/molecular mechanical dynamics of DFsc, were used to relax local frustrations at the dimetal site that were apparent in the initial NMR structure and provide a more realistic description of the structure. The MD model is consistent with NMR restraints, and in good agreement with the structural and functional properties expected for DF proteins. This work demonstrates that NMR structures of metalloproteins can be further refined using classical and first-principles molecular dynamics methods in the presence of explicit solvent to provide otherwise unavailable insight into the geometry of the metal center.

Nuclear quantum effects in water exchange around lithium and fluoride ions

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

Wilkins, David M.; Manolopoulos, David E.; Dang, Liem X.

2015-02-14

We employ classical and ring polymer molecular dynamics simulations to study the effect of nuclear quantum fluctuations on the structure and the water exchange dynamics of aqueous solutions of lithium and fluoride ions. While we obtain reasonably good agreement with experimental data for solutions of lithium by augmenting the Coulombic interactions between the ion and the water molecules with a standard Lennard-Jones ion-oxygen potential, the same is not true for solutions of fluoride, for which we find that a potential with a softer repulsive wall gives much better agreement. A small degree of destabilization of the first hydration shell ismore » found in quantum simulations of both ions when compared with classical simulations, with the shell becoming less sharply defined and the mean residence time of the water molecules in the shell decreasing. In line with these modest differences, we find that the mechanisms of the exchange processes are unaffected by quantization, so a classical description of these reactions gives qualitatively correct and quantitatively reasonable results. We also find that the quantum effects in solutions of lithium are larger than in solutions of fluoride. This is partly due to the stronger interaction of lithium with water molecules, partly due to the lighter mass of lithium and partly due to competing quantum effects in the hydration of fluoride, which are absent in the hydration of lithium.« less

A Parallel and Incremental Approach for Data-Intensive Learning of Bayesian Networks.

PubMed

Yue, Kun; Fang, Qiyu; Wang, Xiaoling; Li, Jin; Liu, Weiyi

2015-12-01

Bayesian network (BN) has been adopted as the underlying model for representing and inferring uncertain knowledge. As the basis of realistic applications centered on probabilistic inferences, learning a BN from data is a critical subject of machine learning, artificial intelligence, and big data paradigms. Currently, it is necessary to extend the classical methods for learning BNs with respect to data-intensive computing or in cloud environments. In this paper, we propose a parallel and incremental approach for data-intensive learning of BNs from massive, distributed, and dynamically changing data by extending the classical scoring and search algorithm and using MapReduce. First, we adopt the minimum description length as the scoring metric and give the two-pass MapReduce-based algorithms for computing the required marginal probabilities and scoring the candidate graphical model from sample data. Then, we give the corresponding strategy for extending the classical hill-climbing algorithm to obtain the optimal structure, as well as that for storing a BN by pairs. Further, in view of the dynamic characteristics of the changing data, we give the concept of influence degree to measure the coincidence of the current BN with new data, and then propose the corresponding two-pass MapReduce-based algorithms for BNs incremental learning. Experimental results show the efficiency, scalability, and effectiveness of our methods.

Fragmentation dynamics of ionized neon trimer inside helium nanodroplets: a theoretical study.

PubMed

Bonhommeau, David; Viel, Alexandra; Halberstadt, Nadine

2004-06-22

We report a theoretical study of the fragmentation dynamics of Ne(3) (+) inside helium nanodroplets, following vertical ionization of the neutral neon trimer. The motion of the neon atoms is treated classically, while transitions between the electronic states of the ionic cluster are treated quantum mechanically. A diatomics-in-molecules description of the potential energy surfaces is used, in a minimal basis set consisting of three effective p orbitals on each neon atom for the missing electron. The helium environment is modeled by a friction force acting on the neon atoms when their speed exceeds the Landau velocity. A reasonable range of values for the corresponding friction coefficient is obtained by comparison with existing experimental measurements. (c) 2004 American Institute of Physics.

Modeling quantum fluid dynamics at nonzero temperatures

PubMed Central

Berloff, Natalia G.; Brachet, Marc; Proukakis, Nick P.

2014-01-01

The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures. PMID:24704874

Efficient energy transfer in light-harvesting systems: Quantum-classical comparison, flux network, and robustness analysis

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

Wu Jianlan; Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139; Liu Fan

2012-11-07

Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F. Liu, Y. Shen, J. S. Cao, and R. J. Silbey, New J. Phys. 12, 105012 (2010)], full quantum dynamics and leading-order 'classical' hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker (HSR) model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time ormore » in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model which is also investigated in the third paper [J. Moix, J. L. Wu, P. F. Huo, D. F. Coker, and J. S. Cao, J. Phys. Chem. Lett. 2, 3045 (2011)], the quantum-classical comparison with the flux network analysis is summarized in Appendix C. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.« less

Impact of built-in fields and contact configuration on the characteristics of ultra-thin GaAs solar cells

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

Aeberhard, Urs, E-mail: u.aeberhard@fz-juelich.de

2016-07-18

We discuss the effects of built-in fields and contact configuration on the photovoltaic characteristics of ultra-thin GaAs solar cells. The investigation is based on advanced quantum-kinetic simulations reaching beyond the standard semi-classical bulk picture concerning the consideration of charge carrier states and dynamics in complex potential profiles. The thickness dependence of dark and photocurrent in the ultra-scaled regime is related to the corresponding variation of both, the built-in electric fields and associated modification of the density of states, and the optical intensity in the films. Losses in open-circuit voltage and short-circuit current due to the leakage of electronically and opticallymore » injected carriers at minority carrier contacts are investigated for different contact configurations including electron and hole blocking barrier layers. The microscopic picture of leakage currents is connected to the effect of finite surface recombination velocities in the semi-classical description, and the impact of these non-classical contact regions on carrier generation and extraction is analyzed.« less

Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation

DOE PAGES

Wong, Cheuk-Yin

2017-05-25

In the semi-classical description of the flux-tube fragmentation process for hadron production and hadronization in high-energymore » $e^+e^-$ annihilations and $pp$ collisions, the rapidity-space-time ordering and the local conservation laws of charge, flavor, and momentum provide a set of powerful tools that may allow the reconstruction of the space-time dynamics of quarks and mesons in exclusive measurements of produced hadrons, on an event-by-event basis. We propose procedures to reconstruct the space-time dynamics from event-by-event exclusive hadron data to exhibit explicitly the ordered chain of hadrons produced in a flux tube fragmentation. As a supplementary tool, we infer the average space-time coordinates of the $q$-$$\\bar q$$ pair production vertices from the $$\\pi^-$$ rapidity distribution data obtained by the NA61/SHINE Collaboration in $pp$ collisions at $$\\sqrt{s}$$ = 6.3 to 17.3 GeV.« less

Dynamics of photoexcited Ba+ cations in 4He nanodroplets

NASA Astrophysics Data System (ADS)

Leal, Antonio; Zhang, Xiaohang; Barranco, Manuel; Cargnoni, Fausto; Hernando, Alberto; Mateo, David; Mella, Massimo; Drabbels, Marcel; Pi, Martí

2016-03-01

We present a joint experimental and theoretical study on the desolvation of Ba+ cations in 4He nanodroplets excited via the 6p ← 6s transition. The experiments reveal an efficient desolvation process yielding mainly bare Ba+ cations and Ba+Hen exciplexes with n = 1 and 2. The speed distributions of the ions are well described by Maxwell-Boltzmann distributions with temperatures ranging from 60 to 178 K depending on the excitation frequency and Ba+ Hen exciplex size. These results have been analyzed by calculations based on a time-dependent density functional description for the helium droplet combined with classical dynamics for the Ba+. In agreement with experiment, the calculations reveal the dynamical formation of exciplexes following excitation of the Ba+ cation. In contrast to experimental observation, the calculations do not reveal desolvation of excited Ba+ cations or exciplexes, even when relaxation pathways to lower lying states are included.

Theoretical investigation of the electron capture and loss processes in the collisions of He2+ + Ne.

PubMed

Hong, Xuhai; Wang, Feng; Jiao, Yalong; Su, Wenyong; Wang, Jianguo; Gou, Bingcong

2013-08-28

Based on the time-dependent density functional theory, a method is developed to study ion-atom collision dynamics, which self-consistently couples the quantum mechanical description of electron dynamics with the classical treatment of the ion motion. Employing real-time and real-space method, the coordinate space translation technique is introduced to allow one to focus on the region of target or projectile depending on the actual concerned process. The benchmark calculations are performed for the collisions of He(2+) + Ne, and the time evolution of electron density distribution is monitored, which provides interesting details of the interaction dynamics between the electrons and ion cores. The cross sections of single and many electron capture and loss have been calculated in the energy range of 1-1000 keV/amu, and the results show a good agreement with the available experiments over a wide range of impact energies.

Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation

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

Wong, Cheuk-Yin

In the semi-classical description of the flux-tube fragmentation process for hadron production and hadronization in high-energymore » $e^+e^-$ annihilations and $pp$ collisions, the rapidity-space-time ordering and the local conservation laws of charge, flavor, and momentum provide a set of powerful tools that may allow the reconstruction of the space-time dynamics of quarks and mesons in exclusive measurements of produced hadrons, on an event-by-event basis. We propose procedures to reconstruct the space-time dynamics from event-by-event exclusive hadron data to exhibit explicitly the ordered chain of hadrons produced in a flux tube fragmentation. As a supplementary tool, we infer the average space-time coordinates of the $q$-$$\\bar q$$ pair production vertices from the $$\\pi^-$$ rapidity distribution data obtained by the NA61/SHINE Collaboration in $pp$ collisions at $$\\sqrt{s}$$ = 6.3 to 17.3 GeV.« less

Dynamical Symmetries in Classical Mechanics

ERIC Educational Resources Information Center

Boozer, A. D.

2012-01-01

We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

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

Donangelo, R.J.

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, andmore » therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed.« less

A Force Balanced Fragmentation Method for ab Initio Molecular Dynamic Simulation of Protein.

PubMed

Xu, Mingyuan; Zhu, Tong; Zhang, John Z H

2018-01-01

A force balanced generalized molecular fractionation with conjugate caps (FB-GMFCC) method is proposed for ab initio molecular dynamic simulation of proteins. In this approach, the energy of the protein is computed by a linear combination of the QM energies of individual residues and molecular fragments that account for the two-body interaction of hydrogen bond between backbone peptides. The atomic forces on the caped H atoms were corrected to conserve the total force of the protein. Using this approach, ab initio molecular dynamic simulation of an Ace-(ALA) 9 -NME linear peptide showed the conservation of the total energy of the system throughout the simulation. Further a more robust 110 ps ab initio molecular dynamic simulation was performed for a protein with 56 residues and 862 atoms in explicit water. Compared with the classical force field, the ab initio molecular dynamic simulations gave better description of the geometry of peptide bonds. Although further development is still needed, the current approach is highly efficient, trivially parallel, and can be applied to ab initio molecular dynamic simulation study of large proteins.

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.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice

NASA Astrophysics Data System (ADS)

Reddy, Sandeep K.; Straight, Shelby C.; Bajaj, Pushp; Huy Pham, C.; Riera, Marc; Moberg, Daniel R.; Morales, Miguel A.; Knight, Chris; Götz, Andreas W.; Paesani, Francesco

2016-11-01

The MB-pol many-body potential has recently emerged as an accurate molecular model for water simulations from the gas to the condensed phase. In this study, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with experimental data and high-level ab initio calculations. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calculated with MB-pol are in excellent agreement with reference data obtained at the coupled cluster level. Several structural, thermodynamic, and dynamical properties of the liquid phase at atmospheric pressure are investigated through classical molecular dynamics simulations as a function of temperature. The structural properties of the liquid phase are in nearly quantitative agreement with X-ray diffraction data available over the temperature range from 268 to 368 K. The analysis of other thermodynamic and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, especially at low temperature, for a physically correct description of the properties of liquid water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water.

Emergent mechanics, quantum and un-quantum

NASA Astrophysics Data System (ADS)

Ralston, John P.

2013-10-01

There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications

Milgrom's revision of Newton's laws - Dynamical and cosmological consequences

NASA Technical Reports Server (NTRS)

Felten, J. E.

1984-01-01

Milgrom's (1983) recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. It is shown by simple examples that a Milgrom acceleration, in the form presented so far, implies other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a 'Milgrom universe' will recollapse even if the classical closure parameter Omega is much less than unity. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A new theory of gravitation will be needed before the behavior of a Milgrom universe can be predicted.

Milgrom's revision of cosmic dynamics: Amending Newton's laws or Keplers?

NASA Technical Reports Server (NTRS)

Felten, J. E.

1983-01-01

Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. Simple examples show that a Milgrom acceleration, in the form presented so far, imply other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a Milgrom universe will recollapse even if the classical closure parameter theta is less than 1. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A theory of gravitation needed before the behavior of a Milgrom universe can be predicted.

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

Lott, Martin; Remillieux, Marcel; Garnier, Vincent; ...

2017-07-17

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists ofmore » the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.« less

Coherence penalty functional: A simple method for adding decoherence in Ehrenfest dynamics

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

Akimov, Alexey V., E-mail: alexvakimov@gmail.com, E-mail: oleg.prezhdo@rochester.edu; Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973; Long, Run

2014-05-21

We present a new semiclassical approach for description of decoherence in electronically non-adiabatic molecular dynamics. The method is formulated on the grounds of the Ehrenfest dynamics and the Meyer-Miller-Thoss-Stock mapping of the time-dependent Schrödinger equation onto a fully classical Hamiltonian representation. We introduce a coherence penalty functional (CPF) that accounts for decoherence effects by randomizing the wavefunction phase and penalizing development of coherences in regions of strong non-adiabatic coupling. The performance of the method is demonstrated with several model and realistic systems. Compared to other semiclassical methods tested, the CPF method eliminates artificial interference and improves agreement with the fullymore » quantum calculations on the models. When applied to study electron transfer dynamics in the nanoscale systems, the method shows an improved accuracy of the predicted time scales. The simplicity and high computational efficiency of the CPF approach make it a perfect practical candidate for applications in realistic systems.« less

Multiscale Modeling of Plasmon-Exciton Dynamics of Malachite Green Monolayers on Gold Nanoparticles

NASA Astrophysics Data System (ADS)

Smith, Holden; Karam, Tony; Haber, Louis; Lopata, Kenneth

A multi-scale hybrid quantum/classical approach using classical electrodynamics and a collection of discrete two level quantum system is used to investigate the coupling dynamics of malachite green monolayers adsorbed to the surface of a spherical gold nanoparticle (NP). This method utilizes finite difference time domain (FDTD) to describe the plasmonic response of the NP and a two-level quantum description for the molecule via the Maxwell/Liouville equation. The molecular parameters are parameterized using CASPT2 for the energies and transition dipole moments, with the dephasing lifetime fit to experiment. This approach is suited to simulating thousands of molecules on the surface of a plasmonic NP. There is good agreement with experimental extinction measurements, predicting the plasmon and molecule depletions. Additionally, this model captures the polariton peaks overlapped with a Fano-type resonance profile observed in the experimental extinction measurements. This technique shows promise for modeling plasmon/molecule interactions in chemical sensing and light harvesting in multi-chromophore systems. This material is based upon work supported by the National Science Foundation under the NSF EPSCoR Cooperative Agreement No. EPS-1003897 and the Louisiana Board of Regents Research Competitiveness Subprogram under Contract Number LEQSF(2014-17)-RD-A-0.

Multiscale Modeling of Plasmon-Exciton Dynamics of Malachite Green Monolayers on Gold Nanoparticles

NASA Astrophysics Data System (ADS)

Smith, Holden; Karam, Tony; Haber, Louis; Lopata, Kenneth

A multi-scale hybrid quantum/classical approach using classical electrodynamics and a collection of discrete two-level quantum system is used to investigate the coupling dynamics of malachite green monolayers adsorbed to the surface of a spherical gold nanoparticle (NP). This method utilizes finite difference time domain (FDTD) to describe the plasmonic response of the NP and a two-level quantum description for the molecule via the Maxwell/Liouville equation. The molecular parameters are parameterized using CASPT2 for the energies and transition dipole moments, with the dephasing lifetime fit to experiment. This approach is suited to simulating thousands of molecules on the surface of a plasmonic NP. There is good agreement with experimental extinction measurements, predicting the plasmon and molecule depletions. Additionally, this model captures the polariton peaks overlapped with a Fano-type resonance profile observed in the experimental extinction measurements. This technique shows promise for modeling plasmon/molecule interactions in chemical sensing and light harvesting in multi-chromophore systems. This material is based upon work supported by the National Science Foundation under the NSF EPSCoR Cooperative Agreement No. EPS-1003897 and by the Louisiana Board of Regents Research Competitiveness Subprogram under Contract Number LEQSF(2014-17)-RD-A-0.

Solvent effects on the properties of hyperbranched polythiophenes.

PubMed

Torras, Juan; Zanuy, David; Aradilla, David; Alemán, Carlos

2016-09-21

The structural and electronic properties of all-thiophene dendrimers and dendrons in solution have been evaluated using very different theoretical approaches based on quantum mechanical (QM) and hybrid QM/molecular mechanics (MM) methodologies: (i) calculations on minimum energy conformations using an implicit solvation model in combination with density functional theory (DFT) or time-dependent DFT (TD-DFT) methods; (ii) hybrid QM/MM calculations, in which the solute and solvent molecules are represented at the DFT level as point charges, respectively, on snapshots extracted from classical molecular dynamics (MD) simulations using explicit solvent molecules, and (iii) QM/MM-MD trajectories in which the solute is described at the DFT or TD-DFT level and the explicit solvent molecules are represented using classical force-fields. Calculations have been performed in dichloromethane, tetrahydrofuran and dimethylformamide. A comparison of the results obtained using the different approaches with the available experimental data indicates that the incorporation of effects associated with both the conformational dynamics of the dendrimer and the explicit solvent molecules is strictly necessary to satisfactorily reproduce the properties of the investigated systems. Accordingly, QM/MM-MD simulations are able to capture such effects providing a reliable description of electronic properties-conformational flexibility relationships in all-Th dendrimers.

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.

Variational processes and stochastic versions of mechanics

NASA Astrophysics Data System (ADS)

Zambrini, J. C.

1986-09-01

The dynamical structure of any reasonable stochastic version of classical mechanics is investigated, including the version created by Nelson [E. Nelson, Quantum Fluctuations (Princeton U.P., Princeton, NJ, 1985); Phys. Rev. 150, 1079 (1966)] for the description of quantum phenomena. Two different theories result from this common structure. One of them is the imaginary time version of Nelson's theory, whose existence was unknown, and yields a radically new probabilistic interpretation of the heat equation. The existence and uniqueness of all the involved stochastic processes is shown under conditions suggested by the variational approach of Yasue [K. Yasue, J. Math. Phys. 22, 1010 (1981)].

Specifying structural constraints of architectural patterns in the ARCHERY language

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

Sanchez, Alejandro; HASLab INESC TEC and Universidade do Minho, Campus de Gualtar, 4710-057 Braga; Barbosa, Luis S.

ARCHERY is an architectural description language for modelling and reasoning about distributed, heterogeneous and dynamically reconfigurable systems in terms of architectural patterns. The language supports the specification of architectures and their reconfiguration. This paper introduces a language extension for precisely describing the structural design decisions that pattern instances must respect in their (re)configurations. The extension is a propositional modal logic with recursion and nominals referencing components, i.e., a hybrid µ-calculus. Its expressiveness allows specifying safety and liveness constraints, as well as paths and cycles over structures. Refinements of classic architectural patterns are specified.

Energy band alignment and electronic states of amorphous carbon surfaces in vacuo and in aqueous environment

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

Caro, Miguel A., E-mail: mcaroba@gmail.com; Department of Applied Physics, COMP Centre of Excellence in Computational Nanoscience, Aalto University, Espoo; Määttä, Jukka

2015-01-21

In this paper, we obtain the energy band positions of amorphous carbon (a–C) surfaces in vacuum and in aqueous environment. The calculations are performed using a combination of (i) classical molecular dynamics (MD), (ii) Kohn-Sham density functional theory with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional, and (iii) the screened-exchange hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE). PBE allows an accurate generation of a-C and the evaluation of the local electrostatic potential in the a-C/water system, HSE yields an improved description of energetic positions which is critical in this case, and classical MD enables a computationally affordable description of water. Ourmore » explicit calculation shows that, both in vacuo and in aqueous environment, the a-C electronic states available in the region comprised between the H{sub 2}/H{sub 2}O and O{sub 2}/H{sub 2}O levels of water correspond to both occupied and unoccupied states within the a-C pseudogap region. These are localized states associated to sp{sup 2} sites in a-C. The band realignment induces a shift of approximately 300 meV of the a-C energy band positions with respect to the redox levels of water.« less

Trajectory-based understanding of the quantum-classical transition for barrier scattering

NASA Astrophysics Data System (ADS)

Chou, Chia-Chun

2018-06-01

The quantum-classical transition of wave packet barrier scattering is investigated using a hydrodynamic description in the framework of a nonlinear Schrödinger equation. The nonlinear equation provides a continuous description for the quantum-classical transition of physical systems by introducing a degree of quantumness. Based on the transition equation, the transition trajectory formalism is developed to establish the connection between classical and quantum trajectories. The quantum-classical transition is then analyzed for the scattering of a Gaussian wave packet from an Eckart barrier and the decay of a metastable state. Computational results for the evolution of the wave packet and the transmission probabilities indicate that classical results are recovered when the degree of quantumness tends to zero. Classical trajectories are in excellent agreement with the transition trajectories in the classical limit, except in some regions where transition trajectories cannot cross because of the single-valuedness of the transition wave function. As the computational results demonstrate, the process that the Planck constant tends to zero is equivalent to the gradual removal of quantum effects originating from the quantum potential. This study provides an insightful trajectory interpretation for the quantum-classical transition of wave packet barrier scattering.

Fluctuating local field method probed for a description of small classical correlated lattices

NASA Astrophysics Data System (ADS)

Rubtsov, Alexey N.

2018-05-01

Thermal-equilibrated finite classical lattices are considered as a minimal model of the systems showing an interplay between low-energy collective fluctuations and single-site degrees of freedom. Standard local field approach, as well as classical limit of the bosonic DMFT method, do not provide a satisfactory description of Ising and Heisenberg small lattices subjected to an external polarizing field. We show that a dramatic improvement can be achieved within a simple approach, in which the local field appears to be a fluctuating quantity related to the low-energy degree(s) of freedom.

Dynamics of two-phase interfaces and surface tensions: A density-functional theory perspective

NASA Astrophysics Data System (ADS)

Yatsyshin, Petr; Sibley, David N.; Duran-Olivencia, Miguel A.; Kalliadasis, Serafim

2016-11-01

Classical density functional theory (DFT) is a statistical mechanical framework for the description of fluids at the nanoscale, where the inhomogeneity of the fluid structure needs to be carefully accounted for. By expressing the grand free-energy of the fluid as a functional of the one-body density, DFT offers a theoretically consistent and computationally accessible way to obtain two-phase interfaces and respective interfacial tensions in a ternary solid-liquid-gas system. The dynamic version of DFT (DDFT) can be rigorously derived from the Smoluchowsky picture of the dynamics of colloidal particles in a solvent. It is generally agreed that DDFT can capture the diffusion-driven evolution of many soft-matter systems. In this context, we use DDFT to investigate the dynamic behaviour of two-phase interfaces in both equilibrium and dynamic wetting and discuss the possibility of defining a time-dependent surface tension, which still remains in debate. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from the Engineering and Physical Sciences Research Council of the UK via Grants No. EP/L027186 and EP/L020564.

Regular black holes from semi-classical down to Planckian size

NASA Astrophysics Data System (ADS)

Spallucci, Euro; Smailagic, Anais

In this paper, we review various models of curvature singularity free black holes (BHs). In the first part of the review, we describe semi-classical solutions of the Einstein equations which, however, contains a “quantum” input through the matter source. We start by reviewing the early model by Bardeen where the metric is regularized by-hand through a short-distance cutoff, which is justified in terms of nonlinear electro-dynamical effects. This toy-model is useful to point-out the common features shared by all regular semi-classical black holes. Then, we solve Einstein equations with a Gaussian source encoding the quantum spread of an elementary particle. We identify, the a priori arbitrary, Gaussian width with the Compton wavelength of the quantum particle. This Compton-Gauss model leads to the estimate of a terminal density that a gravitationally collapsed object can achieve. We identify this density to be the Planck density, and reformulate the Gaussian model assuming this as its peak density. All these models, are physically reliable as long as the BH mass is big enough with respect to the Planck mass. In the truly Planckian regime, the semi-classical approximation breaks down. In this case, a fully quantum BH description is needed. In the last part of this paper, we propose a nongeometrical quantum model of Planckian BHs implementing the Holographic Principle and realizing the “classicalization” scenario recently introduced by Dvali and collaborators. The classical relation between the mass and radius of the BH emerges only in the classical limit, far away from the Planck scale.

On the emergence of classical gravity

NASA Astrophysics Data System (ADS)

Larjo, Klaus

In this thesis I will discuss how certain black holes arise as an effective, thermodynamical description from non-singular microstates in string theory. This provides a possible solution to the information paradox, and strengthens the case for treating black holes as thermodynamical objects. I will characterize the data defining a microstate of a black hole in several settings, and demonstrate that most of the data is unmeasurable for a classical observer. I will further show that the data that is measurable is universal for nearly all microstates, making it impossible for a classical observer to distinguish between microstates, thus giving rise to an effective statistical description for the black hole. In the first half of the thesis I will work with two specific systems: the half-BPS sector of [Special characters omitted.] = 4 super Yang-Mills the and the conformal field theory corresponding to the D1/D5 system; in both cases the high degree of symmetry present provides great control over potentially intractable computations. For these systems, I will further specify the conditions a quantum mechanical microstate must satisfy in order to have a classical description in terms of a unique metric, and define a 'metric operator' whose eigenstates correspond to classical geometries. In the second half of the thesis I will consider a much broader setting, general [Special characters omitted.] = I superconformal quiver gauge the= ories and their dual gravity theories, and demonstrate that a similar effective description arises also in this setting.

Paraconsistent Reasoning for OWL 2

NASA Astrophysics Data System (ADS)

Ma, Yue; Hitzler, Pascal

A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basic description logic mathcal{ALC}. In this paper, we further study how to extend the four-valued semantics to the more expressive description logic mathcal{SROIQ} which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapted to tractable description logics including mathcal{EL++}, DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for mathcal{ALC} and show that we can retain most of the desired properties.

On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice

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

Reddy, Sandeep K.; Straight, Shelby C.; Bajaj, Pushp

The MB-pol many-body potential has recently emerged as an accurate molecular model for water simulations from the gas to the condensed phase. In this study, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with experimental data and high-level ab initio calculations. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calculated with MB-pol are in excellent agreement with reference data obtained at the coupled cluster level. Several structural, thermodynamic, and dynamical properties of the liquid phase at atmospheric pressure are investigated through classical molecular dynamics simulationsmore » as a function of temperature. The structural properties of the liquid phase are in nearly quantitative agreement with X-ray diffraction data available over the temperature range from 268 to 368 K. The analysis of other thermodynamic and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, especially at low temperature, for a physically correct description of the properties of liquid water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water. Published by AIP Publishing.« less

On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice [How good is the MB-pol many-body potential for water?

DOE PAGES

Reddy, Sandeep K.; Straight, Shelby C.; Bajaj, Pushp; ...

2016-11-17

The MB-pol many-body potential has recently emerged as an accurate molecular model for water simulations from the gas to the condensed phase. Here, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with experimental data and high-level ab initio calculations. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calculated with MB-pol are in excellent agreement with reference data obtained at the coupled cluster level. We investigate several structural, thermodynamic, and dynamical properties of the liquid phase at atmospheric pressure through classical molecular dynamics simulations as amore » function of temperature. Furthermore, the structural properties of the liquid phase are in nearly quantitative agreement with X-ray diffraction data available over the temperature range from 268 to 368 K. The analysis of other thermodynamic and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, especially at low temperature, for a physically correct description of the properties of liquid water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water.« less

On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice [How good is the MB-pol many-body potential for water?

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

Reddy, Sandeep K.; Straight, Shelby C.; Bajaj, Pushp

The MB-pol many-body potential has recently emerged as an accurate molecular model for water simulations from the gas to the condensed phase. Here, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with experimental data and high-level ab initio calculations. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calculated with MB-pol are in excellent agreement with reference data obtained at the coupled cluster level. We investigate several structural, thermodynamic, and dynamical properties of the liquid phase at atmospheric pressure through classical molecular dynamics simulations as amore » function of temperature. Furthermore, the structural properties of the liquid phase are in nearly quantitative agreement with X-ray diffraction data available over the temperature range from 268 to 368 K. The analysis of other thermodynamic and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, especially at low temperature, for a physically correct description of the properties of liquid water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water.« less

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems such as the dynamical description of quantum phase transition (local- ization) and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.

Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

PubMed

Everaers, Ralf; Rosa, Angelo

2012-01-07

The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

Stochastic collective dynamics of charged-particle beams in the stability regime

NASA Astrophysics Data System (ADS)

Petroni, Nicola Cufaro; de Martino, Salvatore; de Siena, Silvio; Illuminati, Fabrizio

2001-01-01

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by λcN, where N is the number of particles in the beam and λc the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called ``quantum-like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.

Information flow dynamics in the brain

NASA Astrophysics Data System (ADS)

Rabinovich, Mikhail I.; Afraimovich, Valentin S.; Bick, Christian; Varona, Pablo

2012-03-01

Timing and dynamics of information in the brain is a hot field in modern neuroscience. The analysis of the temporal evolution of brain information is crucially important for the understanding of higher cognitive mechanisms in normal and pathological states. From the perspective of information dynamics, in this review we discuss working memory capacity, language dynamics, goal-dependent behavior programming and other functions of brain activity. In contrast with the classical description of information theory, which is mostly algebraic, brain flow information dynamics deals with problems such as the stability/instability of information flows, their quality, the timing of sequential processing, the top-down cognitive control of perceptual information, and information creation. In this framework, different types of information flow instabilities correspond to different cognitive disorders. On the other hand, the robustness of cognitive activity is related to the control of the information flow stability. We discuss these problems using both experimental and theoretical approaches, and we argue that brain activity is better understood considering information flows in the phase space of the corresponding dynamical model. In particular, we show how theory helps to understand intriguing experimental results in this matter, and how recent knowledge inspires new theoretical formalisms that can be tested with modern experimental techniques.

Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

NASA Astrophysics Data System (ADS)

Jensen, Christian H.; Nerukh, Dmitry; Glen, Robert C.

2008-03-01

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

Dynamic Heterogeneous Multiscale Filtration Model: Probing Micro- and Macroscopic Filtration Characteristics of Gasoline Particulate Filters.

PubMed

Gong, Jian; Viswanathan, Sandeep; Rothamer, David A; Foster, David E; Rutland, Christopher J

2017-10-03

Motivated by high filtration efficiency (mass- and number-based) and low pressure drop requirements for gasoline particulate filters (GPFs), a previously developed heterogeneous multiscale filtration (HMF) model is extended to simulate dynamic filtration characteristics of GPFs. This dynamic HMF model is based on a probability density function (PDF) description of the pore size distribution and classical filtration theory. The microstructure of the porous substrate in a GPF is resolved and included in the model. Fundamental particulate filtration experiments were conducted using an exhaust filtration analysis (EFA) system for model validation. The particulate in the filtration experiments was sampled from a spark-ignition direct-injection (SIDI) gasoline engine. With the dynamic HMF model, evolution of the microscopic characteristics of the substrate (pore size distribution, porosity, permeability, and deposited particulate inside the porous substrate) during filtration can be probed. Also, predicted macroscopic filtration characteristics including particle number concentration and normalized pressure drop show good agreement with the experimental data. The resulting dynamic HMF model can be used to study the dynamic particulate filtration process in GPFs with distinct microstructures, serving as a powerful tool for GPF design and optimization.

Theoretical princi les of constructing the equations of motion for a spin color-charged particle in gauge and fermion fields

NASA Astrophysics Data System (ADS)

Markov, Yu. A.; Shishmarev, A. A.

2010-11-01

Based on the most general principles of materiality, gauge, and re-parameterized invariance, the problem of constructing an action describing the dynamics of a classical color-charged particle moving in external non-Abelian gauge and fermion fields is considered. The case of a linear Lagrangian dependence on the external fermion fields is discussed. Within the framework of the description of the color degree of freedom of the particle with half-integer spin by the Grassmann color charges, a new concept of the Grassmann color source of the particle being a fermion analog of the conventional color current is introduced.

Numerical studies from quantum to macroscopic scales of carbon nanoparticules in hydrogen plasma

NASA Astrophysics Data System (ADS)

Lombardi, Guillaume; Ngandjong, Alain; Mezei, Zsolt; Mougenot, Jonathan; Michau, Armelle; Hassouni, Khaled; Seydou, Mahamadou; Maurel, François

2016-09-01

Dusty plasmas take part in large scientific domains from Universe Science to nanomaterial synthesis processes. They are often generated by growth from molecular precursor. This growth leads to the formation of larger clusters which induce solid germs nucleation. Particle formed are described by an aerosol dynamic taking into account coagulation, molecular deposition and transport processes. These processes are controlled by the elementary particle. So there is a strong coupling between particle dynamics and plasma discharge equilibrium. This study is focused on the development of a multiscale physic and numeric model of hydrogen plasmas and carbon particles around three essential coupled axes to describe the various physical phenomena: (i) Macro/mesoscopic fluid modeling describing in an auto-coherent way, characteristics of the plasma, molecular clusters and aerosol behavior; (ii) the classic molecular dynamics offering a description to the scale molecular of the chains of chemical reactions and the phenomena of aggregation; (iii) the quantum chemistry to establish the activation barriers of the different processes driving the nanopoarticule formation.

Effective dynamics of a classical point charge

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

Polonyi, Janos, E-mail: polonyi@iphc.cnrs.fr

2014-03-15

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-polemore » of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.« less

Teaching Statistics Using Classic Psychology Research: An Activities-Based Approach

ERIC Educational Resources Information Center

Holmes, Karen Y.; Dodd, Brett A.

2012-01-01

In this article, we discuss a collection of active learning activities derived from classic psychology studies that illustrate the appropriate use of descriptive and inferential statistics. (Contains 2 tables.)

Nitrogen vacancy, self-interstitial diffusion, and Frenkel-pair formation/dissociation in B 1 TiN studied by ab initio and classical molecular dynamics with optimized potentials

NASA Astrophysics Data System (ADS)

Sangiovanni, D. G.; Alling, B.; Steneteg, P.; Hultman, L.; Abrikosov, I. A.

2015-02-01

We use ab initio and classical molecular dynamics (AIMD and CMD) based on the modified embedded-atom method (MEAM) potential to simulate diffusion of N vacancy and N self-interstitial point defects in B 1 TiN. TiN MEAM parameters are optimized to obtain CMD nitrogen point-defect jump rates in agreement with AIMD predictions, as well as an excellent description of Ti Nx(˜0.7

Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures

NASA Astrophysics Data System (ADS)

Bishop, Kevin P.; Roy, Pierre-Nicholas

2018-03-01

Free energy calculations are a crucial part of understanding chemical systems but are often computationally expensive for all but the simplest of systems. Various enhanced sampling techniques have been developed to improve the efficiency of these calculations in numerical simulations. However, the majority of these approaches have been applied using classical molecular dynamics. There are many situations where nuclear quantum effects impact the system of interest and a classical description fails to capture these details. In this work, path integral molecular dynamics has been used in conjunction with umbrella sampling, and it has been observed that correct results are only obtained when the umbrella sampling potential is applied to a single path integral bead post quantization. This method has been validated against a Lennard-Jones benchmark system before being applied to the more complicated water dimer system over a broad range of temperatures. Free energy profiles are obtained, and these are utilized in the calculation of the second virial coefficient as well as the change in free energy from the separated water monomers to the dimer. Comparisons to experimental and ground state calculation values from the literature are made for the second virial coefficient at higher temperature and the dissociation energy of the dimer in the ground state.

Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures.

PubMed

Bishop, Kevin P; Roy, Pierre-Nicholas

2018-03-14

Free energy calculations are a crucial part of understanding chemical systems but are often computationally expensive for all but the simplest of systems. Various enhanced sampling techniques have been developed to improve the efficiency of these calculations in numerical simulations. However, the majority of these approaches have been applied using classical molecular dynamics. There are many situations where nuclear quantum effects impact the system of interest and a classical description fails to capture these details. In this work, path integral molecular dynamics has been used in conjunction with umbrella sampling, and it has been observed that correct results are only obtained when the umbrella sampling potential is applied to a single path integral bead post quantization. This method has been validated against a Lennard-Jones benchmark system before being applied to the more complicated water dimer system over a broad range of temperatures. Free energy profiles are obtained, and these are utilized in the calculation of the second virial coefficient as well as the change in free energy from the separated water monomers to the dimer. Comparisons to experimental and ground state calculation values from the literature are made for the second virial coefficient at higher temperature and the dissociation energy of the dimer in the ground state.

Linear dynamics of classical spin as Mobius transformation

DOE PAGES

Galda, Alexey; Vinokur, Valerii М.

2017-04-26

Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phasemore » transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.« less

Semi-classical statistical description of Fröhlich condensation.

PubMed

Preto, Jordane

2017-06-01

Fröhlich's model equations describing phonon condensation in open systems of biological relevance are reinvestigated within a semi-classical statistical framework. The main assumptions needed to deduce Fröhlich's rate equations are identified and it is shown how they lead us to write an appropriate form for the corresponding master equation. It is shown how solutions of the master equation can be numerically computed and can highlight typical features of the condensation effect. Our approach provides much more information compared to the existing ones as it allows to investigate the time evolution of the probability density function instead of following single averaged quantities. The current work is also motivated, on the one hand, by recent experimental evidences of long-lived excited modes in the protein structure of hen-egg white lysozyme, which were reported as a consequence of the condensation effect, and, on the other hand, by a growing interest in investigating long-range effects of electromagnetic origin and their influence on the dynamics of biochemical reactions.

Nuclear quantum effects in water exchange around lithium and fluoride ions

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

Wilkins, David M.; Manolopoulos, David; Dang, Liem X.

2015-02-14

We employ classical and ring polymer molecular dynamics simulations to study the effect of nuclear quantum fluctuations on the structure and the water exchange dynamics of aqueous solutions of lithium and fluoride ions. While we obtain reasonably good agreement with experimental data for solutions of lithium by augmenting the Coulombic interactions between the ion and the water molecules with a standard Lennard-Jones ion-oxygen potential, the same is not true for solutions of fluoride, for which we find that a potential with a softer repulsive wall gives much better agreement. A small degree of destabilization of the first hydration shell ismore » found in quantum simulations of both ions when compared with classical simulations, with the shell becoming less sharply defined and the mean residence time of the water molecules in the shell decreasing. In line with these modest differences, we find that the mechanisms of the water exchange reactions are unaffected by quantization, so a classical description of these reactions gives qualitatively correct and quantitatively reasonable results. We also find that the quantum effects in solutions of lithium are larger than in solutions of fluoride. This is partly due to the stronger interaction of lithium with water molecules, partly due to the lighter mass of lithium, and partly due to competing quantum effects in the hydration of fluoride, which are absent in the hydration of lithium. LXD was supported by US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.« less

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

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

Kengne, Jacques; Kenmogne, Fabien

2014-12-15

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

The ambiguity of simplicity in quantum and classical simulation

NASA Astrophysics Data System (ADS)

Aghamohammadi, Cina; Mahoney, John R.; Crutchfield, James P.

2017-04-01

A system's perceived simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and express different properties and mechanisms. What is surprising is that, as we demonstrate, simplicity is ambiguous: the relative simplicity between two systems can change sign when moving between classical and quantum descriptions. Here, we associate simplicity with small model-memory. We see that the notions of absolute physical simplicity at best form a partial, not a total, order. This suggests that appeals to principles of physical simplicity, via Ockham's Razor or to the ;elegance; of competing theories, may be fundamentally subjective. Recent rapid progress in quantum computation and quantum simulation suggest that the ambiguity of simplicity will strongly impact statistical inference and, in particular, model selection.

Classic-Ada(TM)

NASA Technical Reports Server (NTRS)

Valley, Lois

1989-01-01

The SPS product, Classic-Ada, is a software tool that supports object-oriented Ada programming with powerful inheritance and dynamic binding. Object Oriented Design (OOD) is an easy, natural development paradigm, but it is not supported by Ada. Following the DOD Ada mandate, SPS developed Classic-Ada to provide a tool which supports OOD and implements code in Ada. It consists of a design language, a code generator and a toolset. As a design language, Classic-Ada supports the object-oriented principles of information hiding, data abstraction, dynamic binding, and inheritance. It also supports natural reuse and incremental development through inheritance, code factoring, and Ada, Classic-Ada, dynamic binding and static binding in the same program. Only nine new constructs were added to Ada to provide object-oriented design capabilities. The Classic-Ada code generator translates user application code into fully compliant, ready-to-run, standard Ada. The Classic-Ada toolset is fully supported by SPS and consists of an object generator, a builder, a dictionary manager, and a reporter. Demonstrations of Classic-Ada and the Classic-Ada Browser were given at the workshop.

Ptosis, extraocular motility disorder, and myopia as features of pompe disease.

PubMed

Slingerland, Niki W R; Polling, Jan Roelof; van Gelder, Catharina M; van der Ploeg, Ans T; Bleyen, Isabel

2011-03-01

The assets of this report are a thorough description of new clinical findings, namely the combination of ptosis, extraocular motility disorder and myopia, in consequence of prolonged survival in classic infantile-onset Pompe disease through enzyme therapy. Single case description. This manuscript describes a combination of ptosis, extraocular motility disorder and myopia in a 4.5-year-old patient with classic infantile-onset Pompe disease, who survived through enzyme therapy. This patient was treated with a bilateral frontalis suspension (modified Crawford technique) using prolene 3-0 sutures. The combination of ptosis, extraocular motility disorder and myopia, is a new clinical finding in children with classic infantile-onset Pompe disease.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Quantum optics. Gravity meets quantum physics

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

Adams, Bernhard W.

2015-02-27

Albert Einstein’s general theory of relativity is a classical formulation but a quantum mechanical description of gravitational forces is needed, not only to investigate the coupling of classical and quantum systems but simply to give a more complete description of our physical surroundings. In this issue of Nature Photonics, Wen-Te Liao and Sven Ahrens reveal a link between quantum and gravitational physics. They propose that in the quantum-optical effect of superradiance, the world line of electromagnetic radiation is changed by the presence of a gravitational field.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

PubMed

Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao

2014-10-06

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

A Comparison of Kinetic Energy and Momentum in Special Relativity and Classical Mechanics

ERIC Educational Resources Information Center

Riggs, Peter J.

2016-01-01

Kinetic energy and momentum are indispensable dynamical quantities in both the special theory of relativity and in classical mechanics. Although momentum and kinetic energy are central to understanding dynamics, the differences between their relativistic and classical notions have not always received adequate treatment in undergraduate teaching.…

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

NASA Astrophysics Data System (ADS)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

Liquid li structure and dynamics: A comparison between OFDFT and second nearest-neighbor embedded-atom method

DOE PAGES

Chen, Mohan; Vella, Joseph R.; Panagiotopoulos, Athanassios Z.; ...

2015-04-08

The structure and dynamics of liquid lithium are studied using two simulation methods: orbital-free (OF) first-principles molecular dynamics (MD), which employs OF density functional theory (DFT), and classical MD utilizing a second nearest-neighbor embedded-atom method potential. The properties we studied include the dynamic structure factor, the self-diffusion coefficient, the dispersion relation, the viscosity, and the bond angle distribution function. Our simulation results were compared to available experimental data when possible. Each method has distinct advantages and disadvantages. For example, OFDFT gives better agreement with experimental dynamic structure factors, yet is more computationally demanding than classical simulations. Classical simulations can accessmore » a broader temperature range and longer time scales. The combination of first-principles and classical simulations is a powerful tool for studying properties of liquid lithium.« less

Qualitative and quantitative descriptions of glenohumeral motion.

PubMed

Hill, A M; Bull, A M J; Wallace, A L; Johnson, G R

2008-02-01

Joint modelling plays an important role in qualitative and quantitative descriptions of both normal and abnormal joints, as well as predicting outcomes of alterations to joints in orthopaedic practice and research. Contemporary efforts in modelling have focussed upon the major articulations of the lower limb. Well-constrained arthrokinematics can form the basis of manageable kinetic and dynamic mathematical predictions. In order to contain computation of shoulder complex modelling, glenohumeral joint representations in both limited and complete shoulder girdle models have undergone a generic simplification. As such, glenohumeral joint models are often based upon kinematic descriptions of inadequate degrees of freedom (DOF) for clinical purposes and applications. Qualitative descriptions of glenohumeral motion range from the parody of a hinge joint to the complex realism of a spatial joint. In developing a model, a clear idea of intention is required in order to achieve a required application. Clinical applicability of a model requires both descriptive and predictive output potentials, and as such, a high level of validation is required. Without sufficient appreciation of the clinical intention of the arthrokinematic foundation to a model, error is all too easily introduced. Mathematical description of joint motion serves to quantify all relevant clinical parameters. Commonly, both the Euler angle and helical (screw) axis methods have been applied to the glenohumeral joint, although concordance between these methods and classical anatomical appreciation of joint motion is limited, resulting in miscommunication between clinician and engineer. Compounding these inconsistencies in motion quantification is gimbal lock and sequence dependency.

Quantum localization for a kicked rotor with accelerator mode islands.

PubMed

Iomin, A; Fishman, S; Zaslavsky, G M

2002-03-01

Dynamical localization of classical superdiffusion for the quantum kicked rotor is studied in the semiclassical limit. Both classical and quantum dynamics of the system become more complicated under the conditions of mixed phase space with accelerator mode islands. Recently, long time quantum flights due to the accelerator mode islands have been found. By exploration of their dynamics, it is shown here that the classical-quantum duality of the flights leads to their localization. The classical mechanism of superdiffusion is due to accelerator mode dynamics, while quantum tunneling suppresses the superdiffusion and leads to localization of the wave function. Coupling of the regular type dynamics inside the accelerator mode island structures to dynamics in the chaotic sea proves increasing the localization length. A numerical procedure and an analytical method are developed to obtain an estimate of the localization length which, as it is shown, has exponentially large scaling with the dimensionless Planck's constant (tilde)h<1 in the semiclassical limit. Conditions for the validity of the developed method are specified.

An Interdisciplinary Twist on Traditional Games

ERIC Educational Resources Information Center

Rattigan, Peter

2006-01-01

This article describes some activities that include descriptions of four classic games, and also incorporates interdisciplinary concepts into the playing of traditional games. These activities can be played indoors or outside, in a gym or a classroom. A description of an interdisciplinary version of the game is included after the description of…

On quantum effects in a theory of biological evolution.

PubMed

Martin-Delgado, M A

2012-01-01

We construct a descriptive toy model that considers quantum effects on biological evolution starting from Chaitin's classical framework. There are smart evolution scenarios in which a quantum world is as favorable as classical worlds for evolution to take place. However, in more natural scenarios, the rate of evolution depends on the degree of entanglement present in quantum organisms with respect to classical organisms. If the entanglement is maximal, classical evolution turns out to be more favorable.

On Quantum Effects in a Theory of Biological Evolution

PubMed Central

Martin-Delgado, M. A.

2012-01-01

We construct a descriptive toy model that considers quantum effects on biological evolution starting from Chaitin's classical framework. There are smart evolution scenarios in which a quantum world is as favorable as classical worlds for evolution to take place. However, in more natural scenarios, the rate of evolution depends on the degree of entanglement present in quantum organisms with respect to classical organisms. If the entanglement is maximal, classical evolution turns out to be more favorable. PMID:22413059

Local probing of ionic diffusion by electrochemical strain microscopy: Spatial resolution and signal formation mechanisms

NASA Astrophysics Data System (ADS)

Morozovska, A. N.; Eliseev, E. A.; Balke, N.; Kalinin, S. V.

2010-09-01

Electrochemical insertion-deintercalation reactions are typically associated with significant change in molar volume of the host compound. This strong coupling between ionic currents and strains underpins image formation mechanisms in electrochemical strain microscopy (ESM), and allows exploring the tip-induced electrochemical processes locally. Here we analyze the signal formation mechanism in ESM, and develop the analytical description of operation in frequency and time domains. The ESM spectroscopic modes are compared to classical electrochemical methods including potentiostatic and galvanostatic intermittent titration, and electrochemical impedance spectroscopy. This analysis illustrates the feasibility of spatially resolved studies of Li-ion dynamics on the sub-10-nm level using electromechanical detection.

SIVEH: numerical computing simulation of wireless energy-harvesting sensor nodes.

PubMed

Sanchez, Antonio; Blanc, Sara; Climent, Salvador; Yuste, Pedro; Ors, Rafael

2013-09-04

The paper presents a numerical energy harvesting model for sensor nodes, SIVEH (Simulator I-V for EH), based on I-V hardware tracking. I-V tracking is demonstrated to be more accurate than traditional energy modeling techniques when some of the components present different power dissipation at either different operating voltages or drawn currents. SIVEH numerical computing allows fast simulation of long periods of time-days, weeks, months or years-using real solar radiation curves. Moreover, SIVEH modeling has been enhanced with sleep time rate dynamic adjustment, while seeking energy-neutral operation. This paper presents the model description, a functional verification and a critical comparison with the classic energy approach.

Might god toss coins?

NASA Astrophysics Data System (ADS)

Pearle, Philip

1982-03-01

In the problem of the gambler's ruin, a classic problem in probability theory, a number of gamblers play against each other until all but one of them is “wiped out.” It is shown that this problem is identical to a previously presented formulation of the reduction of the state vector, so that the state vectors in a linear superposition may be regarded as “playing” against each other until all but one of them is “wiped out.” This is a useful part of the description of an objectively real universe represented by a state vector that is a superposition of macroscopically distinguishable states dynamically created by the Hamiltonian and destroyed by the reduction mechanism.

SIVEH: Numerical Computing Simulation of Wireless Energy-Harvesting Sensor Nodes

PubMed Central

Sanchez, Antonio; Blanc, Sara; Climent, Salvador; Yuste, Pedro; Ors, Rafael

2013-01-01

The paper presents a numerical energy harvesting model for sensor nodes, SIVEH (Simulator I–V for EH), based on I–V hardware tracking. I–V tracking is demonstrated to be more accurate than traditional energy modeling techniques when some of the components present different power dissipation at either different operating voltages or drawn currents. SIVEH numerical computing allows fast simulation of long periods of time—days, weeks, months or years—using real solar radiation curves. Moreover, SIVEH modeling has been enhanced with sleep time rate dynamic adjustment, while seeking energy-neutral operation. This paper presents the model description, a functional verification and a critical comparison with the classic energy approach. PMID:24008287

Theoretical microbial ecology without species

NASA Astrophysics Data System (ADS)

Tikhonov, Mikhail

2017-09-01

Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic and mounting experimental evidence raises the intriguing question whether this perspective is appropriate for the microbial world. Here an alternative formalism is proposed that does not require postulating the existence of species as fundamental ecological variables and provides a naturally hierarchical description of community dynamics. This formalism allows approaching the species problem from the opposite direction. While the classical models treat a world of imperfectly clustered organism types as a perturbation around well-clustered species, the presented approach allows gradually adding structure to a fully disordered background. The relevance of this theoretical construct for describing highly diverse natural ecosystems is discussed.

Parametric representation of open quantum systems and cross-over from quantum to classical environment.

PubMed

Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I; Verrucchi, Paola

2013-04-23

The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the s = 1/2 Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables (θ, ϕ), and broadened according to their quantum probability distribution. Such distribution is independent of ϕ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because ϕ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field.

Refraction of dispersive shock waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M.

2012-09-01

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.

Inertial Manifold and Large Deviations Approach to Reduced PDE Dynamics

NASA Astrophysics Data System (ADS)

Cardin, Franco; Favretti, Marco; Lovison, Alberto

2017-09-01

In this paper a certain type of reaction-diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when reformulated as a variational problem. In this way we gain a finite-dimensional ODE description of the initial system which preserves the gradient structure of the original one and that is exact for the static case and only approximate for the dynamic case. Our main concern is how to deal with this approximate reduced description of the initial PDE. To start with, we note that our approximate reduced ODE is similar to the approximate inertial manifold introduced by Temam and coworkers for Navier-Stokes equations. As a second approach, we take into account the uncertainty (loss of information) introduced with the above mentioned approximate reduction by considering the stochastic version of the ODE. We study this reduced stochastic system using classical tools from large deviations, viscosity solutions and weak KAM Hamilton-Jacobi theory. In the last part we suggest a possible use of a result of our approach in the comprehensive treatment non equilibrium thermodynamics given by Macroscopic Fluctuation Theory.

Petrological Geodynamics of Mantle Melting II. AlphaMELTS + Multiphase Flow: Dynamic Fractional Melting

NASA Astrophysics Data System (ADS)

Tirone, Massimiliano

2018-03-01

In this second installment of a series that aims to investigate the dynamic interaction between the composition and abundance of the solid mantle and its melt products, the classic interpretation of fractional melting is extended to account for the dynamic nature of the process. A multiphase numerical flow model is coupled with the program AlphaMELTS, which provides at the moment possibly the most accurate petrological description of melting based on thermodynamic principles. The conceptual idea of this study is based on a description of the melting process taking place along a 1-D vertical ideal column where chemical equilibrium is assumed to apply in two local sub-systems separately on some spatial and temporal scale. The solid mantle belongs to a local sub-system (ss1) that does not interact chemically with the melt reservoir which forms a second sub-system (ss2). The local melt products are transferred in the melt sub-system ss2 where the melt phase eventually can also crystallize into a different solid assemblage and will evolve dynamically. The main difference with the usual interpretation of fractional melting is that melt is not arbitrarily and instantaneously extracted from the mantle, but instead remains a dynamic component of the model, hence the process is named dynamic fractional melting (DFM). Some of the conditions that may affect the DFM model are investigated in this study, in particular the effect of temperature, mantle velocity at the boundary of the mantle column. A comparison is made with the dynamic equilibrium melting (DEM) model discussed in the first installment. The implications of assuming passive flow or active flow are also considered to some extent. Complete data files of most of the DFM simulations, four animations and two new DEM simulations (passive/active flow) are available following the instructions in the supplementary material.

Ab Initio Calculations of Transport in Titanium and Aluminum Mixtures

NASA Astrophysics Data System (ADS)

Walker, Nicholas; Novak, Brian; Tam, Ka Ming; Moldovan, Dorel; Jarrell, Mark

In classical molecular dynamics simulations, the self-diffusion and shear viscosity of titanium about the melting point have fallen within the ranges provided by experimental data. However, the experimental data is difficult to collect and has been rather scattered, making it of limited value for the validation of these calculations. By using ab initio molecular dynamics simulations within the density functional theory framework, the classical molecular dynamics data can be validated. The dynamical data from the ab initio molecular dynamics can also be used to calculate new potentials for use in classical molecular dynamics, allowing for more accurate classical dynamics simulations for the liquid phase. For metallic materials such as titanium and aluminum alloys, these calculations are very valuable due to an increasing demand for the knowledge of their thermophysical properties that drive the development of new materials. For example, alongside knowledge of the surface tension, viscosity is an important input for modeling the additive manufacturing process at the continuum level. We are developing calculations of the viscosity along with the self-diffusion for aluminum, titanium, and titanium-aluminum alloys with ab initio molecular dynamics. Supported by the National Science Foundation through cooperative agreement OIA-1541079 and the Louisiana Board of Regents.

Sine-Gordon equation and its application to tectonic stress transfer

NASA Astrophysics Data System (ADS)

Bykov, Victor G.

2014-07-01

An overview is given on remarkable progress that has been made in theoretical studies of solitons and other nonlinear wave patterns, excited during the deformation of fault block (fragmented) geological media. The models that are compliant with the classical and perturbed sine-Gordon equations have only been chosen. In these mathematical models, the rotation angle of blocks (fragments) and their translatory displacement of the medium are used as dynamic variables. A brief description of the known models and their geophysical and geodynamic applications is given. These models reproduce the kinematic and dynamic features of the traveling deformation front (kink, soliton) generated in the fragmented media. It is demonstrated that the sine-Gordon equation is applicable to the description of series of the observed seismic data, modeling of strain waves, as well as the features related to fault dynamics and the subduction slab, including slow earthquakes, periodicity of episodic tremor and slow slip (ETS) events, and migration pattern of tremors. The study shows that simple heuristic models and analytical and numerical computations can explain triggering of seismicity by transient processes, such as stress changes associated with solitary strain waves in crustal faults. The need to develop the above-mentioned new (nonlinear) mathematical models of the deformed fault and fragmented media was caused by the reason that it is impossible to explain a lot of the observed effects, particularly, slow redistribution and migration of stresses in the lithosphere, within the framework of the linear elasticity theory.

Computational Nanomechanics of Carbon Nanotubes and Composites

NASA Technical Reports Server (NTRS)

Srivastava, Deepak; Wei, Chenyu; Cho, Kyeongjae; Biegel, Bryan (Technical Monitor)

2002-01-01

Nanomechanics of individual carbon and boron-nitride nanotubes and their application as reinforcing fibers in polymer composites has been reviewed with interplay of theoretical modeling, computer simulations and experimental observations. The emphasis in this work is on elucidating the multi-length scales of the problems involved, and of different simulation techniques that are needed to address specific characteristics of individual nanotubes and nanotube polymer-matrix interfaces. Classical molecular dynamics simulations are shown to be sufficient to describe the generic behavior such as strength and stiffness modulus but are inadequate to describe elastic limit and nature of plastic buckling at large strength. Quantum molecular dynamics simulations are shown to bring out explicit atomic nature dependent behavior of these nanoscale materials objects that are not accessible either via continuum mechanics based descriptions or through classical molecular dynamics based simulations. As examples, we discus local plastic collapse of carbon nanotubes under axial compression and anisotropic plastic buckling of boron-nitride nanotubes. Dependence of the yield strain on the strain rate is addressed through temperature dependent simulations, a transition-state-theory based model of the strain as a function of strain rate and simulation temperature is presented, and in all cases extensive comparisons are made with experimental observations. Mechanical properties of nanotube-polymer composite materials are simulated with diverse nanotube-polymer interface structures (with van der Waals interaction). The atomistic mechanisms of the interface toughening for optimal load transfer through recycling, high-thermal expansion and diffusion coefficient composite formation above glass transition temperature, and enhancement of Young's modulus on addition of nanotubes to polymer are discussed and compared with experimental observations.

Markovian Dynamics of Josephson Parametric Amplification

NASA Astrophysics Data System (ADS)

Kaiser, Waldemar; Haider, Michael; Russer, Johannes A.; Russer, Peter; Jirauschek, Christian

2017-09-01

In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Lattice constants of pure methane and carbon dioxide hydrates at low temperatures. Implementing quantum corrections to classical molecular dynamics studies

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

Costandy, Joseph; Michalis, Vasileios K.; Economou, Ioannis G., E-mail: i.tsimpanogiannis@qatar.tamu.edu, E-mail: ioannis.economou@qatar.tamu.edu

2016-03-28

We introduce a simple correction to the calculation of the lattice constants of fully occupied structure sI methane or carbon dioxide pure hydrates that are obtained from classical molecular dynamics simulations using the TIP4PQ/2005 water force field. The obtained corrected lattice constants are subsequently used in order to obtain isobaric thermal expansion coefficients of the pure gas hydrates that exhibit a trend that is significantly closer to the experimental behavior than previously reported classical molecular dynamics studies.

New constraints for low-momentum electronic excitations in condensed matter: fundamental consequences from classical and quantum dielectric theory.

PubMed

Chantler, C T; Bourke, J D

2015-11-18

We present new constraints for the transportation behaviour of low-momentum electronic excitations in condensed matter systems, and demonstrate that these have both a fundamental physical interpretation and a significant impact on the description of low-energy inelastic electron scattering. The dispersion behaviour and characteristic lifetime properties of plasmon and single-electron excitations are investigated using popular classical, semi-classical and quantum dielectric models. We find that, irrespective of constrained agreement to the well known high-momentum and high-energy Bethe ridge limit, standard descriptions of low-momentum electron excitations are inconsistent and unphysical. These observations have direct impact on calculations of transport properties such as inelastic mean free paths, stopping powers and escape depths of charged particles in condensed matter systems.

Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media

NASA Astrophysics Data System (ADS)

Zyablovsky, A. A.; Andrianov, E. S.; Nechepurenko, I. A.; Dorofeenko, A. V.; Pukhov, A. A.; Vinogradov, A. P.

2017-05-01

Solving the challenging problem of the amplification and generation of an electromagnetic field in nanostructures enables us to implement many properties of the electromagnetic field at the nanoscale in practical applications. A first-principles quantum-mechanical consideration of such a problem is sufficiently restricted by the exponentially large number of degrees of freedom and does not allow the electromagnetic-field dynamics to be described if it involves a high number of interacting atoms and modes of the electromagnetic field. Conversely, the classical description of electromagnetic fields is incorrect at the nanoscale due to the high level of quantum fluctuations connected to high dissipation and noise levels. In this paper, we develop a framework with a significantly reduced number of degrees of freedom, which describes the quantum spatial dynamics of electromagnetic fields interacting with atoms. As an example, we consider the interaction between atoms placed in a metallic subwavelength groove and demonstrate that a spontaneously excited electromagnetic pulse propagates with the group velocity. The developed approach may be exploited to describe nonuniform amplification and propagation of electromagnetic fields in arbitrary dispersive dissipative systems.

Event-by-Event Anisotropic Flow in Heavy-ion Collisions from Combined Yang-Mills and Viscous Fluid Dynamics

NASA Astrophysics Data System (ADS)

Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju

2013-01-01

Anisotropic flow coefficients v1-v5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated vn data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v2, v3 and v4 measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.

Towards cosmological dynamics from loop quantum gravity

NASA Astrophysics Data System (ADS)

Li, Bao-Fei; Singh, Parampreet; Wang, Anzhong

2018-04-01

We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC, causing a nonsingular bounce. Dynamics can be described by the Hamilton or Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one to one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the prebounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the postbounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.

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.

Quantum and classical chaos in kicked coupled Jaynes-Cummings cavities

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

Hayward, A. L. C.; Greentree, Andrew D.

2010-06-15

We consider two Jaynes-Cummings cavities coupled periodically with a photon hopping term. The semiclassical phase space is chaotic, with regions of stability over some ranges of the parameters. The quantum case exhibits dynamic localization and dynamic tunneling between classically forbidden regions. We explore the correspondence between the classical and quantum phase space and propose an implementation in a circuit QED system.

Breakdown of the classical description of a local system.

PubMed

Kot, Eran; Grønbech-Jensen, Niels; Nielsen, Bo M; Neergaard-Nielsen, Jonas S; Polzik, Eugene S; Sørensen, Anders S

2012-06-08

We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig [Phys. Rev. A 83, 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system described by the continuous canonical variables x and p, such as a mechanical or an electrical oscillator and a collective spin of a large ensemble.

Implementation and characterization of active feed-forward for deterministic linear optics quantum computing

NASA Astrophysics Data System (ADS)

Böhi, P.; Prevedel, R.; Jennewein, T.; Stefanov, A.; Tiefenbacher, F.; Zeilinger, A.

2007-12-01

In general, quantum computer architectures which are based on the dynamical evolution of quantum states, also require the processing of classical information, obtained by measurements of the actual qubits that make up the computer. This classical processing involves fast, active adaptation of subsequent measurements and real-time error correction (feed-forward), so that quantum gates and algorithms can be executed in a deterministic and hence error-free fashion. This is also true in the linear optical regime, where the quantum information is stored in the polarization state of photons. The adaptation of the photon’s polarization can be achieved in a very fast manner by employing electro-optical modulators, which change the polarization of a trespassing photon upon appliance of a high voltage. In this paper we discuss techniques for implementing fast, active feed-forward at the single photon level and we present their application in the context of photonic quantum computing. This includes the working principles and the characterization of the EOMs as well as a description of the switching logics, both of which allow quantum computation at an unprecedented speed.

Discovering the influential users oriented to viral marketing based on online social networks

NASA Astrophysics Data System (ADS)

Zhu, Zhiguo

2013-08-01

The target of viral marketing on the platform of popular online social networks is to rapidly propagate marketing information at lower cost and increase sales, in which a key problem is how to precisely discover the most influential users in the process of information diffusion. A novel method is proposed in this paper for helping companies to identify such users as seeds to maximize information diffusion in the viral marketing. Firstly, the user trust network oriented to viral marketing and users’ combined interest degree in the network including isolated users are extensively defined. Next, we construct a model considering the time factor to simulate the process of information diffusion in viral marketing and propose a dynamic algorithm description. Finally, experiments are conducted with a real dataset extracted from the famous SNS website Epinions. The experimental results indicate that the proposed algorithm has better scalability and is less time-consuming. Compared with the classical model, the proposed algorithm achieved a better performance than does the classical method on the two aspects of network coverage rate and time-consumption in our four sub-datasets.

A sensitivity study of the effects of evaporation/condensation accommodation coefficients on transient heat pipe modeling

NASA Astrophysics Data System (ADS)

Hall, Michael L.; Doster, J. Michael

1990-03-01

The dynamic behavior of liquid metal heat pipe models is strongly influenced by the choice of evaporation and condensation modeling techniques. Classic kinetic theory descriptions of the evaporation and condensation processes are often inadequate for real situations; empirical accommodation coefficients are commonly utilized to reflect nonideal mass transfer rates. The complex geometries and flow fields found in proposed heat pipe systems cause considerable deviation from the classical models. the THROHPUT code, which has been described in previous works, was developed to model transient liquid metal heat pipe behavior from frozen startup conditions to steady state full power operation. It is used here to evaluate the sensitivity of transient liquid metal heat pipe models to the choice of evaporation and condensation accommodation coefficients. Comparisons are made with experimental liquid metal heat pipe data. It is found that heat pipe behavior can be predicted with the proper choice of the accommodation coefficients. However, the common assumption of spatially constant accommodation coefficients is found to be a limiting factor in the model.

Hybrid classical/quantum simulation for infrared spectroscopy of water

NASA Astrophysics Data System (ADS)

Maekawa, Yuki; Sasaoka, Kenji; Ube, Takuji; Ishiguro, Takashi; Yamamoto, Takahiro

2018-05-01

We have developed a hybrid classical/quantum simulation method to calculate the infrared (IR) spectrum of water. The proposed method achieves much higher accuracy than conventional classical molecular dynamics (MD) simulations at a much lower computational cost than ab initio MD simulations. The IR spectrum of water is obtained as an ensemble average of the eigenvalues of the dynamical matrix constructed by ab initio calculations, using the positions of oxygen atoms that constitute water molecules obtained from the classical MD simulation. The calculated IR spectrum is in excellent agreement with the experimental IR spectrum.

Exploration of the folding dynamics of human telomeric G-quadruplex with a hybrid atomistic structure-based model

NASA Astrophysics Data System (ADS)

Bian, Yunqiang; Ren, Weitong; Song, Feng; Yu, Jiafeng; Wang, Jihua

2018-05-01

Structure-based models or Gō-like models, which are built from one or multiple particular experimental structures, have been successfully applied to the folding of proteins and RNAs. Recently, a variant termed the hybrid atomistic model advances the description of backbone and side chain interactions of traditional structure-based models, by borrowing the description of local interactions from classical force fields. In this study, we assessed the validity of this model in the folding problem of human telomeric DNA G-quadruplex, where local dihedral terms play important roles. A two-state model was developed and a set of molecular dynamics simulations was conducted to study the folding dynamics of sequence Htel24, which was experimentally validated to adopt two different (3 + 1) hybrid G-quadruplex topologies in K+ solution. Consistent with the experimental observations, the hybrid-1 conformation was found to be more stable and the hybrid-2 conformation was kinetically more favored. The simulations revealed that the hybrid-2 conformation folded in a higher cooperative manner, which may be the reason why it was kinetically more accessible. Moreover, by building a Markov state model, a two-quartet G-quadruplex state and a misfolded state were identified as competing states to complicate the folding process of Htel24. Besides, the simulations also showed that the transition between hybrid-1 and hybrid-2 conformations may proceed an ensemble of hairpin structures. The hybrid atomistic structure-based model reproduced the kinetic partitioning folding dynamics of Htel24 between two different folds, and thus can be used to study the complex folding processes of other G-quadruplex structures.

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.

BOOK REVIEW: Microscopic Dynamics of Plasmas and Chaos

NASA Astrophysics Data System (ADS)

Elskens, Y.; Escande, D.

2003-04-01

Some of the key intellectual foundations of plasma physics are in danger of becoming a lost art. Fortunately, however, this threat recedes with the publication of this valuable book. It renders accessible those aspects of theoretical plasma physics that are best approached from the perspectives of classical mechanics, in both its early nineteenth century and late twentieth century manifestations. Half a century has elapsed since the publication of seminal papers such as those by Bohm and Pines (1951), van Kampen (1955), and Bernstein, Greene and Kruskal (1957). These papers served to address a fundamental question of physics - namely the relation between degrees of freedom that exist at the individual particle level of description, and those that exist at the collective level - in the plasma context. The authors of the present book have played a major role in the investigation of this question from an N-body standpoint, which can be divided into two linked themes. First, those topics that can be illuminated by analytical methods that lie in the tradition of classical mechanics that stretches back to Lagrange, Legendre and Hamilton. Second, those topics that benefit from the insights developed following the redevelopment of classical mechanics in relation to chaos theory in the 1980s and subsequently. The working plasma physicist who wishes to dig more deeply in this field is faced at present with a number of challenges. These may include a perception that this subfield is of limited relevance to mission-oriented questions of plasma performance; a perception of the research literature as being self-contained and inaccessible; and, linked to this, unfamiliarity with the mathematical tools. The latter problem is particularly pressing, given the limited coverage of classical mechanics in many undergraduate physics courses. The book by Elskens and Escande meets many of the challenges outlined above. The rewards begin early, by the end of the second chapter, with beautiful derivations of the self-consistent Lagrangian for wave-particle interactions, followed by an equivalent Hamiltonian formulation in terms of action-angle variables. In the following two chapters, these and related techniques are used to explore the deepest topics of plasma dynamics and wave theory, often from a beam-plasma perspective. The book begins afresh at chapter 5, which is an ambitious attempt to summarise modern classical dynamics. This chapter begins well, with a nice introduction to action-angle variables (these have already been extensively exploited in the preceding chapters, however!), but the account eventually became too compressed for the present reviewer. There follow two further chapters on both diffusion and the single-wave-particle system. Perhaps this book is best considered as a companion to the research literature (indeed there is a useful and extensive bibliography), rather than as a conventionally structured textbook. Certainly it is a book that should be read backwards and sideways, as well as forwards. Most readers, for example, will be more familiar with the Vlasov-Poisson system than with the N-body approach to particles and fields that is developed here: their natural starting point will perhaps be appendix G.4 of the present volume. Nor does the book provide a free-standing account of plasma dynamics from the chosen perspective. For example, prior familiarity with van Kampen modes in the Vlasov--Poisson description would greatly assist understanding of chapter 3. Challenging exercises are embedded in the text throughout (even in the otherwise excellent appendices), with answers not necessarily provided. Altogether, this book provides a wealth of theoretical information that is not easily accessible from any other source. It is a book with character, written from a definite viewpoint, but it also facilitates the development of the reader's own perspective by offering a clear path to the original research literature. R O Dendy

Optimizing DER Participation in Inertial and Primary-Frequency Response

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

Dall-Anese, Emiliano; Zhao, Changhong; Guggilam, Swaroop

This paper develops an approach to enable the optimal participation of distributed energy resources (DERs) in inertial and primary-frequency response alongside conventional synchronous generators. Leveraging a reduced-order model description of frequency dynamics, DERs' synthetic inertias and droop coefficients are designed to meet time-domain performance objectives of frequency overshoot and steady-state regulation. Furthermore, an optimization-based method centered around classical economic dispatch is developed to ensure that DERs share the power injections for inertial- and primary-frequency response in proportion to their power ratings. Simulations for a modified New England test-case system composed of ten synchronous generators and six instances of the IEEEmore » 37-node test feeder with frequency-responsive DERs validate the design strategy.« less

Universal ideal behavior and macroscopic work relation of linear irreversible stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Ma, Yi-An; Qian, Hong

2015-06-01

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process as the natural generalization of classical conservative mechanics, a bridge between a family of OU processes with equilibrium fluctuations and thermodynamics is established through the celebrated Helmholtz theorem. The Helmholtz theorem provides an emergent macroscopic ‘equation of state’ of the entire system, which exhibits a universal ideal thermodynamic behavior. Fluctuating macroscopic quantities are studied from the stochastic thermodynamic point of view and a non-equilibrium work relation is obtained in the macroscopic picture, which may facilitate experimental study and application of the equalities due to Jarzynski, Crooks, and Hatano and Sasa.

Temperature Dependence of Thermodynamic Properties of Thallium Chloride and Thallium Bromide

NASA Astrophysics Data System (ADS)

Kavanoz, H. B.

2015-02-01

Thermodynamic properties as lattice parameters, thermal expansion, heat capacities Cp and Cv, bulk modulus, and Gruneisen parameter of ionic halides TlCl and TlBr in solid and liquid phases were studied using classical molecular dynamics simulation (MD) with interionic Vashistha-Rahman (VR) model potential. In addition to the static and transport properties which have been previously reported by the author [13], this study further confirms that temperature dependence of the calculated thermophysical properties of TlCl and TlBr are in agreement with the available experimental data at both solid and liquid phases in terms of providing an alternative rigid ion potential. The results give a fairly good description of TlCl and TlBr in the temperature range 10-1000 K.

Chaos in a 4D dissipative nonlinear fermionic model

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2015-12-01

Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.

Gaussian geometric discord in terms of Hellinger distance

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

Suciu, Serban, E-mail: serban.suciu@theory.nipne.ro; Isar, Aurelian

2015-12-07

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptoticallymore » to zero in time under the effect of the thermal bath.« less

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

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

Dimitrijević, Dragoljub D., E-mail: ddrag@pmf.ni.ac.rs; Djordjević, Goran S., E-mail: ddrag@pmf.ni.ac.rs; Milošević, Milan, E-mail: ddrag@pmf.ni.ac.rs

2014-11-24

We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking formore » a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.« less

Constrained variational calculus for higher order classical field theories

NASA Astrophysics Data System (ADS)

Campos, Cédric M.; de León, Manuel; Martín de Diego, David

2010-11-01

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Classical-to-Quantum Transition with Broadband Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Vered, Rafi Z.; Shaked, Yaakov; Ben-Or, Yelena; Rosenbluh, Michael; Pe'er, Avi

2015-02-01

A key question of quantum optics is how nonclassical biphoton correlations at low power evolve into classical coherence at high power. Direct observation of the crossover from quantum to classical behavior is desirable, but difficult due to the lack of adequate experimental techniques that cover the ultrawide dynamic range in photon flux from the single photon regime to the classical level. We investigate biphoton correlations within the spectrum of light generated by broadband four-wave mixing over a large dynamic range of ˜80 dB in photon flux across the classical-to-quantum transition using a two-photon interference effect that distinguishes between classical and quantum behavior. We explore the quantum-classical nature of the light by observing the interference contrast dependence on internal loss and demonstrate quantum collapse and revival of the interference when the four-wave mixing gain in the fiber becomes imaginary.

Laryngeal dynamics of pedagogical taan gestures in Indian classical singing.

PubMed

Radhakrishnan, Nandhakumar; Scherer, Ronald C; Bandyopadhyay, Santanu

2011-05-01

Vocal modulations characterize many styles of singing. Vibrato, trill, and trillo are some of the ornaments that Western classical singers use. Likewise, taan is one of the basic frequency modulations demonstrated by Hindustani Indian classical singers. The objective of this descriptive study was to discover the F₀ contour of taan; establish selected acoustic, aerodynamic, and glottographic characteristics of the taan gesture; and explore the pedagogical taan utterances demonstrated by a well-known singer and teacher. Exploratory. Fundamental frequency, alternating current (AC) glottal flow, and electroglottographic width measures were obtained for taan productions by the classical Indian singer and teacher who demonstrated taan rate variations based on his pedagogical approach. The structure of the taan gesture was found to be an F₀ lowering and rising (the "taan dip") followed by a relatively flat portion (the "taan superior surface"). Rate of the F₀ structure of the taan gestures ranged from approximately 1.65 to 3.41Hz, and the F₀ extent ranged from 1.87 to 2.21semitone (ST). As the rate of the taan gesture increased, the superior surface shortened, whereas the taan dip stayed relatively constant (ranging from 170 to 230 ms). AC flow was greater for the lowest frequencies of the dip and faster rates. The pedagogical taan gesture has a specific structure of an F₀ dip followed by a relatively flat F₀ portion that shortens as taan rate increases. The F₀ dip and extent are relatively robust across rate. The taan productions are voluntarily controlled, in contrast to vibrato productions. Copyright © 2011 The Voice Foundation. Published by Mosby, Inc. All rights reserved.

Dynamic Network-Based Epistasis Analysis: Boolean Examples

PubMed Central

Azpeitia, Eugenio; Benítez, Mariana; Padilla-Longoria, Pablo; Espinosa-Soto, Carlos; Alvarez-Buylla, Elena R.

2011-01-01

In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches. PMID:22645556

Time-dependent observables in heavy ion collisions. Part II. In search of pressure isotropization in the φ 4 theory

NASA Astrophysics Data System (ADS)

Kovchegov, Yuri V.; Wu, Bin

2018-03-01

To understand the dynamics of thermalization in heavy ion collisions in the perturbative framework it is essential to first find corrections to the free-streaming classical gluon fields of the McLerran-Venugopalan model. The corrections that lead to deviations from free streaming (and that dominate at late proper time) would provide evidence for the onset of isotropization (and, possibly, thermalization) of the produced medium. To find such corrections we calculate the late-time two-point Green function and the energy-momentum tensor due to a single 2 → 2 scattering process involving two classical fields. To make the calculation tractable we employ the scalar φ 4 theory instead of QCD. We compare our exact diagrammatic results for these quantities to those in kinetic theory and find disagreement between the two. The disagreement is in the dependence on the proper time τ and, for the case of the two-point function, is also in the dependence on the space-time rapidity η: the exact diagrammatic calculation is, in fact, consistent with the free streaming scenario. Kinetic theory predicts a build-up of longitudinal pressure, which, however, is not observed in the exact calculation. We conclude that we find no evidence for the beginning of the transition from the free-streaming classical fields to the kinetic theory description of the produced matter after a single 2 → 2 rescattering.

Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling

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

Tanizaki, Yuya, E-mail: yuya.tanizaki@riken.jp; Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198; Koike, Takayuki, E-mail: tkoike@ms.u-tokyo.ac.jp

Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integralsmore » on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.« less

Stationary stability for evolutionary dynamics in finite populations

DOE PAGES

Harper, Marc; Fryer, Dashiell

2016-08-25

Here, we demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS) candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISSmore » candidates. In various examples, including for the Moran andWright–Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.« less

A discrete geometric approach for simulating the dynamics of thin viscous threads

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

Audoly, B., E-mail: audoly@lmm.jussieu.fr; Clauvelin, N.; Brun, P.-T.

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistencymore » of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.« less

Treelike networks accelerating capillary flow.

PubMed

Shou, Dahua; Ye, Lin; Fan, Jintu

2014-05-01

Transport in treelike networks has received wide attention in natural systems, oil recovery, microelectronic cooling systems, and textiles. Existing studies are focused on transport behaviors under a constant potential difference (including pressure, temperature, and voltage) in a steady state [B. Yu and B. Li, Phys. Rev. E 73, 066302 (2006); J. Chen, B. Yu, P. Xu, and Y. Li, Phys. Rev. E 75, 056301 (2007)]. However, dynamic (time-dependent) transport in such systems has rarely been concerned. In this work, we theoretically investigate the dynamics of capillary flow in treelike networks and design the distribution of radius and length of local branches for the fastest capillary flow. It is demonstrated that capillary flow in the optimized tree networks is faster than in traditional parallel tube nets under fixed constraints. As well, the flow time of the liquid is found to increase approximately linearly with penetration distance, which differs from Washburn's classic description that flow time increases as the square of penetration distance in a uniform tube.

High concentration agglomerate dynamics at high temperatures.

PubMed

Heine, M C; Pratsinis, S E

2006-11-21

The dynamics of agglomerate aerosols are investigated at high solids concentrations that are typical in industrial scale manufacture of fine particles (precursor mole fraction larger than 10 mol %). In particular, formation and growth of fumed silica at such concentrations by chemical reaction, coagulation, and sintering is simulated at nonisothermal conditions and compared to limited experimental data and commercial product specifications. Using recent chemical kinetics for silica formation by SiCl4 hydrolysis and neglecting aerosol polydispersity, the evolution of the diameter of primary particles (specific surface area, SSA), hard- and soft-agglomerates, along with agglomerate effective volume fraction (volume occupied by agglomerate) is investigated. Classic Smoluchowski theory is fundamentally limited for description of soft-agglomerate Brownian coagulation at high solids concentrations. In fact, these high concentrations affect little the primary particle diameter (or SSA) but dominate the soft-agglomerate diameter, structure, and volume fraction, leading to gelation consistent with experimental data. This indicates that restructuring and fragmentation should affect product particle characteristics during high-temperature synthesis of nanostructured particles at high concentrations in aerosol flow reactors.

Polynomic nonlinear dynamical systems - A residual sensitivity method for model reduction

NASA Technical Reports Server (NTRS)

Yurkovich, S.; Bugajski, D.; Sain, M.

1985-01-01

The motivation for using polynomic combinations of system states and inputs to model nonlinear dynamics systems is founded upon the classical theories of analysis and function representation. A feature of such representations is the need to make available all possible monomials in these variables, up to the degree specified, so as to provide for the description of widely varying functions within a broad class. For a particular application, however, certain monomials may be quite superfluous. This paper examines the possibility of removing monomials from the model in accordance with the level of sensitivity displayed by the residuals to their absence. Critical in these studies is the effect of system input excitation, and the effect of discarding monomial terms, upon the model parameter set. Therefore, model reduction is approached iteratively, with inputs redesigned at each iteration to ensure sufficient excitation of remaining monomials for parameter approximation. Examples are reported to illustrate the performance of such model reduction approaches.

Inverse problems and computational cell metabolic models: a statistical approach

NASA Astrophysics Data System (ADS)

Calvetti, D.; Somersalo, E.

2008-07-01

In this article, we give an overview of the Bayesian modelling of metabolic systems at the cellular and subcellular level. The models are based on detailed description of key biochemical reactions occurring in tissue, which may in turn be compartmentalized into cytosol and mitochondria, and of transports between the compartments. The classical deterministic approach which models metabolic systems as dynamical systems with Michaelis-Menten kinetics, is replaced by a stochastic extension where the model parameters are interpreted as random variables with an appropriate probability density. The inverse problem of cell metabolism in this setting consists of estimating the density of the model parameters. After discussing some possible approaches to solving the problem, we address the issue of how to assess the reliability of the predictions of a stochastic model by proposing an output analysis in terms of model uncertainties. Visualization modalities for organizing the large amount of information provided by the Bayesian dynamic sensitivity analysis are also illustrated.

Effective model hierarchies for dynamic and static classical density functional theories

NASA Astrophysics Data System (ADS)

Majaniemi, S.; Provatas, N.; Nonomura, M.

2010-09-01

The origin and methodology of deriving effective model hierarchies are presented with applications to solidification of crystalline solids. In particular, it is discussed how the form of the equations of motion and the effective parameters on larger scales can be obtained from the more microscopic models. It will be shown that tying together the dynamic structure of the projection operator formalism with static classical density functional theories can lead to incomplete (mass) transport properties even though the linearized hydrodynamics on large scales is correctly reproduced. To facilitate a more natural way of binding together the dynamics of the macrovariables and classical density functional theory, a dynamic generalization of density functional theory based on the nonequilibrium generating functional is suggested.

Nonlinear dynamics and quantum entanglement in optomechanical systems.

PubMed

Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2014-03-21

To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Classical Electrodynamics: Lecture notes

NASA Astrophysics Data System (ADS)

Likharev, Konstantin K.

2018-06-01

Essential Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Electrodynamics: Lecture notes is intended to be the basis for a two-semester graduate-level course on electricity and magnetism, including not only the interaction and dynamics charged point particles, but also properties of dielectric, conducting, and magnetic media. The course also covers special relativity, including its kinematics and particle-dynamics aspects, and electromagnetic radiation by relativistic particles.

Lenard-Balescu calculations and classical molecular dynamics simulations of electrical and thermal conductivities of hydrogen plasmas

DOE PAGES

Whitley, Heather D.; Scullard, Christian R.; Benedict, Lorin X.; ...

2014-12-04

Here, we present a discussion of kinetic theory treatments of linear electrical and thermal transport in hydrogen plasmas, for a regime of interest to inertial confinement fusion applications. In order to assess the accuracy of one of the more involved of these approaches, classical Lenard-Balescu theory, we perform classical molecular dynamics simulations of hydrogen plasmas using 2-body quantum statistical potentials and compute both electrical and thermal conductivity from out particle trajectories using the Kubo approach. Our classical Lenard-Balescu results employing the identical statistical potentials agree well with the simulations.

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

Horizons of description: Black holes and complementarity

NASA Astrophysics Data System (ADS)

Bokulich, Peter Joshua Martin

Niels Bohr famously argued that a consistent understanding of quantum mechanics requires a new epistemic framework, which he named complementarity . This position asserts that even in the context of quantum theory, classical concepts must be used to understand and communicate measurement results. The apparent conflict between certain classical descriptions is avoided by recognizing that their application now crucially depends on the measurement context. Recently it has been argued that a new form of complementarity can provide a solution to the so-called information loss paradox. Stephen Hawking argues that the evolution of black holes cannot be described by standard unitary quantum evolution, because such evolution always preserves information, while the evaporation of a black hole will imply that any information that fell into it is irrevocably lost---hence a "paradox." Some researchers in quantum gravity have argued that this paradox can be resolved if one interprets certain seemingly incompatible descriptions of events around black holes as instead being complementary. In this dissertation I assess the extent to which this black hole complementarity can be undergirded by Bohr's account of the limitations of classical concepts. I begin by offering an interpretation of Bohr's complementarity and the role that it plays in his philosophy of quantum theory. After clarifying the nature of classical concepts, I offer an account of the limitations these concepts face, and argue that Bohr's appeal to disturbance is best understood as referring to these conceptual limits. Following preparatory chapters on issues in quantum field theory and black hole mechanics, I offer an analysis of the information loss paradox and various responses to it. I consider the three most prominent accounts of black hole complementarity and argue that they fail to offer sufficient justification for the proposed incompatibility between descriptions. The lesson that emerges from this dissertation is that we have as much to learn from the limitations facing our scientific descriptions as we do from the successes they enjoy. Because all of our scientific theories offer at best limited, effective accounts of the world, an important part of our interpretive efforts will be assessing the borders of these domains of description.

Towards driving mantle convection by mineral physics

NASA Astrophysics Data System (ADS)

Piazzoni, A. S.; Bunge, H.; Steinle-Neumann, G.

2005-12-01

Models of mantle convection have become increasingly sophisticated over the past decade, accounting, for example, for 3 D spherical geometry, and changes in mantle rheology due to variations in temperature and stress. In light of such advances it is surprising that growing constraints on mantle structure derived from mineral physics have not yet been fully brought to bear on mantle convection models. In fact, despite much progress in our understanding of mantle mineralogy a partial description of the equation of state is often used to relate density changes to pressure and temperature alone, without taking into account compositional and mineralogical models of the mantle. Similarly, for phase transitions an incomplete description of thermodynamic constraints is often used, resulting in significant uncertainties in model behavior. While a number of thermodynamic models (some with limited scope) have been constructed recently, some lack the rigor in thermodynamics - for example with respect to the treatment of solid solution - that is needed to make predictions about mantle structure. Here we have constructed a new thermodynamic database for the mantle and have coupled the resulting density dynamically with mantle convection models. The database is build on a self-consistent Gibb's free energy minimization of the system MgO-FeO-SiO2-CaO-Al2O3 that is appropriate for standard (dry) chemical models of the Earth's mantle for relevant high pressure and temperature phases. We have interfaced the database with a high-resolution 2-D convection code (2DTERRA), dynamically coupling the thermodynamic model (density) with the conservation equations of mantle flow. The coupled model is run for different parameterizations of viscosity, initial temperature conditions, and varying the internal vs. external heating. We compare the resulting flow and temperature fields to cases with the Boussinesq approximation and other classical descriptions of the equation of state in mantle dynamics to assess the influence of realistic mineralogical density on mantle convection.

Loop Quantum Cosmology.

PubMed

Bojowald, Martin

2008-01-01

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.

3D analysis of vortical structures in an abdominal aortic aneurysm by stereoscopic PIV

NASA Astrophysics Data System (ADS)

Deplano, Valérie; Guivier-Curien, Carine; Bertrand, Eric

2016-11-01

The present work presents an experimental in vitro three-dimensional analysis of the flow dynamics in an abdominal aortic aneurysm (AAA) through stereoscopic particle image velocimetry (SPIV) measurements. The experimental set-up mimics the pathophysiological context involving a shear thinning blood analogue fluid, compliant AAA and aorto-iliac bifurcation walls and controlled inlet and outlet flow rate and pressure waveforms as well as working fluid temperature. SPIV was carefully calibrated and conducted to assess the three velocity components in the AAA volume. For the first time in the literature, the 3D vortex ring genesis, propagation, and vanishing in the AAA bulge are experimentally described and quantified. In comparison with classical 2-component PIV measurements (2C PIV), the third component of the velocity vector was shown to be of importance in such a geometry, especially, during the deceleration phase of the flow rate. The 3D velocity magnitude reached up more than 20 % of the 2D one showing that 2C PIV are definitively not accurate enough to provide a complete description of flow behaviour in an AAA. In addition to potential clinical implications of a full 3D vortex ring description in AAA evolution, the 3D in vitro experimental quantification of the flow dynamics carried out in the present study offers an interesting tool for the validation of fluid-structure interaction numerical studies dealing with AAA.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Reply to "Comment on `Simple improvements to classical bubble nucleation models'"

NASA Astrophysics Data System (ADS)

Tanaka, Kyoko K.; Tanaka, Hidekazu; Angélil, Raymond; Diemand, Jürg

2016-08-01

We reply to the Comment by Schmelzer and Baidakov [Phys. Rev. E 94, 026801 (2016)]., 10.1103/PhysRevE.94.026801 They suggest that a more modern approach than the classic description by Tolman is necessary to model the surface tension of curved interfaces. Therefore we now consider the higher-order Helfrich correction, rather than the simpler first-order Tolman correction. Using a recent parametrization of the Helfrich correction provided by Wilhelmsen et al. [J. Chem. Phys. 142, 064706 (2015)], 10.1063/1.4907588, we test this description against measurements from our simulations, and find an agreement stronger than what the pure Tolman description offers. Our analyses suggest a necessary correction of order higher than the second for small bubbles with radius ≲1 nm. In addition, we respond to other minor criticism about our results.

A classical treatment of the quadratic Zeeman effect in atomic hydrogen

NASA Astrophysics Data System (ADS)

Al-Laithy, M. A.; Farmer, C. M.; McDowell, M. R. C.

1985-03-01

A description of the non-relativistic classical motion of the electron of a hydrogen atom in the presence of a static magnetic field of arbitrary (non-relativistic) strength is given for arbitrary angular momentum. Applications are given to m = 0 and m = 3 at B = 26.877 kG.

Corkscrew esophagus.

PubMed

Fonseca, Eduardo Kaiser Ururahy Nunes; Yamauchi, Fernando Ide; Tridente, Cassia Franco; Baroni, Ronaldo Hueb

2017-03-01

Corkscrew esophagus (also referred as rosary bead esophagus) is a classic finding of diffuse esophageal spasm (DES) in barium studies reflecting abnormal contractions, leading to compartmentalization and curling of the esophagus, ultimately giving an appearance similar to a corkscrew or rosary beads. We review the pathophysiology of this finding, correlating it to corkscrew and rosary images that originated this classic description.

More on quantum groups from the quantization point of view

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1994-12-01

Star products on the classical double group of a simple Lie group and on corresponding symplectic groupoids are given so that the quantum double and the “quantized tangent bundle” are obtained in the deformation description. “Complex” quantum groups and bicovariant quantum Lie algebras are discussed from this point of view. Further we discuss the quantization of the Poisson structure on the symmetric algebra S(g) leading to the quantized enveloping algebra U h (g) as an example of biquantization in the sense of Turaev. Description of U h (g) in terms of the generators of the bicovariant differential calculus on F(G q ) is very convenient for this purpose. Finaly we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducble representation in the compact case.

High-Resolution Regional Reanalysis in China: Evaluation of 1 Year Period Experiments

NASA Astrophysics Data System (ADS)

Zhang, Qi; Pan, Yinong; Wang, Shuyu; Xu, Jianjun; Tang, Jianping

2017-10-01

Globally, reanalysis data sets are widely used in assessing climate change, validating numerical models, and understanding the interactions between the components of a climate system. However, due to the relatively coarse resolution, most global reanalysis data sets are not suitable to apply at the local and regional scales directly with the inadequate descriptions of mesoscale systems and climatic extreme incidents such as mesoscale convective systems, squall lines, tropical cyclones, regional droughts, and heat waves. In this study, by using a data assimilation system of Gridpoint Statistical Interpolation, and a mesoscale atmospheric model of Weather Research and Forecast model, we build a regional reanalysis system. This is preliminary and the first experimental attempt to construct a high-resolution reanalysis for China main land. Four regional test bed data sets are generated for year 2013 via three widely used methods (classical dynamical downscaling, spectral nudging, and data assimilation) and a hybrid method with data assimilation coupled with spectral nudging. Temperature at 2 m, precipitation, and upper level atmospheric variables are evaluated by comparing against observations for one-year-long tests. It can be concluded that the regional reanalysis with assimilation and nudging methods can better produce the atmospheric variables from surface to upper levels, and regional extreme events such as heat waves, than the classical dynamical downscaling. Compared to the ERA-Interim global reanalysis, the hybrid nudging method performs slightly better in reproducing upper level temperature and low-level moisture over China, which improves regional reanalysis data quality.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

Ratchet effect in the quantum kicked rotor and its destruction by dynamical localization

NASA Astrophysics Data System (ADS)

Hainaut, Clément; Rançon, Adam; Clément, Jean-François; Garreau, Jean Claude; Szriftgiser, Pascal; Chicireanu, Radu; Delande, Dominique

2018-06-01

We study experimentally a quantum kicked rotor with broken parity symmetry, supporting a ratchet effect due to the presence of a classical accelerator mode. We show that the short-time dynamics is very well described by the classical dynamics, characterized by a strongly asymmetric momentum distribution with directed motion on one side, and an anomalous diffusion on the other. At longer times, quantum effects lead to dynamical localization, causing an asymptotic resymmetrization of the wave function.

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

Caruso, M., E-mail: mcaruso@ugr.es; Fanchiotti, H.; Canal, C.A. Garcia

An equivalence between the Schroedinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical systems. We treat the particular case of neutral kaons and found a class of electric networks uniquely related to the kaon system finding the complete map between the matrix elements of the effective Hamiltonian of kaons and those elements of the classical dynamics of the networks. As a consequence, the relevant {epsilon} parameter that measures CP violation in the kaon system is completely determined inmore » terms of network parameters. - Highlights: > We provide a formal equivalence between classical and quantum dynamics. > We make use of the decomplexification concept. > Neutral kaon systems can be represented by electric circuits. > CP symmetry violation can be taken into account by non-reciprocity. > Non-reciprocity is represented by gyrators.« less

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.

X-ray phase-contrast imaging: the quantum perspective

NASA Astrophysics Data System (ADS)

Slowik, J. M.; Santra, R.

2013-08-01

Time-resolved phase-contrast imaging using ultrafast x-ray sources is an emerging method to investigate ultrafast dynamical processes in matter. Schemes to generate attosecond x-ray pulses have been proposed, bringing electronic timescales into reach and emphasizing the demand for a quantum description. In this paper, we present a method to describe propagation-based x-ray phase-contrast imaging in nonrelativistic quantum electrodynamics. We explain why the standard scattering treatment via Fermi’s golden rule cannot be applied. Instead, the quantum electrodynamical treatment of phase-contrast imaging must be based on a different approach. It turns out that it is essential to select a suitable observable. Here, we choose the quantum-mechanical Poynting operator. We determine the expectation value of our observable and demonstrate that the leading order term describes phase-contrast imaging. It recovers the classical expression of phase-contrast imaging. Thus, it makes the instantaneous electron density of non-stationary electronic states accessible to time-resolved imaging. Interestingly, inelastic (Compton) scattering does automatically not contribute in leading order, explaining the success of the semiclassical description.

Generalized activity equations for spiking neural network dynamics.

PubMed

Buice, Michael A; Chow, Carson C

2013-01-01

Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales-the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.

On the self-interference in electron scattering: Copenhagen, Bohmian and geometrical interpretations of quantum mechanics

NASA Astrophysics Data System (ADS)

Tavernelli, Ivano

2018-06-01

Self-interference embodies the essence of the particle-wave formulation of quantum mechanics (QM). According to the Copenhagen interpretation of QM, self-interference by a double-slit requires a large transverse coherence of the incident wavepacket such that it covers the separation between the slits. Bohmian dynamics provides a first step in the separation of the particle-wave character of matter by introducing deterministic trajectories guided by a pilot wave that follows the time-dependent Schrödinger equation. In this work, I present a new description of the phenomenon of self-interference using the geometrical formulation of QM introduced in Tavernelli (2016). In particular, this formalism removes the need for the concept of wavefunction collapse in the interpretation of the act of measurement i.e., the emergence of the classical world. The three QM formulations (Schrödinger, Bohmian, and geometrical) are applied to the description of the scattering of a free electron by a hydrogen atom and a double-slit. The corresponding interpretations of self-interference are compared and discussed.

Classical Electrodynamics: Problems with solutions; Problems with solutions

NASA Astrophysics Data System (ADS)

Likharev, Konstantin K.

2018-06-01

l Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Electrodynamics: Lecture notes is intended to be the basis for a two-semester graduate-level course on electricity and magnetism, including not only the interaction and dynamics charged point particles, but also properties of dielectric, conducting, and magnetic media. The course also covers special relativity, including its kinematics and particle-dynamics aspects, and electromagnetic radiation by relativistic particles.

Optimizing Natural Gas Networks through Dynamic Manifold Theory and a Decentralized Algorithm: Belgium Case Study

NASA Astrophysics Data System (ADS)

Koch, Caleb; Winfrey, Leigh

2014-10-01

Natural Gas is a major energy source in Europe, yet political instabilities have the potential to disrupt access and supply. Energy resilience is an increasingly essential construct and begins with transmission network design. This study proposes a new way of thinking about modelling natural gas flow. Rather than relying on classical economic models, this problem is cast into a time-dependent Hamiltonian dynamics discussion. Traditional Natural Gas constraints, including inelastic demand and maximum/minimum pipe flows, are portrayed as energy functions and built into the dynamics of each pipe flow. Doing so allows the constraints to be built into the dynamics of each pipeline. As time progresses in the model, natural gas flow rates find the minimum energy, thus the optimal gas flow rates. The most important result of this study is using dynamical principles to ensure the output of natural gas at demand nodes remains constant, which is important for country to country natural gas transmission. Another important step in this study is building the dynamics of each flow in a decentralized algorithm format. Decentralized regulation has solved congestion problems for internet data flow, traffic flow, epidemiology, and as demonstrated in this study can solve the problem of Natural Gas congestion. A mathematical description is provided for how decentralized regulation leads to globally optimized network flow. Furthermore, the dynamical principles and decentralized algorithm are applied to a case study of the Fluxys Belgium Natural Gas Network.

Dynamic stabilization of classical Rayleigh-Taylor instability

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

Piriz, A. R.; Piriz, S. A.; Tahir, N. A.

2011-09-15

Dynamic stabilization of classical Rayleigh-Taylor instability is studied by modeling the interface vibration with the simplest possible wave form, namely, a sequence of Dirac deltas. As expected, stabilization results to be impossible. However, in contradiction to previously reported results obtained with a sinusoidal driving, it is found that in general the perturbation amplitude is larger than in the classical case. Therefore, no beneficial effect can be obtained from the vertical vibration of a Rayleigh-Taylor unstable interface between two ideal fluids.

Classical dynamics on curved Snyder space

NASA Astrophysics Data System (ADS)

Ivetić, B.; Meljanac, S.; Mignemi, S.

2014-05-01

We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parameterizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.

Quasi-Classical Trajectory Dynamics Study of the Cl(2P) + C2H6 → HCl(v,j) + C2H5 Reaction. Comparison with Experiment.

PubMed

Espinosa-Garcia, Joaquin; Martinez-Nuñez, Emilio; Rangel, Cipriano

2018-03-15

To understand and simulate the dynamics behavior of the title reaction, QCT calculations were performed on a recently developed global analytical potential energy surface, PES-2017. These calculations combine the classical description of the dynamics with pseudoquantization in the reactants and products to perform a theoretical/experimental comparison on the same footing. Thus, in the products a series of constraints are included to analyze the HCl(v = 0,j) product, which is experimentally detected. At collision energies of 5.5 and 6.7 kcal mol -1 the largest fraction of available energy is deposited as translation, 67%, while the ethyl radical shows significant internal energy, 27%, and so it does not act as a spectator of the reaction, thus reproducing recent experimental evidence. The HCl(v=0, j) rotational distribution is cold, peaking at j = 2, only one unit hotter than experiment, which represents an error of 0.12 kcal mol -1 . At a collision energy of 5.5 kcal mol -1 product translational distribution is slightly hotter than experiment, but at 6.7 kcal mol -1 agreement with recent experiments is practically quantitative, suggesting that the first experiments should be revised. In addition, we observe that the HCl(v=0, j) scattering distribution shifts from isotropic at low values of j to backward at high values of j, which is in agreement with experimental data. Finally, no evidence was found for the "chattering" mechanism suggested to explain the low translational energy of the HCl product in the backward scattering region. In sum, agreement with experiments of a series of sensible dynamic properties permits us to be optimistic on the quality and accuracy of the theoretical tools used in the present work, QCT and PES-2017.

The Contact Dynamics method: A nonsmooth story

NASA Astrophysics Data System (ADS)

Dubois, Frédéric; Acary, Vincent; Jean, Michel

2018-03-01

When velocity jumps are occurring, the dynamics is said to be nonsmooth. For instance, in collections of contacting rigid bodies, jumps are caused by shocks and dry friction. Without compliance at the interface, contact laws are not only non-differentiable in the usual sense but also multi-valued. Modeling contacting bodies is of interest in order to understand the behavior of numerous mechanical systems such as flexible multi-body systems, granular materials or masonry. These granular materials behave puzzlingly either like a solid or a fluid and a description in the frame of classical continuous mechanics would be welcome though far to be satisfactory nowadays. Jean-Jacques Moreau greatly contributed to convex analysis, functions of bounded variations, differential measure theory, sweeping process theory, definitive mathematical tools to deal with nonsmooth dynamics. He converted all these underlying theoretical ideas into an original nonsmooth implicit numerical method called Contact Dynamics (CD); a robust and efficient method to simulate large collections of bodies with frictional contacts and impacts. The CD method offers a very interesting complementary alternative to the family of smoothed explicit numerical methods, often called Distinct Elements Method (DEM). In this paper developments and improvements of the CD method are presented together with a critical comparative review of advantages and drawbacks of both approaches. xml:lang="fr"

Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

PubMed Central

Ge, Hao; Qian, Hong

2011-01-01

A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

PubMed

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

The effect of EIF dynamics on the cryopreservation process of a size distributed cell population.

PubMed

Fadda, S; Briesen, H; Cincotti, A

2011-06-01

Typical mathematical modeling of cryopreservation of cell suspensions assumes a thermodynamic equilibrium between the ice and liquid water in the extracellular solution. This work investigates the validity of this assumption by introducing a population balance approach for dynamic extracellular ice formation (EIF) in the absence of any cryo-protectant agent (CPA). The population balance model reflects nucleation and diffusion-limited growth in the suspending solution whose driving forces are evaluated in the relevant phase diagram. This population balance description of the extracellular compartment has been coupled to a model recently proposed in the literature [Fadda et al., AIChE Journal, 56, 2173-2185, (2010)], which is capable of quantitatively describing and predicting internal ice formation (IIF) inside the cells. The cells are characterized by a size distribution (i.e. through another population balance), thus overcoming the classic view of a population of identically sized cells. From the comparison of the system behavior in terms of the dynamics of the cell size distribution it can be concluded that the assumption of a thermodynamic equilibrium in the extracellular compartment is not always justified. Depending on the cooling rate, the dynamics of EIF needs to be considered. Copyright © 2011 Elsevier Inc. All rights reserved.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

NASA Astrophysics Data System (ADS)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum-Classical Dynamics.

PubMed

Crespo-Otero, Rachel; Barbatti, Mario

2018-05-16

Nonadiabatic mixed quantum-classical (NA-MQC) dynamics methods form a class of computational theoretical approaches in quantum chemistry tailored to investigate the time evolution of nonadiabatic phenomena in molecules and supramolecular assemblies. NA-MQC is characterized by a partition of the molecular system into two subsystems: one to be treated quantum mechanically (usually but not restricted to electrons) and another to be dealt with classically (nuclei). The two subsystems are connected through nonadiabatic couplings terms to enforce self-consistency. A local approximation underlies the classical subsystem, implying that direct dynamics can be simulated, without needing precomputed potential energy surfaces. The NA-MQC split allows reducing computational costs, enabling the treatment of realistic molecular systems in diverse fields. Starting from the three most well-established methods-mean-field Ehrenfest, trajectory surface hopping, and multiple spawning-this review focuses on the NA-MQC dynamics methods and programs developed in the last 10 years. It stresses the relations between approaches and their domains of application. The electronic structure methods most commonly used together with NA-MQC dynamics are reviewed as well. The accuracy and precision of NA-MQC simulations are critically discussed, and general guidelines to choose an adequate method for each application are delivered.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

NASA Astrophysics Data System (ADS)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-01

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory.

PubMed

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE PAGES

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

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

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Ab initio and classical molecular dynamics studies of the structural and dynamical behavior of water near a hydrophobic graphene sheet.

PubMed

Rana, Malay Kumar; Chandra, Amalendu

2013-05-28

The behavior of water near a graphene sheet is investigated by means of ab initio and classical molecular dynamics simulations. The wetting of the graphene sheet by ab initio water and the relation of such behavior to the strength of classical dispersion interaction between surface atoms and water are explored. The first principles simulations reveal a layered solvation structure around the graphene sheet with a significant water density in the interfacial region implying no drying or cavitation effect. It is found that the ab initio results of water density at interfaces can be reproduced reasonably well by classical simulations with a tuned dispersion potential between the surface and water molecules. Calculations of vibrational power spectrum from ab initio simulations reveal a shift of the intramolecular stretch modes to higher frequencies for interfacial water molecules when compared with those of the second solvation later or bulk-like water due to the presence of free OH modes near the graphene sheet. Also, a weakening of the water-water hydrogen bonds in the vicinity of the graphene surface is found in our ab initio simulations as reflected in the shift of intermolecular vibrational modes to lower frequencies for interfacial water molecules. The first principles calculations also reveal that the residence and orientational dynamics of interfacial water are somewhat slower than those of the second layer or bulk-like molecules. However, the lateral diffusion and hydrogen bond relaxation of interfacial water molecules are found to occur at a somewhat faster rate than that of the bulk-like water molecules. The classical molecular dynamics simulations with tuned Lennard-Jones surface-water interaction are found to produce dynamical results that are qualitatively similar to those of ab initio molecular dynamics simulations.

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.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

NASA Astrophysics Data System (ADS)

Lorenzen, F.; de Ponte, M. A.; Moussa, M. H. Y.

2009-09-01

In this paper, employing the Itô stochastic Schrödinger equation, we extend Bell’s beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm’s causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm’s causal dynamics regarding stationary states in quantum mechanics.

Quantum Bohmian model for financial market

NASA Astrophysics Data System (ADS)

Choustova, Olga Al.

2007-01-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

NASA Astrophysics Data System (ADS)

Schubert, Alexander; Falvo, Cyril; Meier, Christoph

2016-08-01

We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking the molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.

LOGISTIC NETWORK REGRESSION FOR SCALABLE ANALYSIS OF NETWORKS WITH JOINT EDGE/VERTEX DYNAMICS

PubMed Central

Almquist, Zack W.; Butts, Carter T.

2015-01-01

Change in group size and composition has long been an important area of research in the social sciences. Similarly, interest in interaction dynamics has a long history in sociology and social psychology. However, the effects of endogenous group change on interaction dynamics are a surprisingly understudied area. One way to explore these relationships is through social network models. Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Although early studies of such processes were primarily descriptive, recent work on this topic has increasingly turned to formal statistical models. Although showing great promise, many of these modern dynamic models are computationally intensive and scale very poorly in the size of the network under study and/or the number of time points considered. Likewise, currently used models focus on edge dynamics, with little support for endogenously changing vertex sets. Here, the authors show how an existing approach based on logistic network regression can be extended to serve as a highly scalable framework for modeling large networks with dynamic vertex sets. The authors place this approach within a general dynamic exponential family (exponential-family random graph modeling) context, clarifying the assumptions underlying the framework (and providing a clear path for extensions), and they show how model assessment methods for cross-sectional networks can be extended to the dynamic case. Finally, the authors illustrate this approach on a classic data set involving interactions among windsurfers on a California beach. PMID:26120218

LOGISTIC NETWORK REGRESSION FOR SCALABLE ANALYSIS OF NETWORKS WITH JOINT EDGE/VERTEX DYNAMICS.

PubMed

Almquist, Zack W; Butts, Carter T

2014-08-01

Change in group size and composition has long been an important area of research in the social sciences. Similarly, interest in interaction dynamics has a long history in sociology and social psychology. However, the effects of endogenous group change on interaction dynamics are a surprisingly understudied area. One way to explore these relationships is through social network models. Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Although early studies of such processes were primarily descriptive, recent work on this topic has increasingly turned to formal statistical models. Although showing great promise, many of these modern dynamic models are computationally intensive and scale very poorly in the size of the network under study and/or the number of time points considered. Likewise, currently used models focus on edge dynamics, with little support for endogenously changing vertex sets. Here, the authors show how an existing approach based on logistic network regression can be extended to serve as a highly scalable framework for modeling large networks with dynamic vertex sets. The authors place this approach within a general dynamic exponential family (exponential-family random graph modeling) context, clarifying the assumptions underlying the framework (and providing a clear path for extensions), and they show how model assessment methods for cross-sectional networks can be extended to the dynamic case. Finally, the authors illustrate this approach on a classic data set involving interactions among windsurfers on a California beach.

Evidence for a Quantum-to-Classical Transition in a Pair of Coupled Quantum Rotors

NASA Astrophysics Data System (ADS)

Gadway, Bryce; Reeves, Jeremy; Krinner, Ludwig; Schneble, Dominik

2013-05-01

The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it may also be an innate property of certain isolated, periodically driven quantum systems. Here, we experimentally realize the simplest such system, consisting of two coupled, kicked quantum rotors, by subjecting a coherent atomic matter wave to two periodically pulsed, incommensurate optical lattices. Momentum transport in this system is found to be radically different from that in a single kicked rotor, with a breakdown of dynamical localization and the emergence of classical diffusion. Our observation, which confirms a long-standing prediction for many-dimensional quantum-chaotic systems, sheds new light on the quantum-classical correspondence.

Rigorous RG Algorithms and Area Laws for Low Energy Eigenstates in 1D

NASA Astrophysics Data System (ADS)

Arad, Itai; Landau, Zeph; Vazirani, Umesh; Vidick, Thomas

2017-11-01

One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance (Landau et al. in Nat Phys, 2015) gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unsolved, including whether there exist efficient algorithms when the ground space is degenerate (and of polynomial dimension in the system size), or for the polynomially many lowest energy states, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of n particles. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly( n) degenerate ground spaces and an n O(log n) algorithm for the poly( n) lowest energy states (under a mild density condition). For these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is {\\tilde{O}(nM(n))} , where M( n) is the time required to multiply two n × n matrices.

Analysis and experiments for a system of two spacecraft paired by means of a flexible link

NASA Astrophysics Data System (ADS)

Sabatini, Marco; Palmerini, Giovanni B.; Gasbarri, Paolo

2016-11-01

A field of current interest in space technology is the on-orbit operation concept, often requiring that a chaser spacecraft captures a target spacecraft. The physical link connecting the two satellites is usually characterized by a high degree of flexibility, because of the special requirements imposed to the space systems, and specifically the constraints on the mass at launch. The focus of this paper is the study of an attitude control of the paired spacecraft system such that the elastic oscillations do not interfere with the attitude dynamics, and the final configuration is reached without residual vibrations. At the scope, a rest-to-rest techniques, that requires an accurate description of the dynamic model of the paired satellites as a flexible multibody setup, is applied. The results of this control are first tested by means of a numerical tool, simulating nominal and non-nominal scenarios. Then the identified control is proved in an experimental test-bed, consisting of two free-floating platforms connected by means of an elastic joint. The performance of the rest-to-rest technique is compared to other classical control laws aiming to minimally excite the system undesired dynamics, showing a promising superiority.

Quantum trajectory analysis of multimode subsystem-bath dynamics.

PubMed

Wyatt, Robert E; Na, Kyungsun

2002-01-01

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

Experimental demonstration of chaotic scattering of microwaves

NASA Astrophysics Data System (ADS)

Doron, E.; Smilansky, U.; Frenkel, A.

1990-12-01

Reflection of microwaves from a cavity is measured in a frequency domain where the underlying classical chaotic scattering leaves a clear mark on the wave dynamics. We check the hypothesis that the fluctuations of the S matrix can be described in terms of parameters characterizing the chaotic classical scatteirng. Absorption of energy in the cavity walls is shown to significantly affect the results, and is linked to time-domain properties of the scattering in a general way. We also show that features whose origin is entirely due to wave dynamics (e.g., the enhancement of the Wigner time delay due to time-reversal symmetry) coexist with other features which characterize the underlying classical dynamics.

Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system

NASA Astrophysics Data System (ADS)

Qureshi, Mumnuna A.; Zhong, Johnny; Qureshi, Zihad; Mason, Peter; Betouras, Joseph J.; Zagoskin, Alexandre M.

2018-03-01

We consider the evolution of the quantum states of a Hamiltonian that is parametrically perturbed via a term proportional to the adiabatic parameter λ (t ) . Starting with the Pechukas-Yukawa mapping of the energy eigenvalue evolution in a generalized Calogero-Sutherland model of a one-dimensional classical gas, we consider the adiabatic approximation with two different expansions of the quantum state in powers of d λ /d t and compare them with a direct numerical simulation. We show that one of these expansions (Magnus series) is especially convenient for the description of nonadiabatic evolution of the system. Applying the expansion to the exact cover 3-satisfiability problem, we obtain the occupation dynamics, which provides insight into the population of states and sources of decoherence in a quantum system.

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

NASA Astrophysics Data System (ADS)

Alber, Mark; Chen, Nan; Glimm, Tilmann; Lushnikov, Pavel M.

2006-05-01

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

Inertia-induced dendriticlike patterns in lifting Hele-Shaw flows

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Dias, Eduardo O.; Miranda, José A.

2017-01-01

The lifting Hele-Shaw cell problem is a variant of the classical constant-gap Hele-Shaw situation in which the cell gap width is time dependent. Experiments on Newtonian fluid flows in lifting Hele-Shaw cells with large lifting velocities reveal the development of dendriticlike fingered structures that compete among themselves. The usual Darcy law description of the problem, where inertial effects are neglected, has not been able to explain the origin of these competing sidebranched patterns. In this work we use a generalized Darcy law and a perturbative mode-coupling theory to investigate the impact of inertia on the pattern-forming dynamics of the system. Two main results are deduced: Inertia induces a mechanism for finger sidebranching formation and favors the intensification of finger competition events.

Joint density-functional theory and its application to systems in solution

NASA Astrophysics Data System (ADS)

Petrosyan, Sahak A.

The physics of solvation, the interaction of water with solutes, plays a central role in chemistry and biochemistry, and it is essential for the very existence of life. Despite the central importance of water and the advent of the quantum theory early in the twentieth century, the link between the fundamental laws of physics and the observable properties of water remain poorly understood to this day. The central goal of this thesis is to develop a new formalism and framework to make the study of systems (solutes or surfaces) in contact with liquid water as practical and accurate as standard electronic structure calculations without the need for explicit averaging over large ensembles of configurations of water molecules. The thesis introduces a new form of density functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. Using the new form of density-functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment, the thesis then presents the first detailed study of the impact of a solvent on the surface chemistry of Cr2O3, the passivating layer of stainless steel alloys. In comparison to a vacuum, we predict that the presence of water has little impact on the adsorption of chloride ions to the oxygen-terminated surface but has a dramatic effect on the binding of hydrogen to that surface. A key ingredient of a successful joint density functional theory is a good approximate functional for describing the solvent. We explore how the simplest examples of the best known class of approximate forms for the classical density functional fail when applied directly to water. The thesis then presents a computationally efficient density-functional theory for water which overcomes this difficulty and gives reasonable agreement with molecular dynamics simulation data for the solvation of hard spheres in water and sufficient agreement with experimental data for hydration of inert gas atoms to justify its use in a joint theory with standard approximate density functionals used in electronic structure calculations. The last study in the thesis combines the previous ideas and presenting an approximate model density functional which includes a description of cavitation effects through a classical density-functional theory; a description of dielectric effects through a non-local polarizability, and a description of the coupling of the solvent to the electrons of the solute through a pseudopotential. Without any empirical fitting of parameters to solvation data, this theory predicts solvation energies at least as well as state-of-the-art quantum-chemical cavity approaches, which do employ such fitting. Although this agreement without adjustable parameters is very encouraging and shows the promise of the joint density-functional approach, the functionals which we develop here are models and do not yet include all of the microscopic physics. The thesis concludes with a description of the directions future work should take to address this weakness.

A Comparative Analysis of the Integration of Faith and Learning between ACSI and ACCS Accredited Schools

ERIC Educational Resources Information Center

Peterson, Daniel Carl

2012-01-01

The purpose of this descriptive quantitative study was to analyze and compare the integration of faith and learning occurring in Christian schools accredited by the Association of Christian Schools International (ACSI) and classical Christian schools accredited by the Association of Classical and Christian Schools (ACCS). ACSI represents the…

Classical molecular dynamics simulation of electronically non-adiabatic processes.

PubMed

Miller, William H; Cotton, Stephen J

2016-12-22

Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born-Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides "quantization" of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).

Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr's doctrine of classical concepts?

NASA Astrophysics Data System (ADS)

Camilleri, Kristian; Schlosshauer, Maximilian

2015-02-01

Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr's doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr's doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum-classical transition that were pursued by several of Bohr's followers and culminated in the development of decoherence theory.

From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics

NASA Astrophysics Data System (ADS)

Kreis, Karsten; Kremer, Kurt; Potestio, Raffaello; Tuckerman, Mark E.

2017-12-01

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

Geometric descriptions of entangled states by auxiliary varieties

NASA Astrophysics Data System (ADS)

Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-01

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n + 1), for n ⩾ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.

Turbulent scaling laws as solutions of the multi-point correlation equation using statistical symmetries

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Rosteck, Andreas; Avsarkisov, Victor

2013-11-01

Text-book knowledge proclaims that Lie symmetries such as Galilean transformation lie at the heart of fluid dynamics. These important properties also carry over to the statistical description of turbulence, i.e. to the Reynolds stress transport equations and its generalization, the multi-point correlation equations (MPCE). Interesting enough, the MPCE admit a much larger set of symmetries, in fact infinite dimensional, subsequently named statistical symmetries. Most important, theses new symmetries have important consequences for our understanding of turbulent scaling laws. The symmetries form the essential foundation to construct exact solutions to the infinite set of MPCE, which in turn are identified as classical and new turbulent scaling laws. Examples on various classical and new shear flow scaling laws including higher order moments will be presented. Even new scaling have been forecasted from these symmetries and in turn validated by DNS. Turbulence modellers have implicitly recognized at least one of the statistical symmetries as this is the basis for the usual log-law which has been employed for calibrating essentially all engineering turbulence models. An obvious conclusion is to generally make turbulence models consistent with the new statistical symmetries.

Classical and quantum fold catastrophe in the presence of axial symmetry

NASA Astrophysics Data System (ADS)

Dhont, G.; Zhilinskií, B. I.

2008-11-01

We introduce a family of Hamiltonians with two degrees of freedom, axial symmetry and complete integrability. The potential function depends on coordinates and one control parameter. A fold catastrophe typically occurs in such a family of potentials and its consequences on the global dynamics are investigated through the energy-momentum map which defines the singular fibration of the four-dimensional phase space. The two inequivalent local canonical forms of the catastrophe are presented: the first case corresponds to the appearance of a second sheet in the image of the energy-momentum map while the second case is associated with the breaking of an already existing second sheet. A special effort is placed on the description of the singularities. In particular, the existence of cuspidal tori is related to a second-order contact point between the energy level set and the reduced phase space. The quantum mechanical aspects of the changes induced by the fold catastrophe are investigated with the quantum eigenstates computed for an octic potential and are interpreted through the quantum-classical correspondence. We note that the singularity exposed in this paper is not an obstruction to a global definition of action-angle variables.

Vortex scaling ranges in two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Burgess, B. H.; Dritschel, D. G.; Scott, R. K.

2017-11-01

We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solutions based upon mixed quantum-classical approximation. I. Proton transfer reaction in water

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

Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu, E-mail: okazaki@apchem.nagoya-u.ac.jp

2014-08-28

In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfermore » process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps{sup −1}, which is about 2.5 times faster than that in vacuum, 0.27 ps{sup −1}. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction.« less

Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects.

PubMed

Sumner, Isaiah; Iyengar, Srinivasan S

2007-10-18

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

Quantized Detector Networks

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2017-12-01

Preface; Acronyms; 1. Introduction; 2. Questions and answers; 3. Classical bits; 4. Quantum bits; 5. Classical and quantum registers; 6. Classical register mechanics; 7. Quantum register dynamics; 8. Partial observations; 9. Mixed states and POVMs; 10. Double-slit experiments; 11. Modules; 12. Computerization and computer algebra; 13. Interferometers; 14. Quantum eraser experiments; 15. Particle decays; 16. Non-locality; 17. Bell inequalities; 18. Change and persistence; 19. Temporal correlations; 20. The Franson experiment; 21. Self-intervening networks; 22. Separability and entanglement; 23. Causal sets; 24. Oscillators; 25. Dynamical theory of observation; 26. Conclusions; Appendix; Index.

The dynamical mass of a classical Cepheid variable star in an eclipsing binary system.

PubMed

Pietrzyński, G; Thompson, I B; Gieren, W; Graczyk, D; Bono, G; Udalski, A; Soszyński, I; Minniti, D; Pilecki, B

2010-11-25

Stellar pulsation theory provides a means of determining the masses of pulsating classical Cepheid supergiants-it is the pulsation that causes their luminosity to vary. Such pulsational masses are found to be smaller than the masses derived from stellar evolution theory: this is the Cepheid mass discrepancy problem, for which a solution is missing. An independent, accurate dynamical mass determination for a classical Cepheid variable star (as opposed to type-II Cepheids, low-mass stars with a very different evolutionary history) in a binary system is needed in order to determine which is correct. The accuracy of previous efforts to establish a dynamical Cepheid mass from Galactic single-lined non-eclipsing binaries was typically about 15-30% (refs 6, 7), which is not good enough to resolve the mass discrepancy problem. In spite of many observational efforts, no firm detection of a classical Cepheid in an eclipsing double-lined binary has hitherto been reported. Here we report the discovery of a classical Cepheid in a well detached, double-lined eclipsing binary in the Large Magellanic Cloud. We determine the mass to a precision of 1% and show that it agrees with its pulsation mass, providing strong evidence that pulsation theory correctly and precisely predicts the masses of classical Cepheids.

Fate of classical solitons in one-dimensional quantum systems.

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

Pustilnik, M.; Matveev, K. A.

We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, andmore » argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.« less

Evaluating the Classical Versus an Emerging Conceptual Model of Peatland Methane Dynamics

Treesearch

Wendy H. Yang; Gavin McNicol; Yit Arn Teh; Katerina Estera-Molina; Tana E. Wood; Whendee L. Silver

2017-01-01

Methane (CH4) is a potent greenhouse gas that is both produced and consumed in soils by microbially mediated processes sensitive to soil redox. We evaluated the classical conceptual model of peatland CH4 dynamics—in which the water table position determines the vertical distribution of methanogenesis and methanotrophy—...

Towards "Thick Description" of Educational Transfer: Understanding a Japanese Institution's "Import" of European Language Policy

ERIC Educational Resources Information Center

Rappleye, Jeremy; Imoto, Yuki; Horiguchi, Sachiko

2011-01-01

Globalisation and convergence in educational policy worldwide has reinvigorated, while rendering more complex, the classic theme of educational transfer. Framed by this wider pursuit of new understandings of a changing transfer/context puzzle, this paper explores how an ethnographic "thick description" might complement and extend recent…

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.

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.

Rydberg Atoms in Strong Fields: a Testing Ground for Quantum Chaos.

NASA Astrophysics Data System (ADS)

Courtney, Michael

1995-01-01

Rydberg atoms in strong static electric and magnetic fields provide experimentally accessible systems for studying the connections between classical chaos and quantum mechanics in the semiclassical limit. This experimental accessibility has motivated the development of reliable quantum mechanical solutions. This thesis uses both experimental and computed quantum spectra to test the central approaches to quantum chaos. These central approaches consist mainly of developing methods to compute the spectra of quantum systems in non -perturbative regimes, correlating statistical descriptions of eigenvalues with the classical behavior of the same Hamiltonian, and the development of semiclassical methods such as periodic-orbit theory. Particular emphasis is given to identifying the spectral signature of recurrences --quantum wave packets which follow classical orbits. The new findings include: the breakdown of the connection between energy-level statistics and classical chaos in odd-parity diamagnetic lithium, the discovery of the signature of very long period orbits in atomic spectra, quantitative evidence for the scattering of recurrences by the alkali -metal core, quantitative description of the behavior of recurrences near bifurcations, and a semiclassical interpretation of the evolution of continuum Stark spectra. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

Wigner flow reveals topological order in quantum phase space dynamics.

PubMed

Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg

2013-01-18

The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

Internal Dynamics and Boundary Forcing Characteristics Associated with Interannual Variability of the Asian Summer Monsoon

NASA Technical Reports Server (NTRS)

Lau, K.- M.; Kim, K.-M.; Yang, S.

1998-01-01

In this paper, we present a description of the internal dynamics and boundary forcing characteristics of two major components of the Asian summer monsoon (ASM), i.e., the South Asian (SAM) and the Southeast-East Asian monsoon (SEAM). The description is based on a new monsoon-climate paradigm in which the variability of ASM is considered as the outcome of the interplay of a "fast" and an "intermediate" monsoon subsystem, under the influenced of the "slow" varying external forcings. Two sets of regional monsoon indices derived from dynamically consistent rainfall and wind data are used in this study. For SAM, the internal dynamics is represented by that of a "classical" monsoon system where the anomalous circulation is governed by Rossby-wave dynamics, i.e., generation of anomalous vorticity induced by an off-equatorial heat source is balanced by planetary vorticity advection. On the other hand, the internal dynamics of SEAM is characterized by a "hybrid" monsoon system featuring multi-cellular meridional circulation over the East Asian section, extending from the deep tropics to midlatitudes. These meridional-cells link tropical heating to extratropical circulation system via the East Asian jetstream, and are responsible for the characteristic occurrences of zonally oriented anomalous rainfall patterns over East Asian and the subtropical western Pacific. In the extratropical regions, the major upper level vorticity balance is by anomalous vorticity advection and generation by the anomalous divergent circulation. A consequence of this is that compared to SAM, the SEAM is associated with stronger teleconnection patterns to regions outside the ASM. A strong SAM is linked to basin-scale sea surface temperature (SST) fluctuation with significant signal in the equatorial eastern Pacific. During the boreal spring SST warming in the Arabian Sea and the subtropical western Pacific may lead to a strong SAM. For SEAM, interannual variability is tied to SSTA over the Sea of Japan and the South China Sea regions, while the linkage to equatorial basin-scale SSTA is weak at best. A large scale SSTA dipole with warming (cooling) in the subtropical central (eastern) Pacific foreshadows a strong SEAM.

Water Lone Pair Delocalization in Classical and Quantum Descriptions of the Hydration of Model Ions

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

Remsing, Richard C.; Duignan, Timothy T.; Baer, Marcel D.

Understanding the nature of ionic hydration at a fundamental level has eluded scientists despite intense interest for nearly a century. In particular, the microscopic origins of the asymmetry of ion solvation thermodynamics with respect to the sign of the ionic charge remains a mystery. Here, we determine the response of accurate quantum mechanical water models to strong nanoscale solvation forces arising from excluded volumes and ionic electrostatic fields. This is compared to the predictions of two important limiting classes of classical models of water with fixed point changes, differing in their treatment of "lone-pair" electrons. Using the quantum water modelmore » as our standard of accuracy, we find that a single fixed classical treatment of lone pair electrons cannot accurately describe solvation of both apolar and cationic solutes, underlining the need for a more flexible description of local electronic effects in solvation processes. However, we explicitly show that all water models studied respond to weak long-ranged electrostatic perturbations in a manner that follows macroscopic dielectric continuum models, as would be expected. We emphasize the importance of these findings in the context of realistic ion models, using density functional theory and empirical models, and discuss the implications of our results for quantitatively accurate reduced descriptions of solvation in dielectric media.« less

Classical noise, quantum noise and secure communication

NASA Astrophysics Data System (ADS)

Tannous, C.; Langlois, J.

2016-01-01

Secure communication based on message encryption might be performed by combining the message with controlled noise (called pseudo-noise) as performed in spread-spectrum communication used presently in Wi-Fi and smartphone telecommunication systems. Quantum communication based on entanglement is another route for securing communications as demonstrated by several important experiments described in this work. The central role played by the photon in unifying the description of classical and quantum noise as major ingredients of secure communication systems is highlighted and described on the basis of the classical and quantum fluctuation dissipation theorems.

Biodiversity research in the “big data” era: GigaScience and Pensoft work together to publish the most data-rich species description

PubMed Central

2013-01-01

With the publication of the first eukaryotic species description, combining transcriptomic, DNA barcoding, and micro-CT imaging data, GigaScience and Pensoft demonstrate how classical taxonomic description of a new species can be enhanced by applying new generation molecular methods, and novel computing and imaging technologies. This 'holistic’ approach in taxonomic description of a new species of cave-dwelling centipede is published in the Biodiversity Data Journal (BDJ), with coordinated data release in the GigaScience GigaDB database. PMID:24229463

Biodiversity research in the "big data" era: GigaScience and Pensoft work together to publish the most data-rich species description.

PubMed

Edmunds, Scott C; Hunter, Chris I; Smith, Vincent; Stoev, Pavel; Penev, Lyubomir

2013-10-28

With the publication of the first eukaryotic species description, combining transcriptomic, DNA barcoding, and micro-CT imaging data, GigaScience and Pensoft demonstrate how classical taxonomic description of a new species can be enhanced by applying new generation molecular methods, and novel computing and imaging technologies. This 'holistic' approach in taxonomic description of a new species of cave-dwelling centipede is published in the Biodiversity Data Journal (BDJ), with coordinated data release in the GigaScience GigaDB database.

Anatomy of the Spinal Meninges.

PubMed

Sakka, Laurent; Gabrillargues, Jean; Coll, Guillaume

2016-06-01

The spinal meninges have received less attention than the cranial meninges in the literature, although several points remain debatable and poorly understood, like their phylogenesis, their development, and their interactions with the spinal cord. Their constancy among the chordates shows their crucial importance in central nervous system homeostasis and suggests a role far beyond mechanical protection of the neuraxis. This work provides an extensive study of the spinal meninges, from an overview of their phylogenesis and embryology to a descriptive and topographic anatomy with clinical implications. It examines their involvement in spinal cord development, functioning, and repair. This work is a review of the literature using PubMed as a search engine on Medline. The stages followed by the meninges along the phylogenesis could not be easily compared with their development in vertebrates for methodological aspects and convergence processes throughout evolution. The distinction between arachnoid and pia mater appeared controversial. Several points of descriptive anatomy remain debatable: the functional organization of the arterial network, and the venous and lymphatic drainages, considered differently by classical anatomic and neuroradiological approaches. Spinal meninges are involved in neurodevelopment and neurorepair producing neural stem cells and morphogens, in cerebrospinal fluid dynamics and neuraxis functioning by the synthesis of active molecules, and the elimination of waste products of central nervous system metabolism. The spinal meninges should be considered as dynamic functional formations evolving over a lifetime, with ultrastructural features and functional interactions with the neuraxis remaining not fully understood.

The expansion of intensive agriculture and ranching in Brazilian Amazonia

NASA Astrophysics Data System (ADS)

Walker, Robert; DeFries, Ruth; del Carmen Vera-Diaz, Maria; Shimabukuro, Yosio; Venturieri, Adriano

Agriculture in Amazonia has often provoked controversy, given the tremendous ecological value of the region's environment. First with ranching, and now with the soybean boom, tractors and cattle have marched across lands that for millennia supported only closed moist forest, resident ecosystems, and dispersed indigenous peoples. The present chapter considers this expansion, focusing on the Brazilian portion of the basin. Its premise is that effective Amazonian policy must be grounded on an understanding of the region's agriculture. The chapter pursues its objectives by first addressing the development initiatives that created the preconditions for Amazonia's current agricultural economy. The region is remote and has therefore required sustained government intervention to release its potential. The policy discussion is followed by descriptions of cattle ranching and soy farming. For each, market settings and trajectories of expansion are presented. Although these sectoral descriptions are data rich, they do not provide a conceptual framework for analyzing the environmental impacts of evolving market conditions. To accomplish this, the chapter invokes the classical land use model of von Thünen to explain Amazonian land cover dynamics in relation to soy-cattle linkages. It addresses these dynamics with remote sensing data from Mato Grosso, Pará, and Rondônia, and then discusses scenarios of agricultural advances on the forest. Conclusions follow, considering possible policy responses to deforestation, and the social context of agricultural intensification, with special attention to the issues of land tenure security and distributional equity.

The effect of multiplicity of stellar encounters and the diffusion coefficients in a locally homogeneous three-dimensional stellar medium: Removing the classical divergence

NASA Astrophysics Data System (ADS)

Rastorguev, A. S.; Utkin, N. D.; Chumak, O. V.

2017-08-01

Agekyan's λ-factor that allows for the effect of multiplicity of stellar encounters with large impact parameters has been used for the first time to directly calculate the diffusion coefficients in the phase space of a stellar system. Simple estimates show that the cumulative effect, i.e., the total contribution of distant encounters to the change in the velocity of a test star, given the multiplicity of stellar encounters, is finite, and the logarithmic divergence inherent in the classical description of diffusion is removed, as was shown previously byKandrup using a different, more complex approach. In this case, the expressions for the diffusion coefficients, as in the classical description, contain the logarithm of the ratio of two independent quantities: the mean interparticle distance and the impact parameter of a close encounter. However, the physical meaning of this logarithmic factor changes radically: it reflects not the divergence but the presence of two characteristic length scales inherent in the stellar medium.

Mixed quantum-classical simulations of the vibrational relaxation of photolyzed carbon monoxide in a hemoprotein

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

Schubert, Alexander, E-mail: schubert@irsamc.ups-tlse.fr; Meier, Christoph; Falvo, Cyril

2016-08-07

We present mixed quantum-classical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the “surfaces” for the classical trajectories of protein and solvent atoms. In return, environmentally induced non-adiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking themore » molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.« less

On the dynamical and geometrical symmetries of Keplerian motion

NASA Astrophysics Data System (ADS)

Wulfman, Carl E.

2009-05-01

The dynamical symmetries of classical, relativistic and quantum-mechanical Kepler systems are considered to arise from geometric symmetries in PQET phase space. To establish their interconnection, the symmetries are related with the aid of a Lie-algebraic extension of Dirac's correspondence principle, a canonical transformation containing a Cunningham-Bateman inversion, and a classical limit involving a preliminary canonical transformation in ET space. The Lie-algebraic extension establishes the conditions under which the uncertainty principle allows the local dynamical symmetry of a quantum-mechanical system to be the same as the geometrical phase-space symmetry of its classical counterpart. The canonical transformation converts Poincaré-invariant free-particle systems into ISO(3,1) invariant relativistic systems whose classical limit produces Keplerian systems. Locally Cartesian relativistic PQET coordinates are converted into a set of eight conjugate position and momentum coordinates whose classical limit contains Fock projective momentum coordinates and the components of Runge-Lenz vectors. The coordinate systems developed via the transformations are those in which the evolution and degeneracy groups of the classical system are generated by Poisson-bracket operators that produce ordinary rotation, translation and hyperbolic motions in phase space. The way in which these define classical Keplerian symmetries and symmetry coordinates is detailed. It is shown that for each value of the energy of a Keplerian system, the Poisson-bracket operators determine two invariant functions of positions and momenta, which together with its regularized Hamiltonian, define the manifold in six-dimensional phase space upon which motions evolve.

Insights into structural and dynamical features of water at halloysite interfaces probed by DFT and classical molecular dynamics simulations.

PubMed

Presti, Davide; Pedone, Alfonso; Mancini, Giordano; Duce, Celia; Tiné, Maria Rosaria; Barone, Vincenzo

2016-01-21

Density functional theory calculations and classical molecular dynamics simulations have been used to investigate the structure and dynamics of water molecules on kaolinite surfaces and confined in the interlayer of a halloysite model of nanometric dimension. The first technique allowed us to accurately describe the structure of the tetrahedral-octahedral slab of kaolinite in vacuum and in interaction with water molecules and to assess the performance of two widely employed empirical force fields to model water/clay interfaces. Classical molecular dynamics simulations were used to study the hydrogen bond network structure and dynamics of water adsorbed on kaolinite surfaces and confined in the halloysite interlayer. The results are in nice agreement with the few experimental data available in the literature, showing a pronounced ordering and reduced mobility of water molecules at the hydrophilic octahedral surfaces of kaolinite and confined in the halloysite interlayer, with respect to water interacting with the hydrophobic tetrahedral surfaces and in the bulk. Finally, this investigation provides new atomistic insights into the structural and dynamical properties of water-clay interfaces, which are of fundamental importance for both natural processes and industrial applications.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

Resolving the biophysics of axon transmembrane polarization in a single closed-form description

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

Melendy, Robert F., E-mail: rfmelendy@liberty.edu

2015-12-28

When a depolarizing event occurs across a cell membrane there is a remarkable change in its electrical properties. A complete depolarization event produces a considerably rapid increase in voltage that propagates longitudinally along the axon and is accompanied by changes in axial conductance. A dynamically changing magnetic field is associated with the passage of the action potential down the axon. Over 75 years of research has gone into the quantification of this phenomenon. To date, no unified model exist that resolves transmembrane polarization in a closed-form description. Here, a simple but formative description of propagated signaling phenomena in the membranemore » of an axon is presented in closed-form. The focus is on using both biophysics and mathematical methods for elucidating the fundamental mechanisms governing transmembrane polarization. The results presented demonstrate how to resolve electromagnetic and thermodynamic factors that govern transmembrane potential. Computational results are supported by well-established quantitative descriptions of propagated signaling phenomena in the membrane of an axon. The findings demonstrate how intracellular conductance, the thermodynamics of magnetization, and current modulation function together in generating an action potential in a unified closed-form description. The work presented in this paper provides compelling evidence that three basic factors contribute to the propagated signaling in the membrane of an axon. It is anticipated this work will compel those in biophysics, physical biology, and in the computational neurosciences to probe deeper into the classical and quantum features of membrane magnetization and signaling. It is hoped that subsequent investigations of this sort will be advanced by the computational features of this model without having to resort to numerical methods of analysis.« less

Spontaneous cavitation in a Lennard-Jones liquid: Molecular dynamics simulation and the van der Waals-Cahn-Hilliard gradient theory

NASA Astrophysics Data System (ADS)

Baidakov, Vladimir G.

2016-02-01

The process of bubble nucleation in a Lennard-Jones (LJ) liquid is studied by molecular dynamics (MD) simulation. The bubble nucleation rate J is determined by the mean life-time method at temperatures above that of the triple point in the region of negative pressures. The results of simulation are compared with classical nucleation theory (CNT) and modified classical nucleation theory (MCNT), in which the work of formation of a critical bubble is determined in the framework of the van der Waals-Cahn-Hilliard gradient theory (GT). It has been found that the values of J obtained in MD simulation systematically exceed the data of CNT, and this excess in the nucleation rate reaches 8-10 orders of magnitude close to the triple point temperature. The results of MCNT are in satisfactory agreement with the data of MD simulation. To describe the properties of vapor-phase nuclei in the framework of GT, an equation of state has been built up which describes stable, metastable and labile regions of LJ fluids. The surface tension of critical bubbles γ has been found from CNT and data of MD simulation as a function of the radius of curvature of the surface of tension R*. The dependence γ(R*) has also been calculated from GT. The Tolman length has been determined, which is negative and in modulus equal to ≈(0.1 - 0.2) σ. The paper discusses the applicability of the Tolman formula to the description of the properties of critical nuclei in nucleation.

Mesoscopic Physics of Electronic and Optical Systems

NASA Astrophysics Data System (ADS)

Hentschel, Martina

2005-10-01

The progress in fabricating and controlling mesoscopic samples opens the possibility to investigate many-body phenomena on the nanoscopic scale, for example in quantum dots or nanoparticles. We recently studied the many-body signatures in the photoabsorption cross-section of those systems. Two counteracting many-body effects (Anderson's orthogonality catastrophe and Mahan's exciton) lead to deviations from the naively expected cross-section and to Fermi-edge singularities in the form of a peaked or rounded edge. We found that mesoscopic-coherent systems can show a many-body response that differs considerably from macroscopic samples. The reason for this lies in the finite number of particles and the lack of rotational symmetry in generic mesoscopic systems. The properties of mesoscopic systems crucially depend on whether the corresponding classical systems possess chaotic or integrable dynamics. Signatures of the underlying classical dynamics in quantum-mechanical behavior are searched for in the field of quantum chaos. We study it in the context of optical microresonators-billiards where reflection at hard walls is replaced by confinement due to total internal reflection. The relation between the simple ray model and the wave description (that has to be used when the wavelength becomes comparable to the system size) is called ``ray-wave correspondence.'' It can be established in both real and phase space. For the latter we generalized the concept of Husimi functions to dielectric boundaries. Although the ray model provides a qualitative understanding of the system properties even into the wave limit, semiclassical corrections of the ray picture are necessary in order to establish quantitative correspondence.

Medium fidelity modelling of loads in wind farms under non-neutral ABL stability conditions - a full-scale validation study

NASA Astrophysics Data System (ADS)

Larsen, G. C.; Larsen, T. J.; Chougule, A.

2017-05-01

The aim of the present paper is to demonstrate the capability of medium fidelity modelling of wind turbine component fatigue loading, when the wind turbines are subjected to wake affected non-stationary flow fields under non-neutral atmospheric stability conditions. To accomplish this we combine the classical Dynamic Wake Meandering model with a fundamental conjecture stating: Atmospheric boundary layer stability affects primary wake meandering dynamics driven by large turbulent scales, whereas wake expansion in the meandering frame of reference is hardly affected. Inclusion of stability (i.e. buoyancy) in description of both large- and small scale atmospheric boundary layer turbulence is facilitated by a generalization of the classical Mann spectral tensor, which consistently includes buoyancy effects. With non-stationary wind turbine inflow fields modelled as described above, fatigue loads are obtained using the state-of-the art aeroelastic model HAWC2. The Lillgrund offshore wind farm (WF) constitute an interesting case study for wind farm model validation, because the WT interspacing is small, which in turn means that wake effects are significant. A huge data set, comprising 5 years of blade and tower load recordings, is available for model validation. For a multitude of wake situations this data set displays a considerable scatter, which to a large degree seems to be caused by atmospheric boundary layer stability effects. Notable is also that rotating wind turbine components predominantly experience high fatigue loading for stable stratification with significant shear, whereas high fatigue loading of non-rotating wind turbine components are associated with unstable atmospheric boundary layer stratification.

Real-Time Quantum Dynamics of Long-Range Electronic Excitation Transfer in Plasmonic Nanoantennas.

PubMed

Ilawe, Niranjan V; Oviedo, M Belén; Wong, Bryan M

2017-08-08

Using large-scale, real-time, quantum dynamics calculations, we present a detailed analysis of electronic excitation transfer (EET) mechanisms in a multiparticle plasmonic nanoantenna system. Specifically, we utilize real-time, time-dependent, density functional tight binding (RT-TDDFTB) to provide a quantum-mechanical description (at an electronic/atomistic level of detail) for characterizing and analyzing these systems, without recourse to classical approximations. We also demonstrate highly long-range electronic couplings in these complex systems and find that the range of these couplings is more than twice the conventional cutoff limit considered by Förster resonance energy transfer (FRET)-based approaches. Furthermore, we attribute these unusually long-ranged electronic couplings to the coherent oscillations of conduction electrons in plasmonic nanoparticles. This long-range nature of plasmonic interactions has important ramifications for EET; in particular, we show that the commonly used "nearest-neighbor" FRET model is inadequate for accurately characterizing EET even in simple plasmonic antenna systems. These findings provide a real-time, quantum-mechanical perspective for understanding EET mechanisms and provide guidance in enhancing plasmonic properties in artificial light-harvesting systems.

A new dynamic 3D virtual methodology for teaching the mechanics of atrial septation as seen in the human heart.

PubMed

Schleich, Jean-Marc; Dillenseger, Jean-Louis; Houyel, Lucile; Almange, Claude; Anderson, Robert H

2009-01-01

Learning embryology remains difficult, since it requires understanding of many complex phenomena. The temporal evolution of developmental events has classically been illustrated using cartoons, which create difficulty in linking spatial and temporal aspects, such correlation being the keystone of descriptive embryology. We synthesized the bibliographic data from recent studies of atrial septal development. On the basis of this synthesis, consensus on the stages of atrial septation as seen in the human heart has been reached by a group of experts in cardiac embryology and pediatric cardiology. This has permitted the preparation of three-dimensional (3D) computer graphic objects for the anatomical components involved in the different stages of normal human atrial septation. We have provided a virtual guide to the process of normal atrial septation, the animation providing an appreciation of the temporal and morphologic events necessary to separate the systemic and pulmonary venous returns. We have shown that our animations of normal human atrial septation increase significantly the teaching of the complex developmental processes involved, and provide a new dynamic for the process of learning.

On the Comparison of the Long Penetration Mode (LPM) Supersonic Counterflowing Jet to the Supersonic Screech Jet

NASA Technical Reports Server (NTRS)

Farr, Rebecca A.; Chang, Chau-Lyan.; Jones, Jess H.; Dougherty, N. Sam

2015-01-01

The authors provide a brief overview of the classic tonal screech noise problem created by underexpanded supersonic jets, briefly describing the fluid dynamic-acoustics feedback mechanism that has been long established as the basis for this well-known aeroacoustics problem. This is followed by a description of the Long Penetration Mode (LPM) supersonic underexpanded counterflowing jet phenomenon which has been demonstrated in several wind tunnel tests and modeled in several computational fluid dynamics (CFD) simulations. The authors provide evidence from test and CFD analysis of LPM that indicates that acoustics feedback and fluid interaction seen in LPM are analogous to the aeroacoustics interactions seen in screech jets. Finally, the authors propose applying certain methodologies to LPM which have been developed and successfully demonstrated in the study of screech jets and mechanically induced excitation in fluid oscillators for decades. The authors conclude that the large body of work done on jet screech, other aeroacoustic phenomena, and fluid oscillators can have direct application to the study and applications of LPM counterflowing supersonic cold flow jets.

The Sagittarius tidal stream as a gravitationnal experiment in the Milky Way

NASA Astrophysics Data System (ADS)

Thomas, G. F.; Famaey, B.; Ibata, R.; Lüghausen, F.; Kroupa, P.

2015-12-01

Modified Newtonian Dynamics (MOND or Milgromian dynamics) gives a successful description of many galaxy properties that are hard to understand in the classical framework. The rotation curves of spiral galaxies are, for instance, perfectly reproduced and understood within this framework. Nevertheless, rotation curves only trace the potential in the galactic plane, and it is thus useful to test the shape of the potential outside the plane. Here we use the Sagittarius tidal stream as a gravitational experiment in the Milky Way, in order to check whether MOND can explain both its characteristics and those of the remnant dwarf spheroidal galaxy progenitor. We show that a MOND model of the Sagittarius stream can both perfectly reproduce the observed positions of stars in the stream, and even more strikingly, perfectly reproduce the observed properties of the remnant. Nevertheless, this first model does not reproduce well the observed radial velocities, which could be a signature of a rotating component in the progenitor or of the presence of a massive hot gaseous halo around the Milky Way.

Modeling the internal dynamics of energy and mass transfer in an imperfectly mixed ventilated airspace.

PubMed

Janssens, K; Van Brecht, A; Zerihun Desta, T; Boonen, C; Berckmans, D

2004-06-01

The present paper outlines a modeling approach, which has been developed to model the internal dynamics of heat and moisture transfer in an imperfectly mixed ventilated airspace. The modeling approach, which combines the classical heat and moisture balance differential equations with the use of experimental time-series data, provides a physically meaningful description of the process and is very useful for model-based control purposes. The paper illustrates how the modeling approach has been applied to a ventilated laboratory test room with internal heat and moisture production. The results are evaluated and some valuable suggestions for future research are forwarded. The modeling approach outlined in this study provides an ideal form for advanced model-based control system design. The relatively low number of parameters makes it well suited for model-based control purposes, as a limited number of identification experiments is sufficient to determine these parameters. The model concept provides information about the air quality and airflow pattern in an arbitrary building. By using this model as a simulation tool, the indoor air quality and airflow pattern can be optimized.

Particle merging algorithm for PIC codes

NASA Astrophysics Data System (ADS)

Vranic, M.; Grismayer, T.; Martins, J. L.; Fonseca, R. A.; Silva, L. O.

2015-06-01

Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in previous works, none of them seemed to be able to conserve fully charge, momentum, energy and their associated distributions. We describe here an alternative algorithm based on the coalescence of N massive or massless particles, considered to be close enough in phase space, into two new macro-particles. The local conservation of charge, momentum and energy are ensured by the resolution of a system of scalar equations. Various simulation comparisons have been carried out with and without the merging algorithm, from classical plasma physics problems to extreme scenarios where quantum electrodynamics is taken into account, showing in addition to the conservation of local quantities, the good reproducibility of the particle distributions. In case where the number of particles ought to increase exponentially in the simulation box, the dynamical merging permits a considerable speedup, and significant memory savings that otherwise would make the simulations impossible to perform.

A Markovian event-based framework for stochastic spiking neural networks.

PubMed

Touboul, Jonathan D; Faugeras, Olivier D

2011-11-01

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.

Quantum versus classical dynamics in the optical centrifuge

NASA Astrophysics Data System (ADS)

Armon, Tsafrir; Friedland, Lazar

2017-09-01

The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

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

Bialas, A.; Czyz, W.; Zalewski, K.

The relation between Renyi entropies and moments of the Wigner function, representing the quantum mechanical description of the M-particle semi-inclusive distribution at freeze-out, is investigated. It is shown that in the limit of infinite volume of the system, the classical and quantum descriptions are equivalent. Finite volume corrections are derived and shown to be small for systems encountered in relativistic heavy ion collisions.

Adam Smith's invisible hand is unstable: physics and dynamics reasoning applied to economic theorizing

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2002-11-01

Neo-classical economic theory is based on the postulated, nonempiric notion of utility. Neo-classical economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics, however, a utility function generally does not exist mathematically due to nonintegrability. Price as a function of demand does not exist and all equilibria are unstable. Qualitatively, and empirically, the neo-classical prediction of price as a function of demand describes neither consumer nor trader demand. We also discuss five inconsistent definitions of equilibrium used in economics and finance, only one of which is correct, and then explain the fallacy in the economists’ notion of ‘temporary price equilibria’.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

PubMed

Shpielberg, O; Akkermans, E

2016-06-17

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

NASA Astrophysics Data System (ADS)

Shpielberg, O.; Akkermans, E.

2016-06-01

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Do planetary seasons play a role in attaining stable climates?

NASA Astrophysics Data System (ADS)

Olsen, Kasper Wibeck; Bohr, Jakob

2018-05-01

A simple phenomenological account for planetary climate instabilities is presented. The description is based on the standard model where the balance of incoming stellar radiation and outward thermal radiation is described by the effective planet temperature. Often, it is found to have three different points, or temperatures, where the influx of radiation is balanced with the out-flux, even with conserved boundary conditions. Two of these points are relatively long-term stable, namely the point corresponding to a cold climate and the point corresponding to a hot climate. In a classical sense these points are equilibrium balance points. The hypothesis promoted in this paper is the possibility that the intermediate third point can become long-term stable by being driven dynamically. The initially unstable point is made relatively stable over a long period by the presence of seasonal climate variations.

cDF Theory Software for mesoscopic modeling of equilibrium and transport phenomena

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

2015-12-01

The approach is based on classical Density Functional Theory ((cDFT) coupled with the Poisson-Nernst-Planck (PNP) transport kinetics model and quantum mechanical description of short-range interaction and elementary transport processes. The model we proposed and implemented is fully atomistic, taking into account pairwise short-range and manybody long-range interactions. But in contrast to standard molecular dynamics (MD) simulations, where long-range manybody interactions are evaluated as a sum of pair-wise atom-atom contributions, we include them analytically based on wellestablished theories of electrostatic and excluded volume interactions in multicomponent systems. This feature of the PNP/cDFT approach allows us to reach well beyond the length-scalesmore » accessible to MD simulations, while retaining the essential physics of interatomic interactions from first principles and in a parameter-free fashion.« less

CRYSTAL GROWTH. Crystallization by particle attachment in synthetic, biogenic, and geologic environments.

PubMed

De Yoreo, James J; Gilbert, Pupa U P A; Sommerdijk, Nico A J M; Penn, R Lee; Whitelam, Stephen; Joester, Derk; Zhang, Hengzhong; Rimer, Jeffrey D; Navrotsky, Alexandra; Banfield, Jillian F; Wallace, Adam F; Michel, F Marc; Meldrum, Fiona C; Cölfen, Helmut; Dove, Patricia M

2015-07-31

Field and laboratory observations show that crystals commonly form by the addition and attachment of particles that range from multi-ion complexes to fully formed nanoparticles. The particles involved in these nonclassical pathways to crystallization are diverse, in contrast to classical models that consider only the addition of monomeric chemical species. We review progress toward understanding crystal growth by particle-attachment processes and show that multiple pathways result from the interplay of free-energy landscapes and reaction dynamics. Much remains unknown about the fundamental aspects, particularly the relationships between solution structure, interfacial forces, and particle motion. Developing a predictive description that connects molecular details to ensemble behavior will require revisiting long-standing interpretations of crystal formation in synthetic systems, biominerals, and patterns of mineralization in natural environments. Copyright © 2015, American Association for the Advancement of Science.

Low-energy dynamics of gravitation

NASA Astrophysics Data System (ADS)

Torma, Tibor

The present status of theories of quantum gravity are reviewed from the low energy point of view. String theory relates classical black-hole type solutions of Einstein- like equations (e.g. axidilaton gravity) to the string vacuum. Several such solutions are proposed and their properties are investigated, including their behavior under supersymmetry transformations. A general feature of all possible quantum theories of gravitation is that they lead to a field theory description at low (as compared to the Planck mass) energies. The theoretical consistency, uniqueness and consequences of such an effective theory are investigated. I show that a power counting theorem allows for the momentum expansion that defines the effective theory even in the presence of large masses. I also show that graviton-graviton scattering is free of potential infrared and collinear divergencies that plague perturbative discussions of Yang-Mills theories.

On the correspondence between quantum and classical variational principles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-06-10

Here, classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and Klein-Gordon particles.

Interference in the classical probabilistic model and its representation in complex Hilbert space

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei Yu.

2005-10-01

The notion of a context (complex of physical conditions, that is to say: specification of the measurement setup) is basic in this paper.We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present already in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and only then probability”. We construct the representation of the general contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function (in particular, Schrödinger's dynamics) can be considered as Hilbert space projections of a realistic dynamics in a “prespace”. The basic condition for representing of the prespace-dynamics is the law of statistical conservation of energy-conservation of probabilities. In general the Hilbert space projection of the “prespace” dynamics can be nonlinear and even irreversible (but it is always unitary). Methods developed in this paper can be applied not only to quantum mechanics, but also to classical statistical mechanics. The main quantum-like structures (e.g., interference of probabilities) might be found in some models of classical statistical mechanics. Quantum-like probabilistic behavior can be demonstrated by biological systems. In particular, it was recently found in some psychological experiments.

Single, Complete, Probability Spaces Consistent With EPR-Bohm-Bell Experimental Data

NASA Astrophysics Data System (ADS)

Avis, David; Fischer, Paul; Hilbert, Astrid; Khrennikov, Andrei

2009-03-01

We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities which only partially define a probability space. Ignoring this conditioning leads to apparent contradictions in the classical probabilistic model (due to Kolmogorov). We show how to make a completely consistent probabilistic model by taking into account the probabilities of selecting the settings of the PBSs. Our model matches both the experimental data and is consistent with classical probability theory.

Extended generalized geometry and a DBI-type effective action for branes ending on branes

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-08-01

Starting from the Nambu-Goto bosonic membrane action, we develop a geometric description suitable for p-brane backgrounds. With tools of generalized geometry we derive the pertinent generalization of the string open-closed relations to the p-brane case. Nambu-Poisson structures are used in this context to generalize the concept of semi-classical noncommutativity of D-branes governed by a Poisson tensor. We find a natural description of the correspondence of recently proposed commutative and noncommutative versions of an effective action for p-branes ending on a p '-brane. We calculate the power series expansion of the action in background independent gauge. Leading terms in the double scaling limit are given by a generalization of a (semi-classical) matrix model.

Mixed quantum/classical investigation of the photodissociation of NH3(Ã) and a practical method for maintaining zero-point energy in classical trajectories

NASA Astrophysics Data System (ADS)

Bonhommeau, David; Truhlar, Donald G.

2008-07-01

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode ν2 with n2=0,…,6 quanta of vibration) in the à electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTU /SD+trajectory projection onto ZPE orbit (TRAPZ) and FSTU /SD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH2 internal energy distributions obtained for n2=0 and n2>1, as observed in experiments. Distributions obtained for n2=1 present an intermediate behavior between distributions obtained for smaller and larger n2 values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH2 internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n2=0 and n2=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.

Mixed quantum/classical investigation of the photodissociation of NH3(A) and a practical method for maintaining zero-point energy in classical trajectories.

PubMed

Bonhommeau, David; Truhlar, Donald G

2008-07-07

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode nu(2) with n(2)=0,[ellipsis (horizontal)],6 quanta of vibration) in the A electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTUSD+trajectory projection onto ZPE orbit (TRAPZ) and FSTUSD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH(2) internal energy distributions obtained for n(2)=0 and n(2)>1, as observed in experiments. Distributions obtained for n(2)=1 present an intermediate behavior between distributions obtained for smaller and larger n(2) values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH(2) internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n(2)=0 and n(2)=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.

Quantum learning of classical stochastic processes: The completely positive realization problem

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

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

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.

Passive Membrane Permeability: Beyond the Standard Solubility-Diffusion Model.

PubMed

Parisio, Giulia; Stocchero, Matteo; Ferrarini, Alberta

2013-12-10

The spontaneous diffusion of solutes through lipid bilayers is still a challenge for theoretical predictions. Since permeation processes remain beyond the capabilities of unbiased molecular dynamics simulations, an alternative strategy is currently adopted to gain insight into their mechanism and time scale. This is based on a monodimensional description of the translocation process only in terms of the position of the solute along the normal to the lipid bilayer, which is formally expressed in the solubility-diffusion model. Actually, a role of orientational and conformational motions has been pointed out, and the use of advanced simulation techniques has been proposed to take into account their effect. Here, we discuss the limitations of the standard solubility-diffusion approach and propose a more general description of membrane translocation as a diffusion process on a free energy surface, which is a function of the translational and rotational degrees of freedom of the molecule. Simple expressions for the permeability coefficient are obtained under suitable conditions. For fast solute reorientation, the classical solubility-diffusion equation is recovered. Under the assumption that well-defined minima can be identified on the free energy landscape, a mechanistic interpretation of the permeability coefficient in terms of all possible permeation paths is given.

Theoretical ecology without species

NASA Astrophysics Data System (ADS)

Tikhonov, Mikhail

The sequencing-driven revolution in microbial ecology demonstrated that discrete ``species'' are an inadequate description of the vast majority of life on our planet. Developing a novel theoretical language that, unlike classical ecology, would not require postulating the existence of species, is a challenge of tremendous medical and environmental significance, and an exciting direction for theoretical physics. Here, it is proposed that community dynamics can be described in a naturally hierarchical way in terms of population fluctuation eigenmodes. The approach is applied to a simple model of division of labor in a multi-species community. In one regime, effective species with a core and accessory genome are shown to naturally appear as emergent concepts. However, the same model allows a transition into a regime where the species formalism becomes inadequate, but the eigenmode description remains well-defined. Treating a community as a black box that expresses enzymes in response to resources reveals mathematically exact parallels between a community and a single coherent organism with its own fitness function. This coherence is a generic consequence of division of labor, requires no cooperative interactions, and can be expected to be widespread in microbial ecosystems. Harvard Center of Mathematical Sciences and Applications;John A. Paulson School of Engineering and Applied Sciences.

Application of Dirac's Generalized Hamiltonian Dynamics to Atomic and Molecular Systems

NASA Astrophysics Data System (ADS)

Uzer, Turgay

2002-10-01

Incorporating electronic degrees of freedom into classical treatments of atoms and molecules is a challenging problem from both the practical and fundamental points of view. Because it goes to the heart of classical-quantal correspondence, there are now a number of prescriptions which differ by the extent of quantal information that they include. We reach back to Dirac for inspiration, who, half a century ago, designed a so-called Generalized Hamiltonian Dynamics (GHD) with applications to field theory in mind. Physically, the GHD is a purely classical formalism for systems with constraints; it incorporates the constraints into the Hamiltonian. We apply the GHD to atomic and molecular physics by choosing integrals of motion as the constraints. We show that this purely classical formalism allows the derivation of energies of non-radiating states.

Geometric descriptions of entangled states by auxiliary varieties

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

Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-15

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete themore » approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.« less

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

NASA Astrophysics Data System (ADS)

Notarnicola, Simone; Iemini, Fernando; Rossini, Davide; Fazio, Rosario; Silva, Alessandro; Russomanno, Angelo

2018-02-01

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N -coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N -dimensional Anderson model. The thermodynamic limit N →∞ , in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N ≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.

Shapes, spectra and new methods in nonlinear spatial optics

NASA Astrophysics Data System (ADS)

Sun, Can

For a myriad of optical applications, the quality of the light source is poor and the beam is inherently spatially partially-coherent. For this broad class of systems, wave dynamics depends not only on the wave intensity, but also on its distribution of spatial frequencies. Unfortunately, this entire spectrum of problems has often been overlooked - for reasons of theoretical ease or experimental difficulties. Here, we remedy this by demonstrating a novel experimental setup which, for the first time, allows arbitrarily modulation of the spatial spectra of light to obtain any distribution of interest. Using modulation instability as an example, we isolate the effect of different spectral shapes and observe distinct beam dynamics. Next, we turn to a thermodynamic description of the long-term evolution of statistical fields. For quantum systems, a major consequence is Bose-Einstein Condensation. However, recent theoretical studies have suggested that quantum mechanics is not necessary for the condensation process: classical waves with random phases can also self-organize into a coherent state. Starting from a random ensemble, nonlinear interactions can lead to a turbulent energy cascade towards longer spatial scales. In complete analogy with the kinetics of a gas system, there is a statistical dynamics of waves in which particle velocities map to wavepacket k-vectors while collisions are mimicked by four-wave mixing. As with collisions, each wave interaction is formally reversible, yet entropy principles mandate that the ensemble evolves towards an equilibrium state of maximum disorder. The result is an equipartition of energy, in the form of a Rayleigh-Jeans spectrum, with information about the condensation process recorded in small-scale fluctuations. Here, we give the first experimental observation of the condensation of classical waves in any media. Using classical light in a self-defocusing photorefractive, we observe all aspects of the condensation process, including the population of a coherent state, spectral redistribution towards the Rayleigh-Jeans spectrum, and formal reversibility of the interactions. The latter is proved experimentally by introducing a digital "Maxwell's Demon" to reverse (phase-conjugate) the momentum of each wavepacket and recover the original "thermal cloud". The results integrate digital and physical methods of nonlinear processing, confirm fundamental ideas in wave turbulence, and greatly extend the range of Bose-Einstein theory.

Insights from molecular dynamics simulations for computational protein design.

PubMed

Childers, Matthew Carter; Daggett, Valerie

2017-02-01

A grand challenge in the field of structural biology is to design and engineer proteins that exhibit targeted functions. Although much success on this front has been achieved, design success rates remain low, an ever-present reminder of our limited understanding of the relationship between amino acid sequences and the structures they adopt. In addition to experimental techniques and rational design strategies, computational methods have been employed to aid in the design and engineering of proteins. Molecular dynamics (MD) is one such method that simulates the motions of proteins according to classical dynamics. Here, we review how insights into protein dynamics derived from MD simulations have influenced the design of proteins. One of the greatest strengths of MD is its capacity to reveal information beyond what is available in the static structures deposited in the Protein Data Bank. In this regard simulations can be used to directly guide protein design by providing atomistic details of the dynamic molecular interactions contributing to protein stability and function. MD simulations can also be used as a virtual screening tool to rank, select, identify, and assess potential designs. MD is uniquely poised to inform protein design efforts where the application requires realistic models of protein dynamics and atomic level descriptions of the relationship between dynamics and function. Here, we review cases where MD simulations was used to modulate protein stability and protein function by providing information regarding the conformation(s), conformational transitions, interactions, and dynamics that govern stability and function. In addition, we discuss cases where conformations from protein folding/unfolding simulations have been exploited for protein design, yielding novel outcomes that could not be obtained from static structures.

Insights from molecular dynamics simulations for computational protein design

PubMed Central

Childers, Matthew Carter; Daggett, Valerie

2017-01-01

A grand challenge in the field of structural biology is to design and engineer proteins that exhibit targeted functions. Although much success on this front has been achieved, design success rates remain low, an ever-present reminder of our limited understanding of the relationship between amino acid sequences and the structures they adopt. In addition to experimental techniques and rational design strategies, computational methods have been employed to aid in the design and engineering of proteins. Molecular dynamics (MD) is one such method that simulates the motions of proteins according to classical dynamics. Here, we review how insights into protein dynamics derived from MD simulations have influenced the design of proteins. One of the greatest strengths of MD is its capacity to reveal information beyond what is available in the static structures deposited in the Protein Data Bank. In this regard simulations can be used to directly guide protein design by providing atomistic details of the dynamic molecular interactions contributing to protein stability and function. MD simulations can also be used as a virtual screening tool to rank, select, identify, and assess potential designs. MD is uniquely poised to inform protein design efforts where the application requires realistic models of protein dynamics and atomic level descriptions of the relationship between dynamics and function. Here, we review cases where MD simulations was used to modulate protein stability and protein function by providing information regarding the conformation(s), conformational transitions, interactions, and dynamics that govern stability and function. In addition, we discuss cases where conformations from protein folding/unfolding simulations have been exploited for protein design, yielding novel outcomes that could not be obtained from static structures. PMID:28239489

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

NASA Astrophysics Data System (ADS)

Ciaglia, Florio M.; Cosmo, Fabio Di; Felice, Domenico; Mancini, Stefano; Marmo, Giuseppe; Pérez-Pardo, Juan M.

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

Duality constructions from quantum state manifolds

NASA Astrophysics Data System (ADS)

Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.

2015-11-01

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

Stochastic analysis of surface roughness models in quantum wires

NASA Astrophysics Data System (ADS)

Nedjalkov, Mihail; Ellinghaus, Paul; Weinbub, Josef; Sadi, Toufik; Asenov, Asen; Dimov, Ivan; Selberherr, Siegfried

2018-07-01

We present a signed particle computational approach for the Wigner transport model and use it to analyze the electron state dynamics in quantum wires focusing on the effect of surface roughness. Usually surface roughness is considered as a scattering model, accounted for by the Fermi Golden Rule, which relies on approximations like statistical averaging and in the case of quantum wires incorporates quantum corrections based on the mode space approach. We provide a novel computational approach to enable physical analysis of these assumptions in terms of phase space and particles. Utilized is the signed particles model of Wigner evolution, which, besides providing a full quantum description of the electron dynamics, enables intuitive insights into the processes of tunneling, which govern the physical evolution. It is shown that the basic assumptions of the quantum-corrected scattering model correspond to the quantum behavior of the electron system. Of particular importance is the distribution of the density: Due to the quantum confinement, electrons are kept away from the walls, which is in contrast to the classical scattering model. Further quantum effects are retardation of the electron dynamics and quantum reflection. Far from equilibrium the assumption of homogeneous conditions along the wire breaks even in the case of ideal wire walls.

Mathematical modeling of the crack growth in linear elastic isotropic materials by conventional fracture mechanics approaches and by molecular dynamics method: crack propagation direction angle under mixed mode loading

NASA Astrophysics Data System (ADS)

Stepanova, Larisa; Bronnikov, Sergej

2018-03-01

The crack growth directional angles in the isotropic linear elastic plane with the central crack under mixed-mode loading conditions for the full range of the mixity parameter are found. Two fracture criteria of traditional linear fracture mechanics (maximum tangential stress and minimum strain energy density criteria) are used. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-scale Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains 400000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide diapason of temperatures (from 0.1 К to 800 К) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.

Determination of Solvent Effects on Keto-Enol Equilibria of 1,3-Dicarbonyl Compounds Using NMR: Revisiting a Classic Physical Chemistry Experiment

ERIC Educational Resources Information Center

Cook, A. Gilbert; Feltman, Paul M.

2007-01-01

The use of proton NMR to determine the equilibrium position of tautomeric 1,3-dicarbonyl compounds in various solvents has been a classic physical chemistry experiment. We are presenting an expansion of the excellent description of this experiment by Garland, Shoemaker, and Nibler. Often the assumption is made that the keto tautomer is always the…

Communication: Symmetrical quasi-classical analysis of linear optical spectroscopy

NASA Astrophysics Data System (ADS)

Provazza, Justin; Coker, David F.

2018-05-01

The symmetrical quasi-classical approach for propagation of a many degree of freedom density matrix is explored in the context of computing linear spectra. Calculations on a simple two state model for which exact results are available suggest that the approach gives a qualitative description of peak positions, relative amplitudes, and line broadening. Short time details in the computed dipole autocorrelation function result in exaggerated tails in the spectrum.

Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

NASA Astrophysics Data System (ADS)

Aubry, R.; Oñate, E.; Idelsohn, S. R.

2006-09-01

The method presented in Aubry et al. (Comput Struc 83:1459-1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505-526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.

Surface-hopping dynamics and decoherence with quantum equilibrium structure.

PubMed

Grunwald, Robbie; Kim, Hyojoon; Kapral, Raymond

2008-04-28

In open quantum systems, decoherence occurs through interaction of a quantum subsystem with its environment. The computation of expectation values requires a knowledge of the quantum dynamics of operators and sampling from initial states of the density matrix describing the subsystem and bath. We consider situations where the quantum evolution can be approximated by quantum-classical Liouville dynamics and examine the circumstances under which the evolution can be reduced to surface-hopping dynamics, where the evolution consists of trajectory segments exclusively evolving on single adiabatic surfaces, with probabilistic hops between these surfaces. The justification for the reduction depends on the validity of a Markovian approximation on a bath averaged memory kernel that accounts for quantum coherence in the system. We show that such a reduction is often possible when initial sampling is from either the quantum or classical bath initial distributions. If the average is taken only over the quantum dispersion that broadens the classical distribution, then such a reduction is not always possible.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Photosynthetic Energy Transfer at the Quantum/Classical Border.

PubMed

Keren, Nir; Paltiel, Yossi

2018-06-01

Quantum mechanics diverges from the classical description of our world when very small scales or very fast processes are involved. Unlike classical mechanics, quantum effects cannot be easily related to our everyday experience and are often counterintuitive to us. Nevertheless, the dimensions and time scales of the photosynthetic energy transfer processes puts them close to the quantum/classical border, bringing them into the range of measurable quantum effects. Here we review recent advances in the field and suggest that photosynthetic processes can take advantage of the sensitivity of quantum effects to the environmental 'noise' as means of tuning exciton energy transfer efficiency. If true, this design principle could be a base for 'nontrivial' coherent wave property nano-devices. Copyright © 2018 Elsevier Ltd. All rights reserved.

Computational Investigation of the Interplay of Substrate Positioning and Reactivity in Catechol O-Methyltransferase

PubMed Central

Patra, Niladri; Ioannidis, Efthymios I.

2016-01-01

Catechol O-methyltransferase (COMT) is a SAM- and Mg2+-dependent methyltransferase that regulates neurotransmitters through methylation. Simulations and experiments have identified divergent catecholamine substrate orientations in the COMT active site: molecular dynamics simulations have favored a monodentate coordination of catecholate substrates to the active site Mg2+, and crystal structures instead preserve bidentate coordination along with short (2.65 Å) methyl donor-acceptor distances. We carry out longer dynamics (up to 350 ns) to quantify interconversion between bidentate and monodentate binding poses. We provide a systematic determination of the relative free energy of the monodentate and bidentate structures in order to identify whether structural differences alter the nature of the methyl transfer mechanism and source of enzymatic rate enhancement. We demonstrate that the bidentate and monodentate binding modes are close in energy but separated by a 7 kcal/mol free energy barrier. Analysis of interactions in the two binding modes reveals that the driving force for monodentate catecholate orientations in classical molecular dynamics simulations is derived from stronger electrostatic stabilization afforded by alternate Mg2+ coordination with strongly charged active site carboxylates. Mixed semi-empirical-classical (SQM/MM) substrate C-O distances (2.7 Å) for the bidentate case are in excellent agreement with COMT X-ray crystal structures, as long as charge transfer between the substrates, Mg2+, and surrounding ligands is permitted. SQM/MM free energy barriers for methyl transfer from bidentate and monodentate catecholate configurations are comparable at around 21–22 kcal/mol, in good agreement with experiment (18–19 kcal/mol). Overall, the work suggests that both binding poses are viable for methyl transfer, and accurate descriptions of charge transfer and electrostatics are needed to provide balanced relative barriers when multiple binding poses are accessible, for example in other transferases. PMID:27564542

Analogy between electromagnetic potentials and wave-like dynamic variables with connections to quantum theory

NASA Astrophysics Data System (ADS)

Yang, Chen

2018-05-01

The transitions from classical theories to quantum theories have attracted many interests. This paper demonstrates the analogy between the electromagnetic potentials and wave-like dynamic variables with their connections to quantum theory for audiences at advanced undergraduate level and above. In the first part, the counterpart relations in the classical electrodynamics (e.g. gauge transform and Lorenz condition) and classical mechanics (e.g. Legendre transform and free particle condition) are presented. These relations lead to similar governing equations of the field variables and dynamic variables. The Lorenz gauge, scalar potential and vector potential manifest a one-to-one similarity to the action, Hamiltonian and momentum, respectively. In the second part, the connections between the classical pictures of electromagnetic field and particle to quantum picture are presented. By characterising the states of electromagnetic field and particle via their (corresponding) variables, their evolution pictures manifest the same algebraic structure (isomorphic). Subsequently, pictures of the electromagnetic field and particle are compared to the quantum picture and their interconnections are given. A brief summary of the obtained results are presented at the end of the paper.

Protonation-induced stereoisomerism in nicotine: Conformational studies using classical (AMBER) and ab initio (Car Parrinello) molecular dynamics

NASA Astrophysics Data System (ADS)

Hammond, Philip S.; Wu, Yudong; Harris, Rebecca; Minehardt, Todd J.; Car, Roberto; Schmitt, Jeffrey D.

2005-01-01

A variety of biologically active small molecules contain prochiral tertiary amines, which become chiral centers upon protonation. S-nicotine, the prototypical nicotinic acetylcholine receptor agonist, produces two diastereomers on protonation. Results, using both classical (AMBER) and ab initio (Car-Parrinello) molecular dynamical studies, illustrate the significant differences in conformational space explored by each diastereomer. As is expected, this phenomenon has an appreciable effect on nicotine's energy hypersurface and leads to differentiation in molecular shape and divergent sampling. Thus, protonation induced isomerism can produce dynamic effects that may influence the behavior of a molecule in its interaction with a target protein. We also examine differences in the conformational dynamics for each diastereomer as quantified by both molecular dynamics methods.

IR and SFG vibrational spectroscopy of the water bend in the bulk liquid and at the liquid-vapor interface, respectively.

PubMed

Ni, Yicun; Skinner, J L

2015-07-07

Vibrational spectroscopy of the water bending mode has been investigated experimentally to study the structure of water in condensed phases. In the present work, we calculate the theoretical infrared (IR) and sum-frequency generation (SFG) spectra of the HOH bend in liquid water and at the water liquid/vapor interface using a mixed quantum/classical approach. Classical molecular dynamics simulation is performed by using a recently developed water model that explicitly includes three-body interactions and yields a better description of the water surface. Ab-initio-based transition frequency, dipole, polarizability, and intermolecular coupling maps are developed for the spectral calculations. The calculated IR and SFG spectra show good agreement with the experimental measurements. In the theoretical imaginary part of the SFG susceptibility for the water liquid/vapor interface, we find two features: a negative band centered at 1615 cm(-1) and a positive band centered at 1670 cm(-1). We analyze this spectrum in terms of the contributions from molecules in different hydrogen-bond classes to the SFG spectral density and also compare to SFG results for the OH stretch. SFG of the water bending mode provides a complementary picture of the heterogeneous hydrogen-bond configurations at the water surface.

IR and SFG vibrational spectroscopy of the water bend in the bulk liquid and at the liquid-vapor interface, respectively

NASA Astrophysics Data System (ADS)

Ni, Yicun; Skinner, J. L.

2015-07-01

Vibrational spectroscopy of the water bending mode has been investigated experimentally to study the structure of water in condensed phases. In the present work, we calculate the theoretical infrared (IR) and sum-frequency generation (SFG) spectra of the HOH bend in liquid water and at the water liquid/vapor interface using a mixed quantum/classical approach. Classical molecular dynamics simulation is performed by using a recently developed water model that explicitly includes three-body interactions and yields a better description of the water surface. Ab-initio-based transition frequency, dipole, polarizability, and intermolecular coupling maps are developed for the spectral calculations. The calculated IR and SFG spectra show good agreement with the experimental measurements. In the theoretical imaginary part of the SFG susceptibility for the water liquid/vapor interface, we find two features: a negative band centered at 1615 cm-1 and a positive band centered at 1670 cm-1. We analyze this spectrum in terms of the contributions from molecules in different hydrogen-bond classes to the SFG spectral density and also compare to SFG results for the OH stretch. SFG of the water bending mode provides a complementary picture of the heterogeneous hydrogen-bond configurations at the water surface.

IR and SFG vibrational spectroscopy of the water bend in the bulk liquid and at the liquid-vapor interface, respectively

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

Ni, Yicun; Skinner, J. L.

Vibrational spectroscopy of the water bending mode has been investigated experimentally to study the structure of water in condensed phases. In the present work, we calculate the theoretical infrared (IR) and sum-frequency generation (SFG) spectra of the HOH bend in liquid water and at the water liquid/vapor interface using a mixed quantum/classical approach. Classical molecular dynamics simulation is performed by using a recently developed water model that explicitly includes three-body interactions and yields a better description of the water surface. Ab-initio-based transition frequency, dipole, polarizability, and intermolecular coupling maps are developed for the spectral calculations. The calculated IR and SFGmore » spectra show good agreement with the experimental measurements. In the theoretical imaginary part of the SFG susceptibility for the water liquid/vapor interface, we find two features: a negative band centered at 1615 cm{sup −1} and a positive band centered at 1670 cm{sup −1}. We analyze this spectrum in terms of the contributions from molecules in different hydrogen-bond classes to the SFG spectral density and also compare to SFG results for the OH stretch. SFG of the water bending mode provides a complementary picture of the heterogeneous hydrogen-bond configurations at the water surface.« less

Classical analogs for Rabi-oscillations, Ramsey-fringes, and spin-echo in Josephson junctions

NASA Astrophysics Data System (ADS)

Marchese, J. E.; Cirillo, M.; Grønbech-Jensen, N.

2007-08-01

We investigate the results of recently published experiments on the quantum behavior of Josephson circuits in terms of the classical modeling based on the resistively and capacitively-shunted (RCSJ) junction model. Our analysis shows evidence for a close analogy between the nonlinear behavior of a pulsed microwave-driven Josephson junction at low temperature and low dissipation and the experimental observations reported for the Josephson circuits. Specifically, we demonstrate that Rabi-oscillations, Ramsey-fringes, and spin-echo observations are not phenomena with a unique quantum interpretation. In fact, they are natural consequences of transients to phase-locking in classical nonlinear dynamics and can be observed in a purely classical model of a Josephson junction when the experimental recipe for the application of microwaves is followed and the experimental detection scheme followed. We therefore conclude that classical nonlinear dynamics can contribute to the understanding of relevant experimental observations of Josephson response to various microwave perturbations at very low temperature and low dissipation.

Smoothed quantum-classical states in time-irreversible hybrid dynamics

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2017-09-01

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.

Emerging Connections: Quantum & Classical Optics Incubator Program Book

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

Lesky, Marcia

The Emerging Connections: Quantum & Classical Optics Incubator was a scientific meeting held in Washington, DC on 6-8 November 2016. This Incubator provided unique and focused experiences and valuable opportunities to discuss advances, challenges and opportunities regarding this important area of research. Quantum optics and classical optics have coexisted for nearly a century as two distinct, but consistent descriptions of light in their respective domains. Recently, a number of detailed examinations of the structure of classical light beams have revealed that effects widely thought to be solely quantum in origin also have a place in classical optics. These new quantum-classicalmore » connections are informing classical optics in meaningful ways specifically by expanding understanding of optical coherence. Simultaneously, relationships discovered with classical light beams now also serve as a vehicle to illuminate concepts that no longer solely belong to the quantum realm. Interference, polarization, coherence, complementarity and entanglement are a partial list of elementary notions that now appear to belong to both quantum and classical optics. The goal of this meeting was to bring emerging quantum-classical links into wider view and to indicate directions in which forthcoming and future work would promote discussion and lead to a more unified understanding of optics.« less

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Experimental studies of tuned particle damper: Design and characterization

NASA Astrophysics Data System (ADS)

Zhang, Kai; Xi, Yanhui; Chen, Tianning; Ma, Zhihao

2018-01-01

To better suppress the structural vibration in the micro vibration and harsh environment, a new type of damper, tuned particle damper (TPD), was designed by combining the advantage of classical dynamic vibration absorber (DVA) and particle damper (PD). An equivalent theoretical model was established to describe the dynamic behavior of a cantilever system treated with TPD. By means of a series of sine sweep tests, the dynamic characteristic of TPD under different excitation intensity was explored and the damping performance of TPD was investigated by comparing with classical DVA and PD with the same mass ratio. Experimental results show that with the increasing of excitation intensity TPD shows two different dynamic characteristics successively, i.e., PD-like and DVA-like. TPD shows a wider suppression frequency band than classical DVA and better practicability than PD in the micro vibration environment. Moreover, to characterize the dynamic characteristic of TPD, a simple evaluation of the equivalent dynamic mass and equivalent dynamic damping of the cantilever system treated with TPD was performed by fitting the experimental data to the presented theoretical model. Finally, based on the rheology behaviors of damping particles reported by the previous research results, an approximate phase diagram which shows the motion states of damping particles in TPD was employed to analyze the dynamic characteristic of TPD and several motion states of damping particles in TPD were presented via a high-speed camera.

Quantum Model of a Charged Black Hole

NASA Astrophysics Data System (ADS)

Gladush, V. D.

A canonical approach for constructing of the classical and quantum description spherically-symmetric con guration gravitational and electromagnetic elds is considered. According to the sign of the square of the Kodama vector, space-time is divided into R-and T-regions. By virtue of the generalized Birkho theorem, one can choose coordinate systems such that the desired metric functions in the T-region depend on the time, and in the R-domain on the space coordinate. Then, the initial action for the con guration breaks up into terms describing the elds in the T- and R-regions with the time and space evolutionary variable, respectively. For these regions, Lagrangians of the con guration are constructed, which contain dynamic and non-dynamic degrees of freedom, leading to constrains. We concentrate our attention on dynamic T-regions. There are two additional conserved physical quantities: the charge and the total mass of the system. The Poisson bracket of the total mass with the Hamiltonian function vanishes in the weak sense. A classical solution of the eld equations in the con guration space (minisuperspace) is constructed without xing non-dynamic variable. In the framework of the canonical approach to the quantum mechanics of the system under consideration, physical states are found by solving the Hamiltonian constraint in the operator form (the DeWitt equation) for the system wave function Ψ. It also requires that Ψ is an eigenfunction of the operators of charge and total mass. For the symmetric of the mass operator the corresponding ordering of operators is carried out. Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψem with a defined total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the con guration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result.

Optimum Onager: The Classical Mechanics of a Classical Siege Engine

ERIC Educational Resources Information Center

Denny, Mark

2009-01-01

The onager is a throwing weapon of classical antiquity, familiar to both the ancient Greeks and Romans. Here we analyze the dynamics of onager operation and derive the optimum angle for launching a projectile to its maximum range. There is plenty of scope for further considerations about increasing onager range, and so by thinking about how this…

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Roughness as classicality indicator of a quantum state

NASA Astrophysics Data System (ADS)

Lemos, Humberto C. F.; Almeida, Alexandre C. L.; Amaral, Barbara; Oliveira, Adélcio C.

2018-03-01

We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L2 (R2) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [ 0 , 1 ], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness approaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.

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.

Quantum-classical correspondence in the vicinity of periodic orbits

NASA Astrophysics Data System (ADS)

Kumari, Meenu; Ghose, Shohini

2018-05-01

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

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.

Dynamic condensation of non-classically damped structures using the method of Maclaurin expansion of the frequency response function in Laplace domain

NASA Astrophysics Data System (ADS)

Esmaeilzad, Armin; Khanlari, Karen

2018-07-01

As the number of degrees of freedom (DOFs) in structural dynamic problems becomes larger, the analyzing complexity and CPU usage of computers increase drastically. Condensation (or reduction) method is an efficient technique to reduce the size of the full model or the dimension of the structural matrices by eliminating the unimportant DOFs. After the first presentation of condensation method by Guyan in 1965 for undamped structures, which ignores the dynamic effects of the mass term, various forms of dynamic condensation methods were presented to overcome this issue. Moreover, researchers have tried to expand the dynamic condensation method to non-classically damped structures. Dynamic reduction of such systems is far more complicated than undamped systems. The proposed non-iterative method in this paper is introduced as 'Maclaurin Expansion of the frequency response function in Laplace Domain' (MELD) applied for dynamic reduction of non-classically damped structures. The present approach is implemented in four numerical examples of 2D bending-shear-axial frames with various numbers of stories and spans and also a floating raft isolation system. The results of natural frequencies and dynamic responses of models are compared with each other before and after the dynamic reduction. It is shown that the result accuracy has acceptable convergence in both cases. In addition, it is indicated that the result of the proposed method is more accurate than the results of some other existing condensation methods.

Application of singular value decomposition to structural dynamics systems with constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Pinson, L. D.

1985-01-01

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Structural aspects of the solvation shell of lysine and acetylated lysine: A Car-Parrinello and classical molecular dynamics investigation

NASA Astrophysics Data System (ADS)

Carnevale, V.; Raugei, S.

2009-12-01

Lysine acetylation is a post-translational modification, which modulates the affinity of protein-protein and/or protein-DNA complexes. Its crucial role as a switch in signaling pathways highlights the relevance of charged chemical groups in determining the interactions between water and biomolecules. A great effort has been recently devoted to assess the reliability of classical molecular dynamics simulations in describing the solvation properties of charged moieties. In the spirit of these investigations, we performed classical and Car-Parrinello molecular dynamics simulations on lysine and acetylated-lysine in aqueous solution. A comparative analysis between the two computational schemes is presented with a focus on the first solvation shell of the charged groups. An accurate structural analysis unveils subtle, yet statistically significant, differences which are discussed in connection to the significant electronic density charge transfer occurring between the solute and the surrounding water molecules.

Reproducing Quantum Probability Distributions at the Speed of Classical Dynamics: A New Approach for Developing Force-Field Functors.

PubMed

Sundar, Vikram; Gelbwaser-Klimovsky, David; Aspuru-Guzik, Alán

2018-04-05

Modeling nuclear quantum effects is required for accurate molecular dynamics (MD) simulations of molecules. The community has paid special attention to water and other biomolecules that show hydrogen bonding. Standard methods of modeling nuclear quantum effects like Ring Polymer Molecular Dynamics (RPMD) are computationally costlier than running classical trajectories. A force-field functor (FFF) is an alternative method that computes an effective force field that replicates quantum properties of the original force field. In this work, we propose an efficient method of computing FFF using the Wigner-Kirkwood expansion. As a test case, we calculate a range of thermodynamic properties of Neon, obtaining the same level of accuracy as RPMD, but with the shorter runtime of classical simulations. By modifying existing MD programs, the proposed method could be used in the future to increase the efficiency and accuracy of MD simulations involving water and proteins.

An Experimental and Theoretical Study of Nitrogen-Broadened Acetylene Lines

NASA Technical Reports Server (NTRS)

Thibault, Franck; Martinez, Raul Z.; Bermejo, Dionisio; Ivanov, Sergey V.; Buzykin, Oleg G.; Ma, Qiancheng

2014-01-01

We present experimental nitrogen-broadening coefficients derived from Voigt profiles of isotropic Raman Q-lines measured in the 2 band of acetylene (C2H2) at 150 K and 298 K, and compare them to theoretical values obtained through calculations that were carried out specifically for this work. Namely, full classical calculations based on Gordon's approach, two kinds of semi-classical calculations based on Robert Bonamy method as well as full quantum dynamical calculations were performed. All the computations employed exactly the same ab initio potential energy surface for the C2H2N2 system which is, to our knowledge, the most realistic, accurate and up-to-date one. The resulting calculated collisional half-widths are in good agreement with the experimental ones only for the full classical and quantum dynamical methods. In addition, we have performed similar calculations for IR absorption lines and compared the results to bibliographic values. Results obtained with the full classical method are again in good agreement with the available room temperature experimental data. The quantum dynamical close-coupling calculations are too time consuming to provide a complete set of values and therefore have been performed only for the R(0) line of C2H2. The broadening coefficient obtained for this line at 173 K and 297 K also compares quite well with the available experimental data. The traditional Robert Bonamy semi-classical formalism, however, strongly overestimates the values of half-width for both Qand R-lines. The refined semi-classical Robert Bonamy method, first proposed for the calculations of pressure broadening coefficients of isotropic Raman lines, is also used for IR lines. By using this improved model that takes into account effects from line coupling, the calculated semi-classical widths are significantly reduced and closer to the measured ones.

Signatures of chaos in the Brillouin zone.

PubMed

Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

2017-10-01

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Reviving Complementarity: John Wheeler's efforts to apply complementarity toward a quantum description of gravitation

NASA Astrophysics Data System (ADS)

Halpern, Paul

2017-01-01

In 1978, John Wheeler proposed the delayed-choice thought experiment as a generalization of the classic double slit experiment intended to help elucidate the nature of decision making in quantum measurement. In particular, he wished to illustrate how a decision made after a quantum system was prepared might retrospectively affect the outcome. He extended his methods to the universe itself, raising the question of whether the universe is a ``self-excited circuit'' in which scientific measurements in the present affect the quantum dynamics in the past. In this talk we'll show how Wheeler's approach revived the notion of Bohr's complementarity, which had by then faded from the prevailing discourse of quantum measurement theory. Wheeler's advocacy reflected, in part, his wish to eliminate the divide in quantum theory between measurer and what was being measured, bringing greater consistency to the ideas of Bohr, a mentor whom he deeply respected.

Optical Peaking Enhancement in High-Speed Ring Modulators

PubMed Central

Müller, J.; Merget, F.; Azadeh, S. Sharif; Hauck, J.; García, S. Romero; Shen, B.; Witzens, J.

2014-01-01

Ring resonator modulators (RRM) combine extreme compactness, low power consumption and wavelength division multiplexing functionality, making them a frontrunner for addressing the scalability requirements of short distance optical links. To extend data rates beyond the classically assumed bandwidth capability, we derive and experimentally verify closed form equations of the electro-optic response and asymmetric side band generation resulting from inherent transient time dynamics and leverage these to significantly improve device performance. An equivalent circuit description with a commonly used peaking amplifier model allows straightforward assessment of the effect on existing communication system architectures. A small signal analytical expression of peaking in the electro-optic response of RRMs is derived and used to extend the electro-optic bandwidth of the device above 40 GHz as well as to open eye diagrams penalized by intersymbol interference at 32, 40 and 44 Gbps. Predicted peaking and asymmetric side band generation are in excellent agreement with experiments. PMID:25209255

Coordinate space translation technique for simulation of electronic process in the ion-atom collision.

PubMed

Wang, Feng; Hong, Xuhai; Wang, Jian; Kim, Kwang S

2011-04-21

Recently we developed a theoretical model of ion-atom collisions, which was made on the basis of a time-dependent density functional theory description of the electron dynamics and a classical treatment of the heavy particle motion. Taking advantage of the real-space grid method, we introduce a "coordinate space translation" technique to allow one to focus on a certain space of interest such as the region around the projectile or the target. Benchmark calculations are given for collisions between proton and oxygen over a wide range of impact energy. To extract the probability of charge transfer, the formulation of Lüdde and Dreizler [J. Phys. B 16, 3973 (1983)] has been generalized to ensemble-averaging application in the particular case of O((3)P). Charge transfer total cross sections are calculated, showing fairly good agreements between experimental data and present theoretical results.

Superconformal Algebraic Approach to Hadron Structure

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

de Teramond, Guy F.; Brodsky, Stanley J.; Deur, Alexandre

2017-03-01

Fundamental aspects of nonperturbative QCD dynamics which are not obvious from its classical Lagrangian, such as the emergence of a mass scale and confinement, the existence of a zero mass bound state, the appearance of universal Regge trajectories and the breaking of chiral symmetry are incorporated from the onset in an effective theory based on superconformal quantum mechanics and its embedding in a higher dimensional gravitational theory. In addition, superconformal quantum mechanics gives remarkable connections between the light meson and nucleon spectra. This new approach to hadron physics is also suitable to describe nonperturbative QCD observables based on structure functions,more » such as GPDs, which are not amenable to a first-principle computation. The formalism is also successful in the description of form factors, the nonperturbative behavior of the strong coupling and diffractive processes. We also discuss in this article how the framework can be extended rather successfully to the heavy-light hadron sector.« less

Skating on a Film of Air: Drops Impacting on a Surface

NASA Astrophysics Data System (ADS)

Kolinski, John M.; Rubinstein, Shmuel M.; Mandre, Shreyas; Brenner, Michael P.; Weitz, David A.; Mahadevan, L.

2012-02-01

The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.

Mass density fluctuations in quantum and classical descriptions of liquid water

NASA Astrophysics Data System (ADS)

Galib, Mirza; Duignan, Timothy T.; Misteli, Yannick; Baer, Marcel D.; Schenter, Gregory K.; Hutter, Jürg; Mundy, Christopher J.

2017-06-01

First principles molecular dynamics simulation protocol is established using revised functional of Perdew-Burke-Ernzerhof (revPBE) in conjunction with Grimme's third generation of dispersion (D3) correction to describe the properties of water at ambient conditions. This study also demonstrates the consistency of the structure of water across both isobaric (NpT) and isothermal (NVT) ensembles. Going beyond the standard structural benchmarks for liquid water, we compute properties that are connected to both local structure and mass density fluctuations that are related to concepts of solvation and hydrophobicity. We directly compare our revPBE results to the Becke-Lee-Yang-Parr (BLYP) plus Grimme dispersion corrections (D2) and both the empirical fixed charged model (SPC/E) and many body interaction potential model (MB-pol) to further our understanding of how the computed properties herein depend on the form of the interaction potential.

Mass density fluctuations in quantum and classical descriptions of liquid water

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

Galib, Mirza; Duignan, Timothy T.; Misteli, Yannick

First principles molecular dynamics simulation protocol is established using revised functional of Perdew-Burke-Ernzerhof (revPBE) in conjunction with Grimme's third generation of dispersion (D3) correction to describe properties of water at ambient conditions. This study also demonstrates the consistency of the structure of water across both isobaric (NpT) and isothermal (NVT) ensembles. Going beyond the standard structural benchmarks for liquid water, we compute properties that are connected to both local structure and mass density fluctuations that are related to concepts of solvation and hydrophobicity. We directly compare our revPBE results to the Becke-Lee-Yang-Parr (BLYP) plus Grimme dispersion corrections (D2) and bothmore » the empirical fixed charged model (SPC/E) and many body interaction potential model (MB-pol) to further our understanding of how the computed properties herein depend on the form of the interaction potential.« less

Computational study of the interplay between intermolecular interactions and CO2 orientations in type I hydrates.

PubMed

Pérez-Rodríguez, M; Vidal-Vidal, A; Míguez, J M; Blas, F J; Torré, J-P; Piñeiro, M M

2017-01-25

Carbon dioxide (CO 2 ) molecules show a rich orientation landscape when they are enclathrated in type I hydrates. Previous studies have described experimentally their preferential orientations, and some theoretical works have explained, but only partially, these experimental results. In the present paper, we use classical molecular dynamics and electronic density functional theory to advance in the theoretical description of CO 2 orientations within type I hydrates. Our results are fully compatible with those previously reported, both theoretical and experimental, the geometric shape of the cavities in hydrate being, and therefore, the steric constraints, responsible for some (but not all) preferential angles. In addition, our calculations also show that guest-guest interactions in neighbouring cages are a key factor to explain the remaining experimental angles. Besides the implication concerning equation of state hydrate modeling approximations, the conclusion is that these guest-guest interactions should not be neglected, contrary to the usual practice.

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

NASA Astrophysics Data System (ADS)

Farrés, Ariadna; Jorba, Àngel; Mondelo, Josep-Maria

2017-09-01

The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

Molecular-dynamics simulations of urea nucleation from aqueous solution

PubMed Central

Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico; Mazzotti, Marco; Parrinello, Michele

2015-01-01

Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete. PMID:25492932

Molecular-dynamics simulations of urea nucleation from aqueous solution.

PubMed

Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico; Mazzotti, Marco; Parrinello, Michele

2015-01-06

Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.

Perspective: Ring-polymer instanton theory

NASA Astrophysics Data System (ADS)

Richardson, Jeremy O.

2018-05-01

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

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

Harstad, E. N.; Harlow, Francis Harvey,; Schreyer, H. L.

Our goal is to develop constitutive relations for the behavior of a solid polymer during high-strain-rate deformations. In contrast to the classic thermodynamic techniques for deriving stress-strain response in static (equilibrium) circumstances, we employ a statistical-mechanics approach, in which we evolve a probability distribution function (PDF) for the velocity fluctuations of the repeating units of the chain. We use a Langevin description for the dynamics of a single repeating unit and a Lioville equation to describe the variations of the PDF. Moments of the PDF give the conservation equations for a single polymer chain embedded in other similar chains. Tomore » extract single-chain analytical constitutive relations these equations have been solved for representative loading paths. By this process we discover that a measure of nonuniform chain link displacement serves this purpose very well. We then derive an evolution equation for the descriptor function, with the result being a history-dependent constitutive relation.« less

Shearing single crystal magnesium in the close-packed basal plane at different temperatures

NASA Astrophysics Data System (ADS)

Han, Ming; Li, Lili; Zhao, Guangming

2018-05-01

Shear behaviors of single crystal magnesium (Mg) in close-packed (0001) basal plane along the [ 1 bar 2 1 bar 0 ], [ 1 2 bar 10 ], [ 10 1 bar 0 ] and [ 1 bar 010 ] directions were studied using molecular dynamics simulations via EAM potential. The results show that both shear stress-strain curves along the four directions and the motion path of free atoms during shearing behave periodic characteristics. It reveals that the periodic shear displacement is inherently related to the crystallographic orientation in single crystal Mg. Moreover, different temperatures in a range from 10 to 750 K were considered, demonstrating that shear modulus decreases with increasing temperatures. The results agree well with the MTS model. It is manifested that the modulus is independent with the shear direction and the size of the atomic model. This work also demonstrates that the classical description of shear modulus is still effective at the nanoscale.

Some comments on the nature and use of the concept of psyche in psychoanalysis and psychodynamic psychotherapy.

PubMed

Brookes, Crittenden E

2004-01-01

The term psyche is central to the field of mental health and dysfunction. And yet the term is seldom talked about directly, and is seldom elaborated by the professionals who function under its rubric. This article elaborates this term, and sets forth a definition for the purposes of psychology and psychodynamics as science in the sense of the establishment of psychological knowledge. Psyche is defined in this article as a hypothetical construct, as outlined in the classic article in the theory of psychological science by MacCorquodale and Meehl (1948). Psyche is to be distinguished from the concept of mind, which is identified here as a strictly phenomenological (subjective) concept. Use of psyche in this way allows it to be utilized in descriptions of its dynamics (psychodynamics), as a central concept in a science which utilizes phenomenological (subjective rather than objective) data.

Experimental Evidence of Radiation Reaction in the Collision of a High-Intensity Laser Pulse with a Laser-Wakefield Accelerated Electron Beam

NASA Astrophysics Data System (ADS)

Cole, J. M.; Behm, K. T.; Gerstmayr, E.; Blackburn, T. G.; Wood, J. C.; Baird, C. D.; Duff, M. J.; Harvey, C.; Ilderton, A.; Joglekar, A. S.; Krushelnick, K.; Kuschel, S.; Marklund, M.; McKenna, P.; Murphy, C. D.; Poder, K.; Ridgers, C. P.; Samarin, G. M.; Sarri, G.; Symes, D. R.; Thomas, A. G. R.; Warwick, J.; Zepf, M.; Najmudin, Z.; Mangles, S. P. D.

2018-02-01

The dynamics of energetic particles in strong electromagnetic fields can be heavily influenced by the energy loss arising from the emission of radiation during acceleration, known as radiation reaction. When interacting with a high-energy electron beam, today's lasers are sufficiently intense to explore the transition between the classical and quantum radiation reaction regimes. We present evidence of radiation reaction in the collision of an ultrarelativistic electron beam generated by laser-wakefield acceleration (ɛ >500 MeV ) with an intense laser pulse (a0>10 ). We measure an energy loss in the postcollision electron spectrum that is correlated with the detected signal of hard photons (γ rays), consistent with a quantum description of radiation reaction. The generated γ rays have the highest energies yet reported from an all-optical inverse Compton scattering scheme, with critical energy ɛcrit>30 MeV .

A revised version of the transfer matrix method to analyze one-dimensional structures

NASA Technical Reports Server (NTRS)

Nitzsche, F.

1983-01-01

A new and general method to analyze both free and forced vibration characteristics of one-dimensional structures is discussed in this paper. This scheme links for the first time the classical transfer matrix method with the recently developed integrating matrix technique to integrate systems of differential equations. Two alternative approaches to the problem are presented. The first is based upon the lumped parameter model to account for the inertia properties of the structure. The second releases that constraint allowing a more precise description of the physical system. The free vibration of a straight uniform beam under different support conditions is analyzed to test the accuracy of the two models. Finally some results for the free vibration of a 12th order system representing a curved, rotating beam prove that the present method is conveniently extended to more complicated structural dynamics problems.

The physical vulnerability of elements at risk: a methodology based on fluid and classical mechanics

NASA Astrophysics Data System (ADS)

Mazzorana, B.; Fuchs, S.; Levaggi, L.

2012-04-01

The impacts of the flood events occurred in autumn 2011 in the Italian regions Liguria and Tuscany revived the engagement of the public decision makers to enhance in synergy flood control and land use planning. In this context, the design of efficient flood risk mitigation strategies and their subsequent implementation critically relies on a careful vulnerability analysis of both, the immobile and mobile elements at risk potentially exposed to flood hazards. Based on fluid and classical mechanics notions we developed computation schemes enabling for a dynamic vulnerability and risk analysis facing a broad typological variety of elements at risk. The methodological skeleton consists of (1) hydrodynamic computation of the time-varying flood intensities resulting for each element at risk in a succession of loading configurations; (2) modelling the mechanical response of the impacted elements through static, elasto-static and dynamic analyses; (3) characterising the mechanical response through proper structural damage variables and (4) economic valuation of the expected losses as a function of the quantified damage variables. From a computational perspective we coupled the description of the hydrodynamic flow behaviour and the induced structural modifications of the elements at risk exposed. Valuation methods, suitable to support a correct mapping from the value domains of the physical damage variables to the economic loss values are discussed. In such a way we target to complement from a methodological perspective the existing, mainly empirical, vulnerability and risk assessment approaches to refine the conceptual framework of the cost-benefit analysis. Moreover, we aim to support the design of effective flood risk mitigation strategies by diminishing the main criticalities within the systems prone to flood risk.

On the use of Lagrangian variables in descriptions of unsteady boundary-layer separation

NASA Technical Reports Server (NTRS)

Cowley, Stephen J.; Vandommelen, Leon L.; Lam, Shui T.

1990-01-01

The Lagrangian description of unsteady boundary layer separation is reviewed from both analytical and numerical perspectives. It is explained in simple terms how particle distortion gives rise to unsteady separation, and why a theory centered on Lagrangian coordinates provides the clearest description of this phenomenon. Some of the more recent results for unsteady three dimensional compressible separation are included. The different forms of separation that can arise from symmetries are emphasized. A possible description of separation is also included when the detaching vorticity layer exits the classical boundary layer region, but still remains much closer to the surface than a typical body-lengthscale.

Dynamical stability of the one-dimensional rigid Brownian rotator: the role of the rotator’s spatial size and shape

NASA Astrophysics Data System (ADS)

Jeknić-Dugić, Jasmina; Petrović, Igor; Arsenijević, Momir; Dugić, Miroljub

2018-05-01

We investigate dynamical stability of a single propeller-like shaped molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic situations, rotation of the finite-size cogwheel is subject to the environmentally-induced Brownian-motion effect that we describe by utilizing the quantum Caldeira-Leggett master equation. Assuming the initially narrow (classical-like) standard deviations for the angle and the angular momentum of the rotator, we investigate the dynamics of the first and second moments depending on the size, i.e. on the number of blades of both the free rotator as well as of the rotator in the external harmonic field. The larger the standard deviations, the less stable (i.e. less predictable) rotation. We detect the absence of the simple and straightforward rules for utilizing the rotator’s stability. Instead, a number of the size-related criteria appear whose combinations may provide the optimal rules for the rotator dynamical stability and possibly control. In the realistic situations, the quantum-mechanical corrections, albeit individually small, may effectively prove non-negligible, and also revealing subtlety of the transition from the quantum to the classical dynamics of the rotator. As to the latter, we detect a strong size-dependence of the transition to the classical dynamics beyond the quantum decoherence process.

Electron-phonon interaction within classical molecular dynamics

DOE PAGES

Tamm, A.; Samolyuk, G.; Correa, A. A.; ...

2016-07-14

Here, we present a model for nonadiabatic classical molecular dynamics simulations that captures with high accuracy the wave-vector q dependence of the phonon lifetimes, in agreement with quantum mechanics calculations. It is based on a local view of the e-ph interaction where individual atom dynamics couples to electrons via a damping term that is obtained as the low-velocity limit of the stopping power of a moving ion in a host. The model is parameter free, as its components are derived from ab initio-type calculations, is readily extended to the case of alloys, and is adequate for large-scale molecular dynamics computermore » simulations. We also show how this model removes some oversimplifications of the traditional ionic damped dynamics commonly used to describe situations beyond the Born-Oppenheimer approximation.« less

A shape dynamical approach to holographic renormalization

NASA Astrophysics Data System (ADS)

Gomes, Henrique; Gryb, Sean; Koslowski, Tim; Mercati, Flavio; Smolin, Lee

2015-01-01

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities.

Study of geometric phase using classical coupled oscillators

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sharba; Dey, Biprateep; Mohapatra, Ashok K.

2018-05-01

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

Dynamic multipopulation and density dependent evolutionary games related to replicator dynamics. A metasimplex concept.

PubMed

Argasinski, Krzysztof

2006-07-01

This paper contains the basic extensions of classical evolutionary games (multipopulation and density dependent models). It is shown that classical bimatrix approach is inconsistent with other approaches because it does not depend on proportion between populations. The main conclusion is that interspecific proportion parameter is important and must be considered in multipopulation models. The paper provides a synthesis of both extensions (a metasimplex concept) which solves the problem intrinsic in the bimatrix model. It allows us to model interactions among any number of subpopulations including density dependence effects. We prove that all modern approaches to evolutionary games are closely related. All evolutionary models (except classical bimatrix approaches) can be reduced to a single population general model by a simple change of variables. Differences between classic bimatrix evolutionary games and a new model which is dependent on interspecific proportion are shown by examples.

Structure of water clusters on graphene: A classical molecular dynamics approach

NASA Astrophysics Data System (ADS)

Maekawa, Yuki; Sasaoka, Kenji; Yamamoto, Takahiro

2018-03-01

The microscopic structure of surface water adsorbed on graphene is elucidated theoretically by classical molecular dynamics simulation. At a low temperature (100 K), the main polygon consisting of hydrogen bonds in single-layered water on graphene is tetragonal, whereas the dominant polygons in double-layered water are tetragonal, pentagonal, and hexagonal. On the other hand, at room temperature, the tetragonal, pentagonal, and hexagonal water clusters are the main structures in both single- and double-layered water.

Chaos in the classical mechanics of bound and quasi-bound HX-4He complexes with X = F, Cl, Br, CN.

PubMed

Gamboa, Antonio; Hernández, Henar; Ramilowski, Jordan A; Losada, J C; Benito, R M; Borondo, F; Farrelly, David

2009-10-01

The classical dynamics of weakly bound floppy van der Waals complexes have been extensively studied in the past except for the weakest of all, i.e., those involving He atoms. These complexes are of considerable current interest in light of recent experimental work focussed on the study of molecules trapped in small droplets of the quantum solvent (4)He. Despite a number of quantum investigations, details on the dynamics of how quantum solvation occurs remain unclear. In this paper, the classical rotational dynamics of a series of van der Waals complexes, HX-(4)He with X = F, Cl, Br, CN, are studied. In all cases, the ground state dynamics are found to be almost entirely chaotic, in sharp contrast to other floppy complexes, such as HCl-Ar, for which chaos sets in only at relatively high energies. The consequences of this result for quantum solvation are discussed. We also investigate rotationally excited states with J = 1 which, except for HCN-(4)He, are actually resonances that decay by rotational pre-dissociation.

Zero-Point Energy Constraint for Unimolecular Dissociation Reactions. Giving Trajectories Multiple Chances To Dissociate Correctly.

PubMed

Paul, Amit K; Hase, William L

2016-01-28

A zero-point energy (ZPE) constraint model is proposed for classical trajectory simulations of unimolecular decomposition and applied to CH4* → H + CH3 decomposition. With this model trajectories are not allowed to dissociate unless they have ZPE in the CH3 product. If not, they are returned to the CH4* region of phase space and, if necessary, given additional opportunities to dissociate with ZPE. The lifetime for dissociation of an individual trajectory is the time it takes to dissociate with ZPE in CH3, including multiple possible returns to CH4*. With this ZPE constraint the dissociation of CH4* is exponential in time as expected for intrinsic RRKM dynamics and the resulting rate constant is in good agreement with the harmonic quantum value of RRKM theory. In contrast, a model that discards trajectories without ZPE in the reaction products gives a CH4* → H + CH3 rate constant that agrees with the classical and not quantum RRKM value. The rate constant for the purely classical simulation indicates that anharmonicity may be important and the rate constant from the ZPE constrained classical trajectory simulation may not represent the complete anharmonicity of the RRKM quantum dynamics. The ZPE constraint model proposed here is compared with previous models for restricting ZPE flow in intramolecular dynamics, and connecting product and reactant/product quantum energy levels in chemical dynamics simulations.

Evolutionary dynamics of a smoothed war of attrition game.

PubMed

Iyer, Swami; Killingback, Timothy

2016-05-07

In evolutionary game theory the War of Attrition game is intended to model animal contests which are decided by non-aggressive behavior, such as the length of time that a participant will persist in the contest. The classical War of Attrition game assumes that no errors are made in the implementation of an animal׳s strategy. However, it is inevitable in reality that such errors must sometimes occur. Here we introduce an extension of the classical War of Attrition game which includes the effect of errors in the implementation of an individual׳s strategy. This extension of the classical game has the important feature that the payoff is continuous, and as a consequence admits evolutionary behavior that is fundamentally different from that possible in the original game. We study the evolutionary dynamics of this new game in well-mixed populations both analytically using adaptive dynamics and through individual-based simulations, and show that there are a variety of possible outcomes, including simple monomorphic or dimorphic configurations which are evolutionarily stable and cannot occur in the classical War of Attrition game. In addition, we study the evolutionary dynamics of this extended game in a variety of spatially and socially structured populations, as represented by different complex network topologies, and show that similar outcomes can also occur in these situations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Simple model dielectric functions for insulators

NASA Astrophysics Data System (ADS)

Vos, Maarten; Grande, Pedro L.

2017-05-01

The Drude dielectric function is a simple way of describing the dielectric function of free electron materials, which have an uniform electron density, in a classical way. The Mermin dielectric function describes a free electron gas, but is based on quantum physics. More complex metals have varying electron densities and are often described by a sum of Drude dielectric functions, the weight of each function being taken proportional to the volume with the corresponding density. Here we describe a slight variation on the Drude dielectric functions that describes insulators in a semi-classical way and a form of the Levine-Louie dielectric function including a relaxation time that does the same within the framework of quantum physics. In the optical limit the semi-classical description of an insulator and the quantum physics description coincide, in the same way as the Drude and Mermin dielectric function coincide in the optical limit for metals. There is a simple relation between the coefficients used in the classical and quantum approaches, a relation that ensures that the obtained dielectric function corresponds to the right static refractive index. For water we give a comparison of the model dielectric function at non-zero momentum with inelastic X-ray measurements, both at relative small momenta and in the Compton limit. The Levine-Louie dielectric function including a relaxation time describes the spectra at small momentum quite well, but in the Compton limit there are significant deviations.

Observers' measurements in premetric electrodynamics: Time and radar length

NASA Astrophysics Data System (ADS)

Gürlebeck, Norman; Pfeifer, Christian

2018-04-01

The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of the spacetime, like the classical Michelson-Morley, Ives-Stilwell, Kennedy-Thorndike experiments or frequency comparison experiments in general, it is necessary to describe them in theories, which go beyond the Lorentzian metric structure. However, this requires a description of an observer's measurement without relying on a metric. We provide such a description of an observer's measurement of the fundamental quantities time and length derived from a premetric perturbation of Maxwell's electrodynamics and a discussion on how these measurements influence classical relativistic observables like time dilation and length contraction. Most importantly, we find that the modification of electrodynamics influences the measurements at two instances: the propagation of light is altered as well as the observer's proper time normalization. When interpreting the results of a specific experiment, both effects cannot be disentangled, in general, and have to be taken into account.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

PubMed Central

Ye, Hao; Beamish, Richard J.; Glaser, Sarah M.; Grant, Sue C. H.; Hsieh, Chih-hao; Richards, Laura J.; Schnute, Jon T.; Sugihara, George

2015-01-01

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874

Classical Wigner method with an effective quantum force: application to reaction rates.

PubMed

Poulsen, Jens Aage; Li, Huaqing; Nyman, Gunnar

2009-07-14

We construct an effective "quantum force" to be used in the classical molecular dynamics part of the classical Wigner method when determining correlation functions. The quantum force is obtained by estimating the most important short time separation of the Feynman paths that enter into the expression for the correlation function. The evaluation of the force is then as easy as classical potential energy evaluations. The ideas are tested on three reaction rate problems. The resulting transmission coefficients are in much better agreement with accurate results than transmission coefficients from the ordinary classical Wigner method.

Moments of the Wigner function and Renyi entropies at freeze-out

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.; Zalewski, K.

2006-03-01

The relation between Renyi entropies and moments of the Wigner function, representing the quantum mechanical description of the M-particle semi-inclusive distribution at freeze-out, is investigated. It is shown that in the limit of infinite volume of the system, the classical and quantum descriptions are equivalent. Finite volume corrections are derived and shown to be small for systems encountered in relativistic heavy ion collisions.

Insight into the Li2CO3-K2CO3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics

NASA Astrophysics Data System (ADS)

Corradini, Dario; Coudert, François-Xavier; Vuilleumier, Rodolphe

2016-03-01

We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li2CO3-K2CO3 (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, we present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture's self-diffusion coefficients, viscosity, and ionic conductivity.

Insight into the Li2CO3-K2CO3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics.

PubMed

Corradini, Dario; Coudert, François-Xavier; Vuilleumier, Rodolphe

2016-03-14

We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li2CO3-K2CO3 (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, we present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture's self-diffusion coefficients, viscosity, and ionic conductivity.

Focus on PNA Flexibility and RNA Binding using Molecular Dynamics and Metadynamics

NASA Astrophysics Data System (ADS)

Verona, Massimiliano Donato; Verdolino, Vincenzo; Palazzesi, Ferruccio; Corradini, Roberto

2017-02-01

Peptide Nucleic Acids (PNAs) can efficiently target DNA or RNA acting as chemical tools for gene regulation. Their backbone modification and functionalization is often used to increase the affinity for a particular sequence improving selectivity. The understanding of the trading forces that lead the single strand PNA to bind the DNA or RNA sequence is preparatory for any further rational design, but a clear and unique description of this process is still not complete. In this paper we report further insights into this subject, by a computational investigation aiming at the characterization of the conformations of a single strand PNA and how these can be correlated to its capability in binding DNA/RNA. Employing Metadynamics we were able to better define conformational pre-organizations of the single strand PNA and γ-modified PNA otherwise unrevealed through classical molecular dynamics. Our simulations driven on backbone modified PNAs lead to the conclusion that this γ-functionalization affects the single strand preorganization and targeting properties to the DNA/RNA, in agreement with circular dichroism (CD) spectra obtained for this class of compounds. MD simulations on PNA:RNA dissociation and association mechanisms allowed to reveal the critical role of central bases and preorganization in the binding process.

A new dynamic 3D virtual methodology for teaching the mechanics of atrial septation as seen in the human heart

PubMed Central

Schleich, Jean-Marc; Dillenseger, Jean-Louis; Houyel, Lucile; Almange, Claude; Anderson, Robert H.

2009-01-01

Background Learning embryology remains difficult, since it requires understanding of many complex phenomena. The temporal evolution of developmental events has classically been illustrated using cartoons, which create difficulty in linking spatial and temporal aspects, such correlation being the keystone of descriptive embryology. Methods We synthesized the bibliographic data from recent studies of atrial septal development. On the basis of this synthesis, consensus on the stages of atrial septation as seen in the human heart has been reached by a group of experts in cardiac embryology and paediatric cardiology. This has permitted the preparation of three-dimensional (3-D) computer graphic objects for the anatomical components involved in the different stages of normal human atrial septation. Results We have provided a virtual guide to the process of normal atrial septation, the animation providing an appreciation of the temporal and morphologic events necessary to separate the systemic and pulmonary venous returns. Conclusion We have shown that our animations of normal human atrial septation increase significantly the teaching of the complex developmental processes involved, and provide a new dynamic for the process of learning. PMID:19363807

Continuum description of solvent dielectrics in molecular-dynamics simulations of proteins

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2003-02-01

We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method.

The Mass Function of Cosmic Structures

NASA Astrophysics Data System (ADS)

Audit, E.; Teyssier, R.; Alimi, J.-M.

We investigate some modifications to the Press and Schechter (1974) (PS) prescription resulting from shear and tidal effects. These modifications rely on more realistic treatments of the collapse process than the standard approach based on the spherical model. First, we show that the mass function resulting from a new approximate Lagrangian dynamic (Audit and Alimi, A&A 1996), contains more objects at high mass, than the classical PS mass function and is well fitted by a PS-like function with a threshold density of deltac ≍ 1.4. However, such a Lagrangian description can underestimate the epoch of structure formation since it defines it as the collapse of the first principal axis. We therefore suggest some analytical prescriptions, for computing the collapse time along the second and third principal axes, and we deduce the corresponding mass functions. The collapse along the third axis is delayed by the shear and the number of objects of high mass then decreases. Finally, we show that the shear also strongly affects the formation of low-mass halos. This dynamical effect implies a modification of the low-mass slope of the mass function and allows the reproduction of the observed luminosity function of field galaxies.

Focus on PNA Flexibility and RNA Binding using Molecular Dynamics and Metadynamics.

PubMed

Verona, Massimiliano Donato; Verdolino, Vincenzo; Palazzesi, Ferruccio; Corradini, Roberto

2017-02-17

Peptide Nucleic Acids (PNAs) can efficiently target DNA or RNA acting as chemical tools for gene regulation. Their backbone modification and functionalization is often used to increase the affinity for a particular sequence improving selectivity. The understanding of the trading forces that lead the single strand PNA to bind the DNA or RNA sequence is preparatory for any further rational design, but a clear and unique description of this process is still not complete. In this paper we report further insights into this subject, by a computational investigation aiming at the characterization of the conformations of a single strand PNA and how these can be correlated to its capability in binding DNA/RNA. Employing Metadynamics we were able to better define conformational pre-organizations of the single strand PNA and γ-modified PNA otherwise unrevealed through classical molecular dynamics. Our simulations driven on backbone modified PNAs lead to the conclusion that this γ-functionalization affects the single strand preorganization and targeting properties to the DNA/RNA, in agreement with circular dichroism (CD) spectra obtained for this class of compounds. MD simulations on PNA:RNA dissociation and association mechanisms allowed to reveal the critical role of central bases and preorganization in the binding process.

On the local relaxation of solid neon upon Rydberg excitation of a NO impurity: the role of the NO(A)-Ne interaction potential and zero-point quantum delocalization.

PubMed

Pajón-Suárez, Pedro; Rojas-Lorenzo, Germán A; Rubayo-Soneira, Jesús; Hernández-Lamoneda, Ramón; Larrégaray, Pascal

2009-12-31

The local relaxation of solid neon subsequent to the impulsive excitation of the NO chromophore to its A(3s sigma) Ryberg state is investigated using molecular dynamics simulations. This study makes use of empirical NO(X,A)-Ne isotropic pair potentials as well as a recently developed ab initio triatomic potential energy surface for the excited state. The role of these interaction potentials is analyzed, including many-body effects. In particular, empirical potentials, designed to reproduce correctly both the NO X-A steady-state absorption and emission bands, are shown to lead to a good description of the subpicosecond relaxation dynamics. The 600 fs expansion of the electronic bubble fairly agrees with experimental data. This relatively long time scale with respect to solid Argon, which was previously attributed to the range of the NO(A)-Ne interaction, is presumably related to the quantum nature of the medium. The time-resolved local relaxation of the Ne solid is understandably intermediate between that of classical solids (e.g., Ar) and that of quantum solids (e.g., H(2)).

Impact of compressibility on heat transport characteristics of large terrestrial planets

NASA Astrophysics Data System (ADS)

Čížková, Hana; van den Berg, Arie; Jacobs, Michel

2017-07-01

We present heat transport characteristics for mantle convection in large terrestrial exoplanets (M ⩽ 8M⊕) . Our thermal convection model is based on a truncated anelastic liquid approximation (TALA) for compressible fluids and takes into account a selfconsistent thermodynamic description of material properties derived from mineral physics based on a multi-Einstein vibrational approach. We compare heat transport characteristics in compressible models with those obtained with incompressible models based on the classical- and extended Boussinesq approximation (BA and EBA respectively). Our scaling analysis shows that heat flux scales with effective dissipation number as Nu ∼Dieff-0.71 and with Rayleigh number as Nu ∼Raeff0.27. The surface heat flux of the BA models strongly overestimates the values from the corresponding compressible models, whereas the EBA models systematically underestimate the heat flux by ∼10%-15% with respect to a corresponding compressible case. Compressible models are also systematically warmer than the EBA models. Compressibility effects are therefore important for mantle dynamic processes, especially for large rocky exoplanets and consequently also for formation of planetary atmospheres, through outgassing, and the existence of a magnetic field, through thermal coupling of mantle and core dynamic systems.

On the Reduction of Molecular Degrees of Freedom in Computer Simulations

NASA Astrophysics Data System (ADS)

Lyubartsev, Alexander P.; Laaksonen, Aatto

Molecular simulations, based on atomistic force fields are a standard theoretical tool in materials, polymers and biosciences. While various methods, with quantum chemistry incorporated, have been developed for condensed phase simulations during the last decade, there is another line of development with the purpose to bridge the time and length scales based on coarse-graining. This is expected to lead to some very interesting breakthroughs in the near future. In this lecture we will first give some background to common atomistic force fields. After that, we review a few common simple techniques for reducing the number of motional degrees of freedom to speed up the simulations. Finally, we present a powerful method for reducing uninteresting degrees of freedom. This is done by solving the Inverse Problem to obtain the interaction potentials. More precisely, we make use of the radial distribution functions, and by using the method of Inverse Monte Carlo [Lyubartsev & Laaksonen, Phys. Rev. E. 52, 3730 (1995)], we can construct effective potentials which are consistent with the original RDFs. This makes it possible to simulate much larger system than would have been possible by using atomistic force fields. We present many examples: How to simulate aqueous electrolyte solutions without any water molecules but still having the hydration structure around the ions - at the speed of a primitive electrolyte model calculation. We demonstrate how a coarse-grained model can be constructed for a double-helix DNA and how it can be used. It is accurate enough to reproduce the experimental results for ion condensation around DNA for several different counterions. We also show how we can construct site-site potentials for large-scale atomistic classical simulations of arbitrary liquids from smaller scale ab initio simulations. This methodology allows us to start from a simulation with the electrons and atomic nuclei, to construct a set of atomistic effective interaction potentials, and to use them in classical simulations. As a next step we can construct a new set of potentials beyond the atomistic description and carry out mesoscopic simulations, for example by using Dissipative Particle Dynamics. In this way we can tie together three different levels of description. The Dissipative Particle Dynamics method appears as a very promising tool to use with our coarse-grained potentials.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

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

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.

PubMed

Marsalek, Ondrej; Markland, Thomas E

2016-02-07

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.; ...

2017-10-18

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

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.

Floating-point performance of ARM cores and their efficiency in classical molecular dynamics

NASA Astrophysics Data System (ADS)

Nikolskiy, V.; Stegailov, V.

2016-02-01

Supercomputing of the exascale era is going to be inevitably limited by power efficiency. Nowadays different possible variants of CPU architectures are considered. Recently the development of ARM processors has come to the point when their floating point performance can be seriously considered for a range of scientific applications. In this work we present the analysis of the floating point performance of the latest ARM cores and their efficiency for the algorithms of classical molecular dynamics.

One-electron propagation in Fermi, Pasta, Ulam disordered chains with Gaussian acoustic pulse pumping

NASA Astrophysics Data System (ADS)

Silva, L. D. Da; Dos Santos, J. L. L.; Ranciaro Neto, A.; Sales, M. O.; de Moura, F. A. B. F.

In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron-phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron-lattice interaction promote a sub-diffusive electronic dynamics.

Beyond Classical Information Theory: Advancing the Fundamentals for Improved Geophysical Prediction

NASA Astrophysics Data System (ADS)

Perdigão, R. A. P.; Pires, C. L.; Hall, J.; Bloeschl, G.

2016-12-01

Information Theory, in its original and quantum forms, has gradually made its way into various fields of science and engineering. From the very basic concepts of Information Entropy and Mutual Information to Transit Information, Interaction Information and respective partitioning into statistical synergy, redundancy and exclusivity, the overall theoretical foundations have matured as early as the mid XX century. In the Earth Sciences various interesting applications have been devised over the last few decades, such as the design of complex process networks of descriptive and/or inferential nature, wherein earth system processes are "nodes" and statistical relationships between them designed as information-theoretical "interactions". However, most applications still take the very early concepts along with their many caveats, especially in heavily non-Normal, non-linear and structurally changing scenarios. In order to overcome the traditional limitations of information theory and tackle elusive Earth System phenomena, we introduce a new suite of information dynamic methodologies towards a more physically consistent and information comprehensive framework. The methodological developments are then illustrated on a set of practical examples from geophysical fluid dynamics, where high-order nonlinear relationships elusive to the current non-linear information measures are aptly captured. In doing so, these advances increase the predictability of critical events such as the emergence of hyper-chaotic regimes in ocean-atmospheric dynamics and the occurrence of hydro-meteorological extremes.

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2014-12-01

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

Elementary test for nonclassicality based on measurements of position and momentum

NASA Astrophysics Data System (ADS)

Fresta, Luca; Borregaard, Johannes; Sørensen, Anders S.

2015-12-01

We generalize a nonclassicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2012), 10.1103/PhysRevLett.108.233601], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving a contradiction with the classical description in terms of a probability distribution in phase space. As opposed to the previous work, we generalize the test to include states without rotational symmetry in phase space. Furthermore, we compare the performance of the nonclassicality test with classical tomography methods based on the inverse Radon transform, which can also be used to establish the quantum nature of a physical system. In particular, we consider a nonclassicality test based on the so-called filtered back-projection formula. We show that the general nonclassicality test is conceptually simpler, requires less assumptions on the system, and is statistically more reliable than the tests based on the filtered back-projection formula. As a specific example, we derive the optimal test for quadrature squeezed single-photon states and show that the efficiency of the test does not change with the degree of squeezing.

Note: A simple picture of subdiffusive polymer motion from stochastic simulations

NASA Astrophysics Data System (ADS)

Gniewek, Pawel; Kolinski, Andrzej

2011-02-01

Entangled polymer solutions and melts exhibit unusual frictional properties. In the entanglement limit self-diffusion coefficient of long flexible polymers decays with the second power of chain length and viscosity increases with 3-3.5 power of chain length.1 It is very difficult to provide detailed molecular-level explanation of the entanglement effect.2 Perhaps, the problem of many entangled polymer chains is the most complex multibody issue of classical physics. There are different approaches to polymer melt dynamics. Some of these recognize hydrodynamic interactions as a dominant term, while topological constraints for polymer chains are assumed as a secondary factor. Other theories consider the topological constraints as the most important factors controlling polymer dynamics. Herman and co-workers describe polymer dynamics in melts, as a lateral sliding of a chain along other chains until complete mutual disentanglement. Despite the success in explaining the power-laws for viscosity, the model has some limitations. First of all, memory effects are ignored, that is, polymer segments are treated independently. Also, each entanglement/obstacle is treated as a separate entity, which is certainly a simplification of the memory effect problem. In addition to that, correlated motions of segments are addressed within the framework of renormalized Rouse-chain theory,7 without calling any topological entanglements in advance. This approach leads to the generalized Langevin equation characterized by distinct memory kernels describing local and nonlocal segment correlations or to the Smoluchowski equation in which the segments' mobility is treated as a stochastic variable.11 Both models describe the polymer segments motion at a microscopic level. An interesting alternative is to solve the integrodifferential equation for the chain relaxation with a sophisticated kernel function.12 The design of the kernel function is based on a mesoscopic description of the polymer melt. These theories explain some experimental data, although the description of the crossover between the Rouse and non-Rouse behavior is not satisfactory. Obviously, within the scope of a short note we cannot review all theoretical concepts of the polymer melt dynamics. Here we focus just on the interpretation of the observed single segment autocorrelation function.

Chromatin fibers: from classical descriptions to modern interpretation.

PubMed

Kuznetsova, Maria A; Sheval, Eugene V

2016-11-01

The first description of intrachromosomal fibers was made by Baranetzky in 1880. Since that time, a plethora of fibrillar substructures have been described inside the mitotic chromosomes, and published data indicate that chromosomes may be formed as a result of the hierarchical folding of chromatin fibers. In this review, we examine the evolution and the current state of research on the morphological organization of mitotic chromosomes. © 2016 International Federation for Cell Biology.

Max Schottelius: Pioneer in Pheochromocytoma

PubMed Central

Tischler, Arthur S.; Schmid, Kurt W.; Leijon, Helena; Eng, Charis; Neumann, Hartmut P. H.

2017-01-01

First descriptions of diseases attract tremendous interest because they reveal scientific insight even in retrospect. Max Schottelius, the pathologist contributing the first histological description of pheochromocytoma, remains anonymous. We reviewed the description by Schottelius and weighed the report in modern context. Schottelius described the classical diagnostic elements of pheochromocytoma, including the brown appearance after exposure to chromate-containing Mueller’s fixative. This color change, known as chromaffin reaction, results from oxidation of catecholamines and is reflected in the name pheochromocytoma, meaning dusky-colored chromate-positive tumor. Thus Schottelius performed the first known histochemical contribution to diagnosis, which is today standard with immunohistochemistry for chromogranin. PMID:29264546

Building Rate Into a Dynamic Theory of Linguistic Description.

ERIC Educational Resources Information Center

Bailey, Charles-James N.

1970-01-01

This study of linguistic change is done within the "dynamic paradigm" of linguistic description, in which the strict dichotomy between diachronic and synchronic linguistics found in "static paradigms" is not maintained. The chief purpose here is to indicate how rate could be built into a linguistic description of sound change, such change being…

Entanglement as a signature of quantum chaos.

PubMed

Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi

2004-01-01

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Ab Initio Classical Dynamics Simulations of CO_2 Line-Mixing Effects in Infrared Bands

NASA Astrophysics Data System (ADS)

Lamouroux, Julien; Hartmann, Jean-Michel; Tran, Ha; Snels, Marcel; Stefani, Stefania; Piccioni, Giuseppe

2013-06-01

Ab initio calculations of line-mixing effects in CO_2 infrared bands are presented and compared with experiments. The predictions were carried using requantized Classical Dynamics Molecular Simulations (rCDMS) based on an approach previously developed and successfully tested for CO_2 isolated line shapes. Using classical dynamics equations, the force and torque applied to each molecule by the surrounding molecules (described by an ab initio intermolecular potential) are computed at each time step. This enables, using a requantization procedure, to predict dipole and isotropic polarizability auto-correlation functions whose Fourier-Laplace transforms yield the spectra. The quality of the rCDMS calculations is demonstrated by comparisons with measured spectra in the spectral regions of the 3ν_3 and 2ν_1+2ν_2+ν_3 Infrared bands. J.-M. Hartmann, H. Tran, N. H. Ngo, et al., Phys. Rev. Lett. A {87} (2013), 013403. H. Tran, C. Boulet, M. Snels, S. Stefani, J. Quant. Spectrosc. Radiat. Transfer {112} (2011), 925-936.

Classical continuum theory limits to determine the size-dependency of mechanical properties of GaN NWs

NASA Astrophysics Data System (ADS)

Zamani Kouhpanji, Mohammad Reza; Behzadirad, Mahmoud; Busani, Tito

2017-12-01

We used the stable strain gradient theory including acceleration gradients to investigate the classical and nonclassical mechanical properties of gallium nitride (GaN) nanowires (NWs). We predicted the static length scales, Young's modulus, and shear modulus of the GaN NWs from the experimental data. Combining these results with atomic simulations, we also found the dynamic length scale of the GaN NWs. Young's modulus, shear modulus, static, and dynamic length scales were found to be 318 GPa, 131 GPa, 8 nm, and 8.9 nm, respectively, usable for demonstrating the static and dynamic behaviors of GaN NWs having diameters from a few nm to bulk dimensions. Furthermore, the experimental data were analyzed with classical continuum theory (CCT) and compared with the available literature to illustrate the size-dependency of the mechanical properties of GaN NWs. This practice resolves the previous published discrepancies that happened due to the limitations of CCT used for determining the mechanical properties of GaN NWs and their size-dependency.

Density-functional theory simulation of large quantum dots

NASA Astrophysics Data System (ADS)

Jiang, Hong; Baranger, Harold U.; Yang, Weitao

2003-10-01

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

Classical Molecular Dynamics with Mobile Protons.

PubMed

Lazaridis, Themis; Hummer, Gerhard

2017-11-27

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

Mathematical model of the SH-3G helicopter

NASA Technical Reports Server (NTRS)

Phillips, J. D.

1982-01-01

A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

Identifying a Superfluid Reynolds Number via Dynamical Similarity.

PubMed

Reeves, M T; Billam, T P; Anderson, B P; Bradley, A S

2015-04-17

The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, Re(s), that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at Re(s)≈0.7, irrespective of obstacle width.

The science of space-time

NASA Astrophysics Data System (ADS)

Raine, D. J.; Heller, M.

Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics; Copernican kinematics; Newtonian dynamics; the space-time of classical dynamics; classical space-time in the presence of gravity; the space-time of special relativity; the space-time of general relativity; solutions and problems in general relativity; Mach's principle and the dynamics of space-time; theories of inertial mass; the integral formation of general relativity; and the frontiers of relativity (e.g., unified field theories and quantum gravity).

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

Accurate frequency domain measurement of the best linear time-invariant approximation of linear time-periodic systems including the quantification of the time-periodic distortions

NASA Astrophysics Data System (ADS)

Louarroudi, E.; Pintelon, R.; Lataire, J.

2014-10-01

Time-periodic (TP) phenomena occurring, for instance, in wind turbines, helicopters, anisotropic shaft-bearing systems, and cardiovascular/respiratory systems, are often not addressed when classical frequency response function (FRF) measurements are performed. As the traditional FRF concept is based on the linear time-invariant (LTI) system theory, it is only approximately valid for systems with varying dynamics. Accordingly, the quantification of any deviation from this ideal LTI framework is more than welcome. The “measure of deviation” allows us to define the notion of the best LTI (BLTI) approximation, which yields the best - in mean square sense - LTI description of a linear time-periodic LTP system. By taking into consideration the TP effects, it is shown in this paper that the variability of the BLTI measurement can be reduced significantly compared with that of classical FRF estimators. From a single experiment, the proposed identification methods can handle (non-)linear time-periodic [(N)LTP] systems in open-loop with a quantification of (i) the noise and/or the NL distortions, (ii) the TP distortions and (iii) the transient (leakage) errors. Besides, a geometrical interpretation of the BLTI approximation is provided, leading to a framework called vector FRF analysis. The theory presented is supported by numerical simulations as well as real measurements mimicking the well-known mechanical Mathieu oscillator.

Electron capture and excitation processes in H+-H collisions in dense quantum plasmas

NASA Astrophysics Data System (ADS)

Jakimovski, D.; Markovska, N.; Janev, R. K.

2016-10-01

Electron capture and excitation processes in proton-hydrogen atom collisions taking place in dense quantum plasmas are studied by employing the two-centre atomic orbital close-coupling (TC-AOCC) method. The Debye-Hückel cosine (DHC) potential is used to describe the plasma screening effects on the Coulomb interaction between charged particles. The properties of a hydrogen atom with DHC potential are investigated as a function of the screening strength of the potential. It is found that the decrease in binding energy of nl levels with increasing screening strength is considerably faster than in the case of the Debye-Hückel (DH) screening potential, appropriate for description of charged particle interactions in weakly coupled classical plasmas. This results in a reduction in the number of bound states in the DHC potential with respect to that in the DH potential for the same plasma screening strength, and is reflected in the dynamics of excitation and electron capture processes for the two screened potentials. The TC-AOCC cross sections for total and state-selective electron capture and excitation cross sections with the DHC potential are calculated for a number of representative screening strengths in the 1-300 keV energy range and compared with those for the DH and pure Coulomb potential. The total capture cross sections for a selected number of screening strengths are compared with the available results from classical trajectory Monte Carlo calculations.

Effects of tunnelling and asymmetry for system-bath models of electron transfer

NASA Astrophysics Data System (ADS)

Mattiat, Johann; Richardson, Jeremy O.

2018-03-01

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

'Swapna' in the Indian classics: Mythology or science?

PubMed

Tendulkar, Sonali S; Dwivedi, R R

2010-04-01

There are many concepts in Ayurveda as well as the ancient sciences that are untouched or unexplored. One such concept is that of the Swapna (dreams). Being an abstract phenomenon it makes it difficult to be explained and understood; probably because of this the descriptions related to Swapna in the Indian classics are supported by mythology, to make them acceptable. Variations in these explanations are seen according to the objective of the school of thought; that is, in the ancient texts where dreams are used to delve into the knowledge of the Atman and are related to spirituality, its description in the Ayurvedic texts evolves around the Sharira and Manas. Although all these explanations seem to be shrouded in uncertainty and mythology; there definitely seems to be a logical and rational science behind these quotations. They only need research, investigation, and explanation on the basis of logic, and a laboratory.

‘Swapna’ in the Indian classics: Mythology or science?

PubMed Central

Tendulkar, Sonali S.; Dwivedi, R. R.

2010-01-01

There are many concepts in Ayurveda as well as the ancient sciences that are untouched or unexplored. One such concept is that of the Swapna (dreams). Being an abstract phenomenon it makes it difficult to be explained and understood; probably because of this the descriptions related to Swapna in the Indian classics are supported by mythology, to make them acceptable. Variations in these explanations are seen according to the objective of the school of thought; that is, in the ancient texts where dreams are used to delve into the knowledge of the Atman and are related to spirituality, its description in the Ayurvedic texts evolves around the Sharira and Manas. Although all these explanations seem to be shrouded in uncertainty and mythology; there definitely seems to be a logical and rational science behind these quotations. They only need research, investigation, and explanation on the basis of logic, and a laboratory. PMID:22131706

Water clusters adsorbed on polycyclic aromatic hydrocarbons: Energetics and conformational dynamics

NASA Astrophysics Data System (ADS)

Simon, Aude; Spiegelman, Fernand

2013-05-01

In this work, we present some classical molecular dynamics (MD) simulations and finite temperature infrared (IR) spectra of water clusters adsorbed on coronene (C24H12), a compact polycyclic aromatic hydrocarbon (PAH). The potential energy surface is obtained within the self-consistent-charge density-functional based tight-binding approach with modifications insuring the correct description of water-water and water-PAH interactions. This scheme is benchmarked for the minimal energy structures of (C24H12)(H2O)n (n = 3-10) against density-functional theory (DFT) calculations and for the low-energy isomers of (H2O)6 and (C6H6)(H2O)3 against correlated wavefunction and DFT calculations. A detailed study of the low energy isomers of (C24H12)(H2O)3, 6 complexes is then provided. On-the-fly Born-Oppenheimer MD simulations are performed in the temperature T range 10-350 K for (C24H12)(H2O)n (n = 3-7) complexes. The description of the evolution of the systems with T is provided with emphasis on (C24H12)(H2O)n (n = 3,6). For T in the range 50-150 K, isomerisation processes are observed and when T increases, a solid-to-liquid phase-change like behavior is shown. The desorption of one water molecule is frequently observed at 300 K. The isomerisation processes are evidenced on the finite temperature IR spectra and the results are presented for (C24H12)(H2O)n (n = 3,6). A signature for the edge-coordination of the water cluster on the PAH is also proposed.

Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

NASA Astrophysics Data System (ADS)

Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min

1990-12-01

Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

Approximate Quantum Dynamics using Ab Initio Classical Separable Potentials: Spectroscopic Applications.

PubMed

Hirshberg, Barak; Sagiv, Lior; Gerber, R Benny

2017-03-14

Algorithms for quantum molecular dynamics simulations that directly use ab initio methods have many potential applications. In this article, the ab initio classical separable potentials (AICSP) method is proposed as the basis for approximate algorithms of this type. The AICSP method assumes separability of the total time-dependent wave function of the nuclei and employs mean-field potentials that govern the dynamics of each degree of freedom. In the proposed approach, the mean-field potentials are determined by classical ab initio molecular dynamics simulations. The nuclear wave function can thus be propagated in time using the effective potentials generated "on the fly". As a test of the method for realistic systems, calculations of the stationary anharmonic frequencies of hydrogen stretching modes were carried out for several polyatomic systems, including three amino acids and the guanine-cytosine pair of nucleobases. Good agreement with experiments was found. The method scales very favorably with the number of vibrational modes and should be applicable for very large molecules, e.g., peptides. The method should also be applicable for properties such as vibrational line widths and line shapes. Work in these directions is underway.

Quench dynamics of a dissipative Rydberg gas in the classical and quantum regimes

NASA Astrophysics Data System (ADS)

Gribben, Dominic; Lesanovsky, Igor; Gutiérrez, Ricardo

2018-01-01

Understanding the nonequilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time postquench quantum dynamics. In classical many-body systems, the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first-order phase transition. Here, we show that a similar approach can be applied for shedding light on the quench dynamics of an interacting gas of Rydberg atoms, which has become an important experimental platform for the investigation of quantum nonequilibrium effects. We are able to gain an analytical understanding of the time evolution following a sudden quench from an initial state devoid of Rydberg atoms and identify strikingly different behaviors of the excitation growth in the classical and quantum regimes. Our approach allows us to describe quenches near a nonequilibrium phase transition and provides an approximate analytical solution deep in the quantum domain.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

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

Marsalek, Ondrej; Markland, Thomas E., E-mail: tmarkland@stanford.edu

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding asmore » a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.« less

Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

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

Albert, Julian; Kaiser, Dustin; Engel, Volker

2016-05-07

Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion ismore » treated on the same footing.« less

Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations

NASA Astrophysics Data System (ADS)

Cotton, Stephen Joshua

An approach has been developed for extracting approximate quantum state-to-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible. To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H2 reactive scattering calculations were performed [S.J. Cotton and W.H. Miller, J. Phys. Chem. A 117, 7190 (2013)] with SQC-quantization applied to the H 2 vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1/2-unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasi-classical procedure. The SQC approach was then applied [S.J. Cotton and W.H. Miller, J. Chem. Phys. 139, 234112 (2013)] to the much more interesting and challenging problem of incorporating non-adiabatic effects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model---representing the occupations of the electronic states---in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for a range of standard benchmark models of electronically non-adiabatic processes, including applications where "quantum" coherence effects are significant. Notably, among these benchmarks was the well-studied "spin-boson" model of condensed phase non-adiabatic dynamics, in both its symmetric and asymmetric forms---the latter of which many classical approaches fail to treat successfully. The SQC/MM approach to the treatment of non-adiabatic dynamics was next applied [S.J. Cotton, K. Igumenshchev, and W.H. Miller, J. Chem. Phys., 141, 084104 (2014)] to several recently proposed models of condensed phase electron transfer (ET) processes. For these problems, a flux-side correlation function framework modified for consistency with the SQC approach was developed for the calculation of thermal ET rate constants, and excellent accuracy was seen over wide ranges of non-adiabatic coupling strength and energetic bias/exothermicity. Significantly, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory was reproduced quantitatively for these models---representing the successful treatment of another regime that classical approaches generally have difficulty in correctly describing. Relatedly, a model of photoinduced proton coupled electron transfer (PCET) was also addressed, and it was shown that the SQC/MM approach could reasonably model the explicit population dynamics of the photoexcited electron donor and acceptor states over the four parameter regimes considered. The potential utility of the SQC/MM technique lies in its stunning simplicity and the ease by which it may readily be incorporated into "ordinary" molecular dynamics (MD) simulations. In short, a typical MD simulation may be augmented to take non-adiabatic effects into account simply by introducing an auxiliary pair of classical "electronic" action-angle variables for each energetically viable Born-Oppenheimer surface, and time-evolving these auxiliary variables via Hamilton's equations (using the MM electronic Hamiltonian) in the same manner that the other classical variables---i.e., the coordinates of all the nuclei---are evolved forward in time. In a complex molecular system involving many hundreds or thousands of nuclear DOFs, the propagation of these extra "electronic" variables represents a modest increase in computational effort, and yet, the examples presented herein suggest that in many instances the SQC/MM approach will describe the true non-adiabatic quantum dynamics to a reasonable and useful degree of quantitative accuracy.

Semiclassical description of hyperfine interaction in calculating chemically induced dynamic nuclear polarization in weak magnetic fields

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

Purtov, P.A.; Salikhov, K.M.

1987-09-01

Semiclassical HFI description is applicable to calculating the integral CIDNP effect in weak fields. The HFI has been calculated for radicals with sufficiently numerous magnetically equivalent nuclei (n greater than or equal to 5) in satisfactory agreement with CIDNP calculations based on quantum-mechanical description of radical-pair spin dynamics.

Phase space explorations in time dependent density functional theory

NASA Astrophysics Data System (ADS)

Rajam, Aruna K.

Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated functional of the co-ordinate density, non-local in space and time. Adiabatic approximations (such as ALDA), which are local in time, are most commonly used in the increasing applications of the field. Going beyond ALDA, has been proved difficult leading to mathematical inconsistencies. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from two electron model systems. In this thesis work we propose a phase-space extension of the TDDFT. We want to answer the challenges the theory is facing currently by exploring the one-body phase-space. We give a general introduction to this theory and its mathematical background in the first chapter. In second chapter, we carryout a detailed study of instantaneous phase-space densities and argue that the functionals of distributions can be a better alternative to the nonlocality issue of the exchange-correlation potentials. For this we study in detail the interacting and the non-interacting phase-space distributions for Hookes atom model. The applicability of ALDA-based TDDFT for the dynamics in strongfields can become severely problematic due to the failure of single-Slater determinant picture.. In the third chapter, we analyze how the phase-space distributions can shine some light into this problem. We do a comparative study of Kohn-Sham and interacting phase-space and momentum distributions for single ionization and double ionization systems. Using a simple model of two-electron systems, we have showed that the momentum distribution computed directly from the exact KS system contains spurious oscillations: a non-classical description of the essentially classical two-electron dynamics. In Time dependent density matrix functional theory (TDDMFT), the evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be expressed in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. In our fourth chapter, we show that by applying the quasi-classical and semi-classical approximations one can capture the natural occupations of the excited systems. We study a time-dependent Moshinsky atom model for this. The fifth chapter contains a comparative work on the existing non-local exchange-correlation kernels that are based on current density response frame work and the co-moving frame work. We show that the two approaches though coinciding with each other in linear response regime, actually turn out to be different in non-linear regime.

Relativistic quantum Darwinism in Dirac fermion and graphene systems

NASA Astrophysics Data System (ADS)

Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis

2012-02-01

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.

The evolution of consciousness

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

Stapp, H.P.

1996-08-16

It is argued that the principles of classical physics are inimical to the development of an adequate science of consciousness. The problem is that insofar as the classical principles are valid consciousness can have no effect on the behavior, and hence on the survival prospects, of the organisms in which it inheres. Thus within the classical framework it is not possible to explain in natural terms the development of consciousness to the high-level form found in human beings. In quantum theory, on the other hand, consciousness can be dynamically efficacious: quantum theory does allow consciousness to influence behavior, and thencemore » to evolve in accordance with the principles of natural selection. However, this evolutionary requirement places important constraints upon the details of the formulation of the quantum dynamical principles.« less

Optimal dimensionality reduction of complex dynamics: the chess game as diffusion on a free-energy landscape.

PubMed

Krivov, Sergei V

2011-07-01

Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game--the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.

Optimal dimensionality reduction of complex dynamics: The chess game as diffusion on a free-energy landscape

NASA Astrophysics Data System (ADS)

Krivov, Sergei V.

2011-07-01

Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game—the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.

Terminal Model Of Newtonian Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

New features in the structure of the classical Kuiper Belt

NASA Astrophysics Data System (ADS)

Gladman, Brett; Bannister, Michele T.; Alexandersen, Mike; Chen, Ying-Tung; Gwyn, Stephen; Kavelaars, J. J.; Petit, Jean-Marc; Volk, Kathryn; OSSOS Collaboration

2016-10-01

We report fascinating new dynamical structures emerging from a higher precision view of the classical Kuiper belt (the plentiful non-resonant orbits with semimajor axes in roughly the a=35-60 au range). The classical Kuiper Belt divides into multiple sub-populations: an 'inner' classical belt (a small group of non-resonant objects with a<39.4 au where the 3:2 resonance is located), an abundant 'main' classical belt (between the 3:2 and the 2:1 at a=47.4 au), and a difficult to study outer classical belt beyond the 2:1. We examine the dynamical structure, as precisely revealed in the detections from OSSOS (the Outer Solar System Origin's Survey); the data set is of superb quality in terms of orbital element and numbers of detections (Kavelaars et al, this meeting).The previous CFEPS survey showed that the main classical belt requires a complex dynamical substructure that goes beyond a simple 'hot versus cold' division based primarily on orbital inclination; the 'cold' inclination component requires two sub-components in the semimajor axis and perihelion distance q space (Petit et al 2011). CFEPS modelled this as a 'stirred' component present at all a=40-47 AU semimajor axes, with a dense superposed 'kernel' near a=44 AU at low eccentricity; the first OSSOS data release remained consistent with this (Bannister et al 2016). As with the main asteroid belt, as statistics and orbital quality improve we see additional significant substructure emerging in the classical belt's orbital distribution.OSSOS continues to add evidence that the cold stirred component extends smoothly beyond the 2:1 (Bannister et al 2016). Unexpectedly, the data also reveal the clear existence of a paucity of orbits just beyond the outer edge of the kernel; there are significantly fewer TNOs in the narrow semimajor axis band from a=44.5-45.0 AU. This may be related to the kernel population's creation, or it may be an independent feature created by planet migration as resonances moved in the primordial Kuiper Belt.

Quantum and classical ripples in graphene

NASA Astrophysics Data System (ADS)

Hašík, Juraj; Tosatti, Erio; MartoÅák, Roman

2018-04-01

Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of freestanding graphene, which show upon cooling a striking classical-quantum evolution of height and angular fluctuations. The crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained. Zero-temperature quantum graphene is flatter and smoother than classical graphene at large scales yet rougher at short scales. The angular fluctuation distribution of the normals can be quantitatively described by coexistence of two Gaussians, one classical strongly T -dependent and one quantum about 2° wide, of zero-point character. The quantum evolution of ripple-induced height and angular spread should be observable in electron diffraction in graphene and other two-dimensional materials, such as MoS2, bilayer graphene, boron nitride, etc.

Coupled Mode Formalism: Connecting Phasor, Matrix, and Geometrical Approaches

DTIC Science & Technology

2014-05-30

the Poincare sphere in classical optics, and was generalized to incoherent light as the Stokes and Mueller approach [4]. The Stokes description reduces...to the Poincare sphere description when one treats monochromatic light, and we restrict ourselves to this case. Background There are several...waves, cast as plane waves of the form g(z, t) = f(z − vt) = Aej(ω t −k z) , (1) namely a sinusoidal wave travelling in the positive z direction at phase

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

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

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Quantum stochastic walks on networks for decision-making.

PubMed

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-31

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

NASA Astrophysics Data System (ADS)

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

PubMed Central

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-01-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making. PMID:27030372

The Computer Simulation of Liquids by Molecular Dynamics.

ERIC Educational Resources Information Center

Smith, W.

1987-01-01

Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

Descriptions of vestibular migraine and Menière's disease in Greek and Chinese antiquity.

PubMed

Huppert, Doreen; Brandt, Thomas

2017-04-01

Background Vestibular migraine and Menière's disease are two types of episodic vertigo syndromes that were already observed in Greek and Chinese antiquity. Descriptions first appeared in the work of the classical Greek physician Aretaeus of Cappadocia, who lived in the 2nd century AD, and in Huangdi Neijing, a seminal medical source in the Chinese Medical Classics, written between the 2nd century BC and the 2nd century AD. Aim The aim of this paper is to search in Aretaeus' book De causis et signis acutorum et chronicorum morborum and in Huangdi Neijing for descriptions of vertigo co-occurring with headache or ear symptoms that resemble current classifications of vestibular migraine or Menière's disease. Results Aretaeus describes a syndrome combining headache, vertigo, visual disturbance, oculomotor phenomena, and nausea that resembles the symptoms of vestibular migraine. In the Chinese book Huangdi Neijing the Yellow Thearch mentions the co-occurrence of episodic dizziness and a ringing noise of the ears that recalls an attack of Menière's disease. Conclusions The descriptions of these two conditions in Greek and Chinese antiquity are similar to the vertigo syndromes currently classified as vestibular migraine and Menière's disease. In clinical practice it may be difficult to clearly differentiate between them, and they may also co-occur.

Children's Magazines: Something for Everyone.

ERIC Educational Resources Information Center

Kuersten, Joan

1983-01-01

A selected list of children's magazines is given, along with brief descriptions of their contents and ordering information. The magazines are on themes such as history, classical literature, science, nature and natural history, health, music, black children, and classroom learning activities. (PP)

Digital Refractometry of Piezoelectric Crystals.

DTIC Science & Technology

Digital Refractometry , Included in the report is a description of the program, classical methods for measuring the refractive index, the foundations of...Digital Refractometry for isotropic and anisotropic materials and the laboratory configuration for Digital Refractometry . In the final section of the

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.

Insight into the Li{sub 2}CO{sub 3}–K{sub 2}CO{sub 3} eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics

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

Corradini, Dario; Vuilleumier, Rodolphe, E-mail: rodolphe.vuilleumier@ens.fr; Sorbonne Universités, UPMC Univ. Paris 06, PASTEUR, 75005 Paris

We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li{sub 2}CO{sub 3}–K{sub 2}CO{sub 3} (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900–1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, wemore » present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture’s self-diffusion coefficients, viscosity, and ionic conductivity.« less

Lattice Boltzmann for Simulation of Gases Mixture in Fruit Storage Chambers

NASA Astrophysics Data System (ADS)

Fabero, J. C.; Barreiro, P.; Casasús, L.

2003-04-01

Fluid Dynamics can be modelled through the Navier-Stokes equations. This description corresponds to a macroscopic definition of the fluid motion phenomena. During the past 20 year new simulation procedures are emerging from Statistical Physics and Computer Science domains. One of them is the Lattice Gas Cellular Automata (LGCA) method. This approach, which is considered to be a microscopic description of the world, in spite of its intuitiveness and numerical efficiency, fails to simulate the real Navier-Stokes equations. Another classical simulation procedure for the fluid motion phenomena is the so called Lattice Boltzmann method [1]. This corresponds to a meso-scale description of the world [2]. Simulation of laminar and turbulent motions of fluids, specially when considering several gas species is still an ongoing research [3]. Nowadays, the use of Low Oxygen and Ultra Low Oxygen Controlled Atmospheres has been recognized as a reliable method to extend the storage life of fruits an vegetables. However, small spatial gradients in gas concentration during storage may generate internal disorders in the commodities. In this work, four different gases will be considered: oxygen, carbon dioxide, water vapor and ethylene. Physiological effects such as transpiration, which affects the level of water vapor, respiration, which modifies both oxygen and carbon dioxide concentrations, and ethylene emission, must be taken into account in the hole model. The numerical model, based on that proposed by Shan and Chen, is implemented, being able to consider the behavior of multiple mixable gas species. Forced air motion, needed to obtain a correct ventilation of the chamber, has also been modelled.

Averaging, passage through resonances, and capture into resonance in two-frequency systems

NASA Astrophysics Data System (ADS)

Neishtadt, A. I.

2014-10-01

Applying small perturbations to an integrable system leads to its slow evolution. For an approximate description of this evolution the classical averaging method prescribes averaging the rate of evolution over all the phases of the unperturbed motion. This simple recipe does not always produce correct results, because of resonances arising in the process of evolution. The phenomenon of capture into resonance consists in the system starting to evolve in such a way as to preserve the resonance property once it has arisen. This paper is concerned with application of the averaging method to a description of evolution in two-frequency systems. It is assumed that the trajectories of the averaged system intersect transversally the level surfaces of the frequency ratio and that certain other conditions of general position are satisfied. The rate of evolution is characterized by a small parameter \\varepsilon. The main content of the paper is a proof of the following result: outside a set of initial data with measure of order \\sqrt \\varepsilon the averaging method describes the evolution to within O(\\sqrt \\varepsilon \\vert\\ln\\varepsilon\\vert) for periods of time of order 1/\\varepsilon. This estimate is sharp. The exceptional set of measure \\sqrt \\varepsilon contains the initial data for phase points captured into resonance. A description of the motion of such phase points is given, along with a survey of related results on averaging. Examples of capture into resonance are presented for some problems in the dynamics of charged particles. Several open problems are stated. Bibliography: 65 titles.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

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

Prigogine, I.; Balescu, R.; Henin, F.

1960-12-01

Work on nonequilibrium statistical mechanics, which allows an extension of the kinetic proof to all results of equilibrium statistical mechanics involving a finite number of degrees of freedom, is summarized. As an introduction to the general N-body problem, the scattering theory in classical mechanics is considered. The general N-body problem is considered for the case of classical mechanics, quantum mechanics with Boltzmann statistics, and quantum mechanics including quantum statistics. Six basic diagrams, which describe the elementary processes of the dynamics of correlations, were obtained. (M.C.G.)

General dynamical density functional theory for classical fluids.

PubMed

Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim

2012-09-21

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Classical and quantum Big Brake cosmology for scalar field and tachyonic models

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

Kamenshchik, A. Yu.; Manti, S.

We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bangmore » and Big Crunch singularities are not traversable.« less

Self-organization in a diversity induced thermodynamics.

PubMed

Scirè, Alessandro; Annovazzi-Lodi, Valerio

2017-01-01

In this work we show how global self-organized patterns can come out of a disordered ensemble of point oscillators, as a result of a deterministic, and not of a random, cooperative process. The resulting system dynamics has many characteristics of classical thermodynamics. To this end, a modified Kuramoto model is introduced, by including Euclidean degrees of freedom and particle polarity. The standard deviation of the frequency distribution is the disorder parameter, diversity, acting as temperature, which is both a source of motion and of disorder. For zero and low diversity, robust static phase-synchronized patterns (crystals) appear, and the problem reverts to a generic dissipative many-body problem. From small to moderate diversity crystals display vibrations followed by structure disintegration in a competition of smaller dynamic patterns, internally synchronized, each of which is capable to manage its internal diversity. In this process a huge variety of self-organized dynamic shapes is formed. Such patterns can be seen again as (more complex) oscillators, where the same description can be applied in turn, renormalizing the problem to a bigger scale, opening the possibility of pattern evolution. The interaction functions are kept local because our idea is to build a system able to produce global patterns when its constituents only interact at the bond scale. By further increasing the oscillator diversity, the dynamics becomes erratic, dynamic patterns show short lifetime, and finally disappear for high diversity. Results are neither qualitatively dependent on the specific choice of the interaction functions nor on the shape of the probability function assumed for the frequencies. The system shows a phase transition and a critical behaviour for a specific value of diversity.

A classical molecular dynamics investigation of the free energy and structure of short polyproline conformers

NASA Astrophysics Data System (ADS)

Moradi, Mahmoud; Babin, Volodymyr; Roland, Christopher; Sagui, Celeste

2010-09-01

Folded polyproline peptides can exist as either left-(PPII) or right-handed (PPI) helices, depending on their environment. In this work, we have characterized the conformations and the free energy landscapes of Ace-(Pro)n-Nme, n =2,3,…,9, and 13 peptides both in vacuo and in an implicit solvent environment. In order to enhance the sampling provided by regular molecular dynamics simulations, we have used the recently developed adaptively biased molecular dynamics method—which provides an accurate description of the free energy landscapes in terms of a set of relevant collective variables—combined with Hamiltonian and temperature replica exchange molecular dynamics methods. The collective variables, which are chosen so as to reflect the stable structures and the "slow modes" of the polyproline system, were based primarily on properties of length and of the cis/trans isomerization associated with the prolyl bonds. Results indicate that the space of peptide structures is characterized not just by pure PPII and PPI structures, but rather by a broad distribution of stable minima with similar free energies. These results are in agreement with recent experimental work. In addition, we have used steered molecular dynamics methods in order to quantitatively estimate the free energy difference of PPI and PPII for peptides of the length n =2,…,5 in vacuo and implicit water and qualitatively investigate transition pathways and mechanisms for the PPII to PPI transitions. A zipper-like mechanism, starting from either the center of the peptide or the amidated end, appear to be the most likely mechanisms for the PPII→PPI transition for the longer peptides.

The science of space-time

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

Raine, D.J.; Heller, M.

1981-01-01

Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics Copernican kinematics Newtonian dynamics the space-time of classical dynamics classical space-time in the presence of gravity the space-time of special relativity the space-time of general relativity solutions and problems in generalmore » relativity Mach's principle and the dynamics of space-time theories of inertial mass the integral formation of general relativity and the frontiers of relativity (e.g., unified field theories and quantum gravity).« less

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations.

PubMed

Sakurai, Atsunori; Tanimura, Yoshitaka

2011-04-28

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.

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.

Picking a Fight with Water, and Water Lost ... an Electron

NASA Astrophysics Data System (ADS)

Herr, Jonathan D.

The global need for energy is increasing, as is the importance of producing energy by green and renewable methodologies. This document outlines a research program dedicated to investigating a possible source for this form of energy generation and storage: solar fuels. The photon-induced splitting of water into molecular hydrogen and oxygen is currently hindered by large overpotentials from the oxidation half-reaction of water-splitting. This study concentrated on fundamental models of water-spitting chemistry, using a physical and computational chemistry analysis. The oxidation was first explored via ab initio electronic structure calculations of bare cationic water clusters, comprised of 2 to 21 molecules, in order to determine key electronic interactions that facilitate oxidation. Deeper understanding of these interactions could serve as guides for the development of viable water oxidation catalysts (WOC) designed to reduce overpotentials. The cationic water cluster study was followed by an investigation into hydrated copper (I) clusters, which acted as precursor models for real WOCs. Analyzing how the copper ion perturbed the properties of water clusters led to important electronic considerations for the development of WOCs, such as copper-water interactions that go beyond simple electrostatics. The importance of diagnostic thermodynamic properties, as well as anharmonic characteristics being persistent throughout oxidized water clusters, necessitated the use of quantum and classical molecular dynamics (MD) routines. Therefore, two new methods for accelerating computationally demanding classical and quantum MD methods were developed to increase their accessibility. The first method utilized a new form of electronic extrapolation - a linear prediction routine incorporating a Burg minimization - to decrease the iterations required for solving the electronic equations throughout the dynamics. The second method utilized a multiple-timestepping description of the potential energy term in the path integral molecular dynamics (PIMD) formalism. This method led to reductions of computational time by allowing the use of less computationally laborious methods for portions of the simulation and resulted in negligible increase of error. The determination of the fundamental driving forces within water oxidation and the development of acceleration techniques for important electronic structure methods will help drive progress into fully solar-initiated water oxidation.

Peptide aggregation and solvent electrostriction in a simple zwitterionic dipeptide via molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Tulip, P. R.; Bates, S. P.

2009-07-01

We investigate the structure of the glycyl-l-alanine dipeptide in aqueous solution at a 1:20 peptide:water concentration via classical, atomistic molecular dynamics simulations using the CHARMM22 force field, and compare to recent neutron diffraction data [S. E. McLain, A. K. Soper, and A. Watts, Eur. Biophys. J. 37, 647 (2008); S. E. McLain, A. K. Soper, I. Diadone, J. C. Smith, and A. Watts, Angew. Chem. Int. Ed. 47, 9059 (2008)]. Comparison between simulations and experiments is made using the static structure factor S (Q ) . The effect of water model (TIP3P, TIP4P, and SPC/E) upon the solution structure is investigated. Agreement between experiment and simulation is generally good across the entire Q range, although some model-dependent variation is observed, particularly in the predicted intensities of features in S (Q ) . Peptide aggregation is found to be driven by "hydrophilic" (often bifurcated) hydrogen bonds formed between carboxy and amine functional groups, although simulations suggest that the degree of aggregation is less than that observed experimentally. It is found that hydrophobic association is not significant, with hydrophobic hydration being preferred to association. Detailed examination of the solute structural motifs reveals the existence of bifurcated motifs that are suggested to be an artifact of the CHARMM force field, and may imply that classical force fields provide a flawed structural and dynamical description of such molecular fluids. Investigation of the water structure reveals the presence of an electrostrictive effect which manifests itself as an increase in the number of interstitial molecules in the water second coordination shell, in contradiction to suggestions that this phenomenon arises owing to hydrogen bond bending. Detailed analysis based upon two-dimensional distribution functions suggests an intimate link between the phenomenon of electrostriction and the behavior of water under high-pressure compression. We find the magnitude of the electrostrictive effect inferred from the neutron diffraction data to be greater than that found in the simulations. Investigation of the solvation structure suggests that the CHARMM force field overhydrates the terminal carboxy group, and that this overhydration is accompanied by the presence of bifurcated hydrogen bonds.

Including Memory Friction in Single- and Two-State Quantum Dynamics Simulations.

PubMed

Brown, Paul A; Messina, Michael

2016-03-03

We present a simple computational algorithm that allows for the inclusion of memory friction in a quantum dynamics simulation of a small, quantum, primary system coupled to many atoms in the surroundings. We show how including a memory friction operator, F̂, in the primary quantum system's Hamiltonian operator builds memory friction into the dynamics of the primary quantum system. We show that, in the harmonic, semi-classical limit, this friction operator causes the classical phase-space centers of a wavepacket to evolve exactly as if it were a classical particle experiencing memory friction. We also show that this friction operator can be used to include memory friction in the quantum dynamics of an anharmonic primary system. We then generalize the algorithm so that it can be used to treat a primary quantum system that is evolving, non-adiabatically on two coupled potential energy surfaces, i.e., a model that can be used to model H atom transfer, for example. We demonstrate this approach's computational ease and flexibility by showing numerical results for both harmonic and anharmonic primary quantum systems in the single surface case. Finally, we present numerical results for a model of non-adiabatic H atom transfer between a reactant and product state that includes memory friction on one or both of the non-adiabatic potential energy surfaces and uncover some interesting dynamical effects of non-memory friction on the H atom transfer process.

An analytical derivation of MC-SCF vibrational wave functions for the quantum dynamical simulation of multiple proton transfer reactions: Initial application to protonated water chains

NASA Astrophysics Data System (ADS)

Drukker, Karen; Hammes-Schiffer, Sharon

1997-07-01

This paper presents an analytical derivation of a multiconfigurational self-consistent-field (MC-SCF) solution of the time-independent Schrödinger equation for nuclear motion (i.e. vibrational modes). This variational MC-SCF method is designed for the mixed quantum/classical molecular dynamics simulation of multiple proton transfer reactions, where the transferring protons are treated quantum mechanically while the remaining degrees of freedom are treated classically. This paper presents a proof that the Hellmann-Feynman forces on the classical degrees of freedom are identical to the exact forces (i.e. the Pulay corrections vanish) when this MC-SCF method is used with an appropriate choice of basis functions. This new MC-SCF method is applied to multiple proton transfer in a protonated chain of three hydrogen-bonded water molecules. The ground state and the first three excited state energies and the ground state forces agree well with full configuration interaction calculations. Sample trajectories are obtained using adiabatic molecular dynamics methods, and nonadiabatic effects are found to be insignificant for these sample trajectories. The accuracy of the excited states will enable this MC-SCF method to be used in conjunction with nonadiabatic molecular dynamics methods. This application differs from previous work in that it is a real-time quantum dynamical nonequilibrium simulation of multiple proton transfer in a chain of water molecules.

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

NASA Technical Reports Server (NTRS)

Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.

1989-01-01

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

Equivalence between contextuality and negativity of the Wigner function for qudits

NASA Astrophysics Data System (ADS)

Delfosse, Nicolas; Okay, Cihan; Bermejo-Vega, Juan; Browne, Dan E.; Raussendorf, Robert

2017-12-01

Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality for quantum systems, negativity of the Wigner function and contextuality for Pauli measurements. We prove that these two notions are equivalent for multi-qudit systems with odd local dimension. For a single qudit, the equivalence breaks down. We show that there exist single qudit states that admit a non-contextual hidden variable model description and whose Wigner functions are negative.

Kuang's Semi-Classical Formalism for Calculating Electron Capture Cross Sections: A Space- Physics Application

NASA Technical Reports Server (NTRS)

Barghouty, A. F.

2014-01-01

Accurate estimates of electroncapture cross sections at energies relevant to the modeling of the transport, acceleration, and interaction of energetic neutral atoms (ENA) in space (approximately few MeV per nucleon) and especially for multi-electron ions must rely on detailed, but computationally expensive, quantum-mechanical description of the collision process. Kuang's semi-classical approach is an elegant and efficient way to arrive at these estimates. Motivated by ENA modeling efforts for apace applications, we shall briefly present this approach along with sample applications and report on current progress.

'Quantum interference with slits' revisited

NASA Astrophysics Data System (ADS)

Rothman, Tony; Boughn, Stephen

2011-01-01

Marcella has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments. He also presents his calculation as if no approximations are employed. We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced. At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.

The Classical Plotline of "The Great Gatsby"

ERIC Educational Resources Information Center

Slattery, Dennis P.

1975-01-01

Argues that an understanding of the craft of fiction is furthered by a return to the original creation, concluding that "The Great Gatsby" is one of the best examples of Aristotle's description of tragedy as set forth in "The Poetics." (RB)

[Clinical forms of secondary syphilis in Cameroun].

PubMed

Koueke, P; Mvele, E D

1978-01-01

Clinical lesions of Secondary Syphilis in Negroes are similar to classical descriptions which confirm what Montel postulated (1972) according to which "Syphilis is almost the same all over"; the essential difference we discovered lies in the frequencies of clinical forms met.

NEPTUNE'S WILD DAYS: CONSTRAINTS FROM THE ECCENTRICITY DISTRIBUTION OF THE CLASSICAL KUIPER BELT

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

Dawson, Rebekah I.; Murray-Clay, Ruth, E-mail: rdawson@cfa.harvard.edu

2012-05-01

Neptune's dynamical history shaped the current orbits of Kuiper Belt objects (KBOs), leaving clues to the planet's orbital evolution. In the 'classical' region, a population of dynamically 'hot' high-inclination KBOs overlies a flat 'cold' population with distinct physical properties. Simulations of qualitatively different histories for Neptune, including smooth migration on a circular orbit or scattering by other planets to a high eccentricity, have not simultaneously produced both populations. We explore a general Kuiper Belt assembly model that forms hot classical KBOs interior to Neptune and delivers them to the classical region, where the cold population forms in situ. First, wemore » present evidence that the cold population is confined to eccentricities well below the limit dictated by long-term survival. Therefore, Neptune must deliver hot KBOs into the long-term survival region without excessively exciting the eccentricities of the cold population. Imposing this constraint, we explore the parameter space of Neptune's eccentricity and eccentricity damping, migration, and apsidal precession. We rule out much of parameter space, except where Neptune is scattered to a moderately eccentric orbit (e > 0.15) and subsequently migrates a distance {Delta}a{sub N} = 1-6 AU. Neptune's moderate eccentricity must either damp quickly or be accompanied by fast apsidal precession. We find that Neptune's high eccentricity alone does not generate a chaotic sea in the classical region. Chaos can result from Neptune's interactions with Uranus, exciting the cold KBOs and placing additional constraints. Finally, we discuss how to interpret our constraints in the context of the full, complex dynamical history of the solar system.« less