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

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

Rotational dynamics with geometric algebra

NASA Technical Reports Server (NTRS)

Hestenes, D.

1983-01-01

A new spinor formulation of rotational dynamics is developed. A general theorem is established reducing the theory of the symmetric top to that of the spherical top. The classical problems of Lagrange and Poinsot are treated in detail, along with a modern application to the theory of magnetic resonance.

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

Identification of asteroid dynamical families

NASA Technical Reports Server (NTRS)

Valsecchi, G. B.; Carusi, A.; Knezevic, Z.; Kresak, L.; Williams, J. G.

1989-01-01

Problems involved in the identification of asteroid dynamical families are discussed, and some methodological guidelines are presented. Asteroid family classifications are reviewed, and differences in the existing classifications are examined with special attention given to the effects of observational selection on the classification of family membership. The paper also discusses various theories of secular perturbations, including the classical linear theory, the theory of Williams (1969), and the higher order/degree theory of Yuasa (1973).

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.

Classical Dynamics of Fullerenes

NASA Astrophysics Data System (ADS)

Sławianowski, Jan J.; Kotowski, Romuald K.

2017-06-01

The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed Lagrangian (material) and Eulerian (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to formulate the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to formulate their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.

Neo-classical theory of competition or Adam Smith's hand as mathematized ideology

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2001-10-01

Orthodox economic theory (utility maximization, rational agents, efficient markets in equilibrium) is based on arbitrarily postulated, nonempiric notions. The disagreement between economic reality and a key feature of neo-classical economic theory was criticized empirically by Osborne. I show that the orthodox theory is internally self-inconsistent for the very reason suggested by Osborne: lack of invertibility of demand and supply as functions of price to obtain price as functions of supply and demand. The reason for the noninvertibililty arises from nonintegrable excess demand dynamics, a feature of their theory completely ignored by economists.

Molecular simulation of disjoining-pressure isotherms for free liquid , Lennard-Jones thin films

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

Bhatt, Divesh; Newman, John; Radke, C.J.

2001-10-01

We present canonical-ensemble molecular-dynamics simulations of disjoining-pressure isotherms in Lennard-Jones free liquid films. Thermodynamics demands that the disjoining pressure is determined uniquely as a function of the chemical potential purely from the phase diagram of the fluid. Our results from molecular dynamics validate this argument. The inverse-sixth-power distance term in the Lennard-Jones intermolecular potential represents van der Waals dispersion forces. Hence, we compare our results with classical Hamaker theory that is based on dispersion forces but assumes a slab geometry for the density profile and completely neglects fluid structure and entropy. We find that the Hamaker constant obtained from ourmore » simulations is about an order of magnitude larger than that from classical theory. To investigate the origin of this discrepancy, we calculate the disjoining-pressure isotherm using a density-functional theory relaxing the inherent assumptions in the Hamaker theory and imparting to the fluid an approximate structure. For disjoining pressure as a function of chemical potential, the results of density-functional theory and molecular dynamics are very close. Even for disjoining-pressure isotherms, and the subsequently calculated Hamaker constant, results of the density-functional theory are closer to the molecular-dynamics simulations by about a factor of 4 compared to Hamaker theory. [References: 44]« less

Applications of Density Functional Theory in Soft Condensed Matter

NASA Astrophysics Data System (ADS)

Löwen, Hartmut

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

PubMed

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

How quantizable matter gravitates: A practitioner's guide

NASA Astrophysics Data System (ADS)

Schuller, Frederic P.; Witte, Christof

2014-05-01

We present the practical step-by-step procedure for constructing canonical gravitational dynamics and kinematics directly from any previously specified quantizable classical matter dynamics, and then illustrate the application of this recipe by way of two completely worked case studies. Following the same procedure, any phenomenological proposal for fundamental matter dynamics must be supplemented with a suitable gravity theory providing the coefficients and kinematical interpretation of the matter theory, before any of the two theories can be meaningfully compared to experimental data.

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

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

The evolving Planck mass in classically scale-invariant theories

NASA Astrophysics Data System (ADS)

Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H.

2017-04-01

We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

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.

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.

Molecular dynamics simulations of classical sound absorption in a monatomic gas

NASA Astrophysics Data System (ADS)

Ayub, M.; Zander, A. C.; Huang, D. M.; Cazzolato, B. S.; Howard, C. Q.

2018-05-01

Sound wave propagation in argon gas is simulated using molecular dynamics (MD) in order to determine the attenuation of acoustic energy due to classical (viscous and thermal) losses at high frequencies. In addition, a method is described to estimate attenuation of acoustic energy using the thermodynamic concept of exergy. The results are compared against standing wave theory and the predictions of the theory of continuum mechanics. Acoustic energy losses are studied by evaluating various attenuation parameters and by comparing the changes in behavior at three different frequencies. This study demonstrates acoustic absorption effects in a gas simulated in a thermostatted molecular simulation and quantifies the classical losses in terms of the sound attenuation constant. The approach can be extended to further understanding of acoustic loss mechanisms in the presence of nanoscale porous materials in the simulation domain.

Individual-based modeling of ecological and evolutionary processes

USGS Publications Warehouse

DeAngelis, Donald L.; Mooij, Wolf M.

2005-01-01

Individual-based models (IBMs) allow the explicit inclusion of individual variation in greater detail than do classical differential-equation and difference-equation models. Inclusion of such variation is important for continued progress in ecological and evolutionary theory. We provide a conceptual basis for IBMs by describing five major types of individual variation in IBMs: spatial, ontogenetic, phenotypic, cognitive, and genetic. IBMs are now used in almost all subfields of ecology and evolutionary biology. We map those subfields and look more closely at selected key papers on fish recruitment, forest dynamics, sympatric speciation, metapopulation dynamics, maintenance of diversity, and species conservation. Theorists are currently divided on whether IBMs represent only a practical tool for extending classical theory to more complex situations, or whether individual-based theory represents a radically new research program. We feel that the tension between these two poles of thinking can be a source of creativity in ecology and evolutionary theory.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches.

PubMed

Antipov, Sergey V; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2017-11-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H 2 , local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

PubMed Central

Antipov, Sergey V.; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2018-01-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research “Molecular Ultrafast Science and Technology,” are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase. PMID:29376107

Tsallis non-extensive statistics and solar wind plasma complexity

NASA Astrophysics Data System (ADS)

Pavlos, G. P.; Iliopoulos, A. C.; Zastenker, G. N.; Zelenyi, L. M.; Karakatsanis, L. P.; Riazantseva, M. O.; Xenakis, M. N.; Pavlos, E. G.

2015-03-01

This article presents novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which took place on 26th September 2011. Solar wind plasma is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields (B → , E →) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto-hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial-temporal functions (MHD theory) or Gaussian statistics (Boltzmann-Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the q-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992).

Stochastic game theory: for playing games, not just for doing theory.

PubMed

Goeree, J K; Holt, C A

1999-09-14

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Linkages between Families and Political Extremism: A Theory of the Authoritarian Personality and Family System Dynamics.

ERIC Educational Resources Information Center

Gaziano, Cecilie

This paper seeks to integrate some ideas from family systems theory and attachment theory within a theory of public opinion and social movement. Citing the classic "The Authoritarian Personality," the paper states that the first authorities children know, their parents or other caregivers, shape children's attitudes toward all…

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.

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.

Classical gluon and graviton radiation from the bi-adjoint scalar double copy

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Prabhu, Siddharth G.; Thompson, Jedidiah O.

2017-09-01

We find double-copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the Bern-Carrasco-Johansson double-copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions are constructed to second order in a perturbative expansion, and map under the double copy onto gauge theory solutions which involve at most cubic gluon self-interactions. If the correspondence is found to persist to higher orders in perturbation theory, our results suggest the possibility of calculating gravitational radiation from colliding compact objects, directly from a scalar field with vastly simpler (purely cubic) Feynman vertices.

Quantum State Diffusion

NASA Astrophysics Data System (ADS)

Percival, Ian

2005-10-01

1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Dynamics of Markets

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2009-09-01

Preface; 1. Econophysics: why and what; 2. Neo-classical economic theory; 3. Probability and stochastic processes; 4. Introduction to financial economics; 5. Introduction to portfolio selection theory; 6. Scaling, pair correlations, and conditional densities; 7. Statistical ensembles: deducing dynamics from time series; 8. Martingale option pricing; 9. FX market globalization: evolution of the dollar to worldwide reserve currency; 10. Macroeconomics and econometrics: regression models vs. empirically based modeling; 11. Complexity; Index.

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.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

DOE PAGES

Benedict, Lorin X.; Surh, Michael P.; Stanton, Liam G.; ...

2017-04-10

Here, we use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n = 10 26cm –3, T i = 10 5K, and 10 7 K < Te < 10 9K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealingmore » to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.« less

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.

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

Semiclassical theory of electronically nonadiabatic transitions in molecular collision processes

NASA Technical Reports Server (NTRS)

Lam, K. S.; George, T. F.

1979-01-01

An introductory account of the semiclassical theory of the S-matrix for molecular collision processes is presented, with special emphasis on electronically nonadiabatic transitions. This theory is based on the incorporation of classical mechanics with quantum superposition, and in practice makes use of the analytic continuation of classical mechanics into the complex space of time domain. The relevant concepts of molecular scattering theory and related dynamical models are described and the formalism is developed and illustrated with simple examples - collinear collision of the A+BC type. The theory is then extended to include the effects of laser-induced nonadiabatic transitions. Two bound continuum processes collisional ionization and collision-induced emission also amenable to the same general semiclassical treatment are discussed.

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).

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

Anomalous dynamics of interstitial dopants in soft crystals

PubMed Central

Tauber, Justin; Higler, Ruben; Sprakel, Joris

2016-01-01

The dynamics of interstitial dopants govern the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically stabilized body-centered cubic (BCC) crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localized and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: (i) The instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and (ii) elastic interactions cause strong dopant–dopant interactions even at low doping fractions. These results illustrate how describing nonclassical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopant–dopant interactions into account. PMID:27856751

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

PubMed

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

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’.

Molecular Dynamics Simulations of Simple Liquids

ERIC Educational Resources Information Center

Speer, Owner F.; Wengerter, Brian C.; Taylor, Ramona S.

2004-01-01

An experiment, in which students were given the opportunity to perform molecular dynamics simulations on a series of molecular liquids using the Amber suite of programs, is presented. They were introduced to both physical theories underlying classical mechanics simulations and to the atom-atom pair distribution function.

A Tour Through Shape Dynamic Black Holes

NASA Astrophysics Data System (ADS)

Herczeg, Gabriel

Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Despite these differences, shape dynamics and general relativity generically predict the same dynamics--there exist gauge-fixings of each theory that ensure agreement with the other. However, these gauge-fixing conditions are not necessarily globally well-defined and it is therefore possible to find solutions of the shape dynamics equations of motion that agree with general relativity on some open neighborhoods, but which have different global structures. In particular, the black hole solutions of the two theories disagree globally. Understanding these novel "shape dynamic black holes" is the primary goal of this thesis.

The polymer physics of single DNA confined in nanochannels.

PubMed

Dai, Liang; Renner, C Benjamin; Doyle, Patrick S

2016-06-01

In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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.

Soliton Gases and Generalized Hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien

2018-01-01

We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.

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.)

Quantum algorithm for energy matching in hard optimization problems

NASA Astrophysics Data System (ADS)

Baldwin, C. L.; Laumann, C. R.

2018-06-01

We consider the ability of local quantum dynamics to solve the "energy-matching" problem: given an instance of a classical optimization problem and a low-energy state, find another macroscopically distinct low-energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here, we show that the introduction of quantum dynamics can provide a speedup over classical algorithms in a large class of hard optimization problems. Tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. Specifically, we study energy matching in the random p -spin model of spin-glass theory. Using perturbation theory and exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field "trapped" phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field "excited" phase, in which the field excites the system into high-energy states, effectively forgetting the initial energy; and (3) the intermediate "tunneling" phase, in which the system succeeds at energy matching. The rate at which distant states are found in the tunneling phase, although exponentially slow in system size, is exponentially faster than classical search algorithms.

Quantum Dynamics and a Semiclassical Description of the Photon.

ERIC Educational Resources Information Center

Henderson, Giles

1980-01-01

Uses computer graphics and nonstationary, superposition wave functions to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.…

Growing-Making Mathematics: A Dynamic Perspective on People, Materials, and Movement in Classrooms

ERIC Educational Resources Information Center

Roth, Wolff-Michael

2016-01-01

Recent theoretical advances on learning (mathematics) emphasize the fact that what results from engagement with curriculum materials is not entirely in the control of the students in the way classical theories of knowing and learning suggest. These new theories distinguish themselves by either invoking distributed agency, some of which is…

Fundamental Structure of Loop Quantum Gravity

NASA Astrophysics Data System (ADS)

Han, Muxin; Ma, Yongge; Huang, Weiming

In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

First-principles calculation of photo-induced electron transfer rate constants in phthalocyanine-C60 organic photovoltaic materials: Beyond Marcus theory

NASA Astrophysics Data System (ADS)

Lee, Myeong H.; Dunietz, Barry D.; Geva, Eitan

2014-03-01

Classical Marcus theory is commonly adopted in solvent-mediated charge transfer (CT) process to obtain the CT rate constant, but it can become questionable when the intramolecular vibrational modes dominate the CT process as in OPV devices because Marcus theory treats these modes classically and therefore nuclear tunneling is not accounted for. We present a computational scheme to obtain the electron transfer rate constant beyond classical Marcus theory. Within this approach, the nuclear vibrational modes are treated quantum-mechanically and a short-time approximation is avoided. Ab initio calculations are used to obtain the basic parameters needed for calculating the electron transfer rate constant. We apply our methodology to phthalocyanine(H2PC)-C60 organic photovoltaic system where one C60 acceptor and one or two H2PC donors are included to model the donor-acceptor interface configuration. We obtain the electron transfer and recombination rate constants for all accessible charge transfer (CT) states, from which the CT exciton dynamics is determined by employing a master equation. The role of higher lying excited states in CT exciton dynamics is discussed. This work is pursued as part of the Center for Solar and Thermal Energy Conversion, an Energy Frontier Research Center funded by the US Department of Energy Office of Science, Office of Basic Energy Sciences under 390 Award No. DE-SC0000957.

Nonequilibrium dynamics of the O( N ) model on dS3 and AdS crunches

NASA Astrophysics Data System (ADS)

Kumar, S. Prem; Vaganov, Vladislav

2018-03-01

We study the nonperturbative quantum evolution of the interacting O( N ) vector model at large- N , formulated on a spatial two-sphere, with time dependent couplings which diverge at finite time. This model - the so-called "E-frame" theory, is related via a conformal transformation to the interacting O( N ) model in three dimensional global de Sitter spacetime with time independent couplings. We show that with a purely quartic, relevant deformation the quantum evolution of the E-frame model is regular even when the classical theory is rendered singular at the end of time by the diverging coupling. Time evolution drives the E-frame theory to the large- N Wilson-Fisher fixed point when the classical coupling diverges. We study the quantum evolution numerically for a variety of initial conditions and demonstrate the finiteness of the energy at the classical "end of time". With an additional (time dependent) mass deformation, quantum backreaction lowers the mass, with a putative smooth time evolution only possible in the limit of infinite quartic coupling. We discuss the relevance of these results for the resolution of crunch singularities in AdS geometries dual to E-frame theories with a classical gravity dual.

Vakonomic Constraints in Higher-Order Classical Field Theory

NASA Astrophysics Data System (ADS)

Campos, Cédric M.

2010-07-01

We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

Chirikov, Boris V.

1993-01-01

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Wavefront aberrations of x-ray dynamical diffraction beams.

PubMed

Liao, Keliang; Hong, Youli; Sheng, Weifan

2014-10-01

The effects of dynamical diffraction in x-ray diffractive optics with large numerical aperture render the wavefront aberrations difficult to describe using the aberration polynomials, yet knowledge of them plays an important role in a vast variety of scientific problems ranging from optical testing to adaptive optics. Although the diffraction theory of optical aberrations was established decades ago, its application in the area of x-ray dynamical diffraction theory (DDT) is still lacking. Here, we conduct a theoretical study on the aberration properties of x-ray dynamical diffraction beams. By treating the modulus of the complex envelope as the amplitude weight function in the orthogonalization procedure, we generalize the nonrecursive matrix method for the determination of orthonormal aberration polynomials, wherein Zernike DDT and Legendre DDT polynomials are proposed. As an example, we investigate the aberration evolution inside a tilted multilayer Laue lens. The corresponding Legendre DDT polynomials are obtained numerically, which represent balanced aberrations yielding minimum variance of the classical aberrations of an anamorphic optical system. The balancing of classical aberrations and their standard deviations are discussed. We also present the Strehl ratio of the primary and secondary balanced aberrations.

Symmetry aspects in emergent quantum mechanics

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2009-06-01

We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantum mechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantum mechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.

Extension of loop quantum gravity to f(R) theories.

PubMed

Zhang, Xiangdong; Ma, Yongge

2011-04-29

The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.

Phase reduction approach to synchronisation of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Nakao, Hiroya

2016-04-01

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.

Transitioning NWChem to the Next Generation of Manycore Machines

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

Bylaska, Eric J.; Apra, Edoardo; Kowalski, Karol

The NorthWest Chemistry (NWChem) modeling software is a popular molecular chemistry simulation software that was designed from the start to work on massively parallel processing supercomputers[6, 28, 49]. It contains an umbrella of modules that today includes Self Consistent Field (SCF), second order Mller-Plesset perturbation theory (MP2), Coupled Cluster, multi-conguration selfconsistent eld (MCSCF), selected conguration interaction (CI), tensor contraction engine (TCE) many body methods, density functional theory (DFT), time-dependent density functional theory (TDDFT), real time time-dependent density functional theory, pseudopotential plane-wave density functional theory (PSPW), band structure (BAND), ab initio molecular dynamics, Car-Parrinello molecular dynamics, classical molecular dynamics (MD), QM/MM,more » AIMD/MM, GIAO NMR, COSMO, COSMO-SMD, and RISM solvation models, free energy simulations, reaction path optimization, parallel in time, among other capabilities[ 22]. Moreover new capabilities continue to be added with each new release.« less

Brane Physics in M-theory

NASA Astrophysics Data System (ADS)

Argurio, Riccardo

1998-07-01

The thesis begins with an introduction to M-theory (at a graduate student's level), starting from perturbative string theory and proceeding to dualities, D-branes and finally Matrix theory. The following chapter treats, in a self-contained way, of general classical p-brane solutions. Black and extremal branes are reviewed, along with their semi-classical thermodynamics. We then focus on intersecting extremal branes, the intersection rules being derived both with and without the explicit use of supersymmetry. The last three chapters comprise more advanced aspects of brane physics, such as the dynamics of open branes, the little theories on the world-volume of branes and how the four dimensional Schwarzschild black hole can be mapped to an extremal configuration of branes, thus allowing for a statistical interpretation of its entropy. The original results were already reported in hep-th/9701042, hep-th/9704190, hep-th/9710027 and hep-th/9801053.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

PubMed

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

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

Application of quantum master equation for long-term prognosis of asset-prices

NASA Astrophysics Data System (ADS)

Khrennikova, Polina

2016-05-01

This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a ;financial bath;. The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.

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.

Continuous Time in Consistent Histories

NASA Astrophysics Data System (ADS)

Savvidou, Konstantina

1999-12-01

We discuss the case of histories labelled by a continuous time parameter in the History Projection Operator consistent-histories quantum theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time averages of the energy. We define the action operator for the consistent histories formalism, as the quantum analogue of the classical action functional, for the simple harmonic oscillator case. We show that the action operator is the generator of two types of time transformations that may be related to the two laws of time-evolution of the standard quantum theory: the `state-vector reduction' and the unitary time-evolution. We construct the corresponding classical histories and demonstrate the relevance with the quantum histories; we demonstrate how the requirement of the temporal logic structure of the theory is sufficient for the definition of classical histories. Furthermore, we show the relation of the action operator to the decoherence functional which describes the dynamics of the system. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.

Response of moderately thick laminated cross-ply composite shells subjected to random excitation

NASA Technical Reports Server (NTRS)

Elishakoff, Isaak; Cederbaum, Gabriel; Librescu, Liviu

1989-01-01

This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).

A time-series approach to dynamical systems from classical and quantum worlds

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

Fossion, Ruben

2014-01-08

This contribution discusses some recent applications of time-series analysis in Random Matrix Theory (RMT), and applications of RMT in the statistial analysis of eigenspectra of correlation matrices of multivariate time series.

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.

Geometrical aspects in optical wave-packet dynamics.

PubMed

Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto

2006-12-01

We construct a semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability, i.e., a nonconducting photonic crystal. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry's phase, in a natural way, and describes an interplay between orbital motion and internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift of an optical beam at an interface reflection or refraction. For a generic incident beam with an arbitrary polarization, an identical result for the transverse shift of each reflected or transmitted beam is given by the following different approaches: (i) analytic evaluation of wave-packet dynamics, (ii) total angular momentum (TAM) conservation for individual photons, and (iii) numerical simulation of wave-packet dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e., classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.

Scalar gravitational waves in the effective theory of gravity

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

Mottola, Emil

As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the trace anomaly is expressed in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Linearized around flat spacetime, this semi-classical EFT admits scalar gravitational wave solutions in addition to the transversely polarized tensor waves of the classical Einstein theory. The amplitude of the scalar wavemore » modes, as well as their energy and energy flux which are positive and contain a monopole moment, are computed. As a result, astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals.« less

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Scalar gravitational waves in the effective theory of gravity

DOE PAGES

Mottola, Emil

2017-07-10

As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the trace anomaly is expressed in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Linearized around flat spacetime, this semi-classical EFT admits scalar gravitational wave solutions in addition to the transversely polarized tensor waves of the classical Einstein theory. The amplitude of the scalar wavemore » modes, as well as their energy and energy flux which are positive and contain a monopole moment, are computed. As a result, astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals.« less

Neural dynamic optimization for control systems.II. Theory.

PubMed

Seong, C Y; Widrow, B

2001-01-01

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the theory of NDO, while the two other companion papers of this topic explain the background for the development of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

Structure of a viscoplastic theory

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1988-01-01

The general structure of a viscoplastic theory is developed from physical and thermodynamical considerations. The flow equation is of classical form. The dynamic recovery approach is shown to be superior to the hardening function approach for incorporating nonlinear strain hardening into the material response through the evolutionary equation for back stress. A novel approach for introducing isotropic strain hardening into the theory is presented, which results in a useful simplification. In particular, the limiting stress for the kinematic saturation of state (not the drag stress) is the chosen scalar-valued state variable. The resulting simplification is that there is no coupling between dynamic and thermal recovery terms in each evolutionary equation. The derived theory of viscoplasticity has the structure of a two-surface plasticity theory when the response is plasticlike, and the structure of a Bailey-Orowan creep theory when the response is creeplike.

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.

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.

Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory

NASA Astrophysics Data System (ADS)

Langenbach, K.; Heilig, M.; Horsch, M.; Hasse, H.

2018-03-01

A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO2). The molecular model of CO2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory.

PubMed

Langenbach, K; Heilig, M; Horsch, M; Hasse, H

2018-03-28

A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO 2 ). The molecular model of CO 2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

Extending geometrical optics: A Lagrangian theory for vector waves

DOE PAGES

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

2017-03-16

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Extending geometrical optics: A Lagrangian theory for vector waves

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

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

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Dynamic Grover search: applications in recommendation systems and optimization problems

NASA Astrophysics Data System (ADS)

Chakrabarty, Indranil; Khan, Shahzor; Singh, Vanshdeep

2017-06-01

In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.

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.

Classical theory of atom-surface scattering: The rainbow effect

NASA Astrophysics Data System (ADS)

Miret-Artés, Salvador; Pollak, Eli

2012-07-01

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.

Classical theory of atom-surface scattering: The rainbow effect

NASA Astrophysics Data System (ADS)

Miret-Artés, Salvador; Pollak, Eli

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the "washboard model" in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.

Quantum-like model of unconscious–conscious dynamics

PubMed Central

Khrennikov, Andrei

2015-01-01

We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions. PMID:26283979

Comparison of Molecular Dynamics with Classical Density Functional and Poisson–Boltzmann Theories of the Electric Double Layer in Nanochannels

PubMed Central

2012-01-01

Comparisons are made among Molecular Dynamics (MD), Classical Density Functional Theory (c-DFT), and Poisson–Boltzmann (PB) modeling of the electric double layer (EDL) for the nonprimitive three component model (3CM) in which the two ion species and solvent molecules are all of finite size. Unlike previous comparisons between c-DFT and Monte Carlo (MC), the present 3CM incorporates Lennard-Jones interactions rather than hard-sphere and hard-wall repulsions. c-DFT and MD results are compared over normalized surface charges ranging from 0.2 to 1.75 and bulk ion concentrations from 10 mM to 1 M. Agreement between the two, assessed by electric surface potential and ion density profiles, is found to be quite good. Wall potentials predicted by PB begin to depart significantly from c-DFT and MD for charge densities exceeding 0.3. Successive layers are observed to charge in a sequential manner such that the solvent becomes fully excluded from each layer before the onset of the next layer. Ultimately, this layer filling phenomenon results in fluid structures, Debye lengths, and electric surface potentials vastly different from the classical PB predictions. PMID:23316120

Emergent "Quantum" Theory in Complex Adaptive Systems.

PubMed

Minic, Djordje; Pajevic, Sinisa

2016-04-30

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

Emergent “Quantum” Theory in Complex Adaptive Systems

PubMed Central

Minic, Djordje; Pajevic, Sinisa

2017-01-01

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective “Planck constant” associated with such emergent “quantum” theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems. PMID:28890591

Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Yamato, Ichiro

2013-07-01

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

Field theory of hyperfluid

NASA Astrophysics Data System (ADS)

Ariki, Taketo

2018-02-01

A hyperfluid model is constructed on the basis of its action entirely free from external constraints, regarding the hyperfluid as a self-consistent classical field. Intrinsic hypermomentum is no longer a supplemental variable given by external constraints, but arises purely from the diffeomorphism covariance of dynamical field. The field-theoretic approach allows natural classification of a hyperfluid on the basis of its symmetry group and corresponding homogeneous space; scalar, spinor, vector, and tensor fluids are introduced as simple examples. Apart from phenomenological constraints, the theory predicts the hypermomentum exchange of fluid via field-theoretic interactions of various classes; fluid–fluid interactions, minimal and non-minimal SU(n) -gauge couplings, and coupling with metric-affine gravity are all successfully formulated within the classical regime.

Branched Hamiltonians and supersymmetry

DOE PAGES

Curtright, Thomas L.; Zachos, Cosmas K.

2014-03-21

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.

Interactions Dominate the Dynamics of Visual Cognition

PubMed Central

Stephen, Damian G.; Mirman, Daniel

2010-01-01

Many cognitive theories have described behavior as the summation of independent contributions from separate components. Contrasting views have emphasized the importance of multiplicative interactions and emergent structure. We describe a statistical approach to distinguishing additive and multiplicative processes and apply it to the dynamics of eye movements during classic visual cognitive tasks. The results reveal interaction-dominant dynamics in eye movements in each of the three tasks, and that fine-grained eye movements are modulated by task constraints. These findings reveal the interactive nature of cognitive processing and are consistent with theories that view cognition as an emergent property of processes that are broadly distributed over many scales of space and time rather than a componential assembly line. PMID:20070957

Cosmological signature change in Cartan gravity with dynamical symmetry breaking

NASA Astrophysics Data System (ADS)

Magueijo, João; Rodríguez-Vázquez, Matías; Westman, Hans; Złośnik, Tom

2014-03-01

We investigate the possibility for classical metric signature change in a straightforward generalization of the first-order formulation of gravity, dubbed "Cartan gravity." The mathematical structure of this theory mimics the electroweak theory in that the basic ingredients are an SO(1,4) Yang-Mills gauge field Aabμ and a symmetry breaking Higgs field Va, with no metric or affine structure of spacetime presupposed. However, these structures can be recovered, with the predictions of general relativity exactly reproduced, whenever the Higgs field breaking the symmetry to SO(1,3) is forced to have a constant (positive) norm VaVa. This restriction is usually imposed "by hand," but in analogy with the electroweak theory we promote the gravitational Higgs field Va to a genuine dynamical field, subject to nontrivial equations of motion. Even though we limit ourselves to actions polynomial in these variables, we discover a rich phenomenology. Most notably we derive classical cosmological solutions exhibiting a smooth transition between Euclidean and Lorentzian signature in the four-metric. These solutions are nonsingular and arise whenever the SO(1,4) norm of the Higgs field changes sign; i.e. the signature of the metric of spacetime is determined dynamically by the gravitational Higgs field. It is possible to find a plethora of such solutions and in some of them this dramatic behavior is confined to the early Universe, with the theory asymptotically tending to Einstein gravity at late times. Curiously the theory can also naturally embody a well-known dark energy model: Peebles-Ratra quintessence.

Ion Correlation Effects in Salt-Doped Block Copolymers

NASA Astrophysics Data System (ADS)

Brown, Jonathan R.; Seo, Youngmi; Hall, Lisa M.

2018-03-01

We apply classical density functional theory to study how salt changes the microphase morphology of diblock copolymers. Polymers are freely jointed and one monomer type favorably interacts with ions, to account for the selective solvation that arises from different dielectric constants of the microphases. By including correlations from liquid state theory of an unbound reference fluid, the theory can treat chain behavior, microphase separation, ion correlations, and preferential solvation, at the same coarse-grained level. We show good agreement with molecular dynamics simulations.

Classical geometry to quantum behavior correspondence in a virtual extra dimension

NASA Astrophysics Data System (ADS)

Dolce, Donatello

2012-09-01

In the Lorentz invariant formalism of compact space-time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) [18] we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) [8]. Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark-Gluon-Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology.

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.

Issues of Dynamic Coalition Formation Among Rational Agents

DTIC Science & Technology

2002-04-01

approaches of forming stable coalitions among rational agents. Issues and problems of dynamic coalition environments are discussed in section 3 while...2.2. 2.1.2 Coalition Algorithm, Coalition Formation Environment and Model Rational agents which are involved in a co-operative game (A,v) are...publicly available simulation environment for coalition formation among rational information agents based on selected classic coalition theories is, for

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.

2016-09-01

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

Using 20-million-year-old amber to test the super-Arrhenius behaviour of glass-forming systems.

PubMed

Zhao, Jing; Simon, Sindee L; McKenna, Gregory B

2013-01-01

Fossil amber offers the opportunity to investigate the dynamics of glass-forming materials far below the nominal glass transition temperature. This is important in the context of classical theory, as well as some new theories that challenge the idea of an 'ideal' glass transition. Here we report results from calorimetric and stress relaxation experiments using a 20-million-year-old Dominican amber. By performing the stress relaxation experiments in a step-wise fashion, we measured the relaxation time at each temperature and, above the fictive temperature of this 20-million-year-old glass, this is an upper bound to the equilibrium relaxation time. The results deviate dramatically from the expectation of classical theory and are consistent with some modern ideas, in which the diverging timescale signature of complex fluids disappears below the glass transition temperature.

Pressure broadening of the electric dipole and Raman lines of CO2 by argon: Stringent test of the classical impact theory at different temperatures on a benchmark system

NASA Astrophysics Data System (ADS)

Ivanov, Sergey V.; Buzykin, Oleg G.

2016-12-01

A classical approach is applied to calculate pressure broadening coefficients of CO2 vibration-rotational spectral lines perturbed by Ar. Three types of spectra are examined: electric dipole (infrared) absorption; isotropic and anisotropic Raman Q branches. Simple and explicit formulae of the classical impact theory are used along with exact 3D Hamilton equations for CO2-Ar molecular motion. The calculations utilize vibrationally independent most accurate ab initio potential energy surface (PES) of Hutson et al. expanded in Legendre polynomial series up to lmax = 24. New improved algorithm of classical rotational frequency selection is applied. The dependences of CO2 half-widths on rotational quantum number J up to J=100 are computed for the temperatures between 77 and 765 K and compared with available experimental data as well as with the results of fully quantum dynamical calculations performed on the same PES. To make the picture complete, the predictions of two independent variants of the semi-classical Robert-Bonamy formalism for dipole absorption lines are included. This method. however, has demonstrated poor accuracy almost for all temperatures. On the contrary, classical broadening coefficients are in excellent agreement both with measurements and with quantum results at all temperatures. The classical impact theory in its present variant is capable to produce quickly and accurately the pressure broadening coefficients of spectral lines of linear molecules for any J value (including high Js) using full-dimensional ab initio - based PES in the cases where other computational methods are either extremely time consuming (like the quantum close coupling method) or give erroneous results (like semi-classical methods).

Mixed quantum-classical studies of energy partitioning in unimolecular chemical reactions

NASA Astrophysics Data System (ADS)

Bladow, Landon Lowell

A mixed quantum-classical reaction path Hamiltonian method is utilized to study the dynamics of unimolecular reactions. The method treats motion along the reaction path classically and treats the transverse vibrations quantum mechanically. The theory leads to equations that predict the disposai of the exit-channel potential energy to product translation and vibration. In addition, vibrational state distributions are obtained for the product normal modes. Vibrational excitation results from the curvature of the minimum energy reaction path. The method is applied to six unimolecular reactions: HF elimination from fluoroethane, 1,1-difluoroethane, 1,1-difluoroethene, and trifluoromethane; and HCl elimination from chloroethane and acetyl chloride. The minimum energy paths were calculated at either the MP2 or B3LYP level of theory. In all cases, the majority of the vibrational excitation of the products occurs in the HX fragment. The results are compared to experimental data and other theoretical results, where available. The best agreement between the experimental and calculated HX vibrational distributions is found for the halogenated ethanes, and the experimental deduction that the majority of the HX vibrational excitation arises from the potential energy release is supported. It is believed that the excess energy provided in experiments contributes to the poorer agreement between experiment and theory observed for HF elimination from 1,1-difluoroethene and trifluoromethane. An attempt is described to incorporate a treatment of the excess energy into the present method. However, the sign of the curvature coupling elements is then found to affect the dynamics. Overall, the method appears to be an efficient dynamical tool for modeling the disposal of the exit-channel potential energy in unimolecular reactions.

Bouncing cosmologies from quantum gravity condensates

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward

2017-02-01

We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

Structural aspects of Hamilton-Jacobi theory

NASA Astrophysics Data System (ADS)

Cariñena, J. F.; Gràcia, X.; Marmo, G.; Martínez, E.; Muñoz-Lecanda, M. C.; Román-Roy, N.

2016-12-01

In our previous papers [J. F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M. C. Muñoz-Lecanda and N. Román-Roy, Geometric Hamilton-Jacobi theory, Int. J. Geom. Meth. Mod. Phys. 3 (2006) 1417-1458; Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems, Int. J. Geom. Meth. Mod. Phys. 7 (2010) 431-454] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (slicing vector fields) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibered manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.

Quantum chemistry simulation on quantum computers: theories and experiments.

PubMed

Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng

2012-07-14

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.

Generalized continued fractions and ergodic theory

NASA Astrophysics Data System (ADS)

Pustyl'nikov, L. D.

2003-02-01

In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

Evanescent radiation, quantum mechanics and the Casimir effect

NASA Technical Reports Server (NTRS)

Schatten, Kenneth H.

1989-01-01

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

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

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stabilitymore » parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.« less

A general relaxation theory of simple liquids

NASA Technical Reports Server (NTRS)

Merilo, M.; Morgan, E. J.

1973-01-01

A relatively simple relaxation theory to account for the behavior of liquids under dynamic conditions was proposed. The general dynamical equations are similar in form to the phenomenological relaxation equations used in theories of viscoelasticity, however, they differ in that all the coefficients of the present equations are expressed in terms of thermodynamic and molecular quantities. The theory is based on the concept that flow in a liquid distorts both the radial and the velocity distribution functions, and that relaxation equations describing the return of these functions to their isotropic distributions, characterizing a stationary liquid, can be written. The theory was applied to the problems of steady and oscillatory shear flows and to the propagation of longitudinal waves. In all cases classical results are predicted for strain rates, and an expression for the viscosity of a liquid, simular to the Macedo-Litovitz equation, is obtained.

Time evolution of linearized gauge field fluctuations on a real-time lattice

NASA Astrophysics Data System (ADS)

Kurkela, A.; Lappi, T.; Peuron, J.

2016-12-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law.

Quantum and classical dynamics of water dissociation on Ni(111): A test of the site-averaging model in dissociative chemisorption of polyatomic molecules

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

Jiang, Bin; Department of Chemical Physics, University of Science and Technology of China, Hefei 230026; Guo, Hua, E-mail: hguo@unm.edu

Recently, we reported the first highly accurate nine-dimensional global potential energy surface (PES) for water interacting with a rigid Ni(111) surface, built on a large number of density functional theory points [B. Jiang and H. Guo, Phys. Rev. Lett. 114, 166101 (2015)]. Here, we investigate site-specific reaction probabilities on this PES using a quasi-seven-dimensional quantum dynamical model. It is shown that the site-specific reactivity is largely controlled by the topography of the PES instead of the barrier height alone, underscoring the importance of multidimensional dynamics. In addition, the full-dimensional dissociation probability is estimated by averaging fixed-site reaction probabilities with appropriatemore » weights. To validate this model and gain insights into the dynamics, additional quasi-classical trajectory calculations in both full and reduced dimensions have also been performed and important dynamical factors such as the steering effect are discussed.« less

Hamiltonian dynamics for complex food webs

NASA Astrophysics Data System (ADS)

Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

2016-03-01

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Radiation and the classical double copy for color charges

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Ridgway, Alexander K.

2017-06-01

We construct perturbative classical solutions of the Yang-Mills equations coupled to dynamical point particles carrying color charge. By applying a set of color to kinematics replacement rules first introduced by Bern, Carrasco and Johansson, these are shown to generate solutions of d -dimensional dilaton gravity, which we also explicitly construct. Agreement between the gravity result and the gauge theory double copy implies a correspondence between non-Abelian particles and gravitating sources with dilaton charge. When the color sources are highly relativistic, dilaton exchange decouples, and the solutions we obtain match those of pure gravity. We comment on possible implications of our findings to the calculation of gravitational waveforms in astrophysical black hole collisions, directly from computationally simpler gluon radiation in Yang-Mills theory.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Interactions dominate the dynamics of visual cognition.

PubMed

Stephen, Damian G; Mirman, Daniel

2010-04-01

Many cognitive theories have described behavior as the summation of independent contributions from separate components. Contrasting views have emphasized the importance of multiplicative interactions and emergent structure. We describe a statistical approach to distinguishing additive and multiplicative processes and apply it to the dynamics of eye movements during classic visual cognitive tasks. The results reveal interaction-dominant dynamics in eye movements in each of the three tasks, and that fine-grained eye movements are modulated by task constraints. These findings reveal the interactive nature of cognitive processing and are consistent with theories that view cognition as an emergent property of processes that are broadly distributed over many scales of space and time rather than a componential assembly line. Copyright 2009 Elsevier B.V. All rights reserved.

Cycle frequency in standard Rock-Paper-Scissors games: Evidence from experimental economics

NASA Astrophysics Data System (ADS)

Xu, Bin; Zhou, Hai-Jun; Wang, Zhijian

2013-10-01

The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work, we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of N=6 players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be 0.029±0.009 period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game.

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.

Li+ solvation and kinetics of Li+-BF4-/PF6- ion pairs in ethylene carbonate. A molecular dynamics study with classical rate theories

NASA Astrophysics Data System (ADS)

Chang, Tsun-Mei; Dang, Liem X.

2017-10-01

Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine the ethylene carbonate (EC) exchange process between the first and second solvation shells around Li+ and the dissociation kinetics of ion pairs Li+-[BF4] and Li+-[PF6] in this solvent. We calculate the exchange rates using transition state theory and correct them with transmission coefficients computed by the reactive flux, Impey, Madden, and McDonald approaches, and Grote-Hynes theory. We found that the residence times of EC around Li+ ions varied from 60 to 450 ps, depending on the correction method used. We found that the relaxation times changed significantly from Li+-[BF4] to Li+-[PF6] ion pairs in EC. Our results also show that, in addition to affecting the free energy of dissociation in EC, the anion type also significantly influences the dissociation kinetics of ion pairing.

Concepts and their dynamics: a quantum-theoretic modeling of human thought.

PubMed

Aerts, Diederik; Gabora, Liane; Sozzo, Sandro

2013-10-01

We analyze different aspects of our quantum modeling approach of human concepts and, more specifically, focus on the quantum effects of contextuality, interference, entanglement, and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, that is, prototype theory, exemplar theory, and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and we shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this article by analyzing human concepts and their dynamics. © 2013 Cognitive Science Society, Inc.

Car and Parrinello meet Green and Kubo: simulating atomic heat transport from equilibrium ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Baroni, Stefano

Modern simulation methods based on electronic-structure theory have long been deemed unfit to compute heat transport coefficients within the Green-Kubo formalism. This is so because the quantum-mechanical energy density from which the heat flux is derived is inherently ill defined, thus allegedly hampering the use of the Green-Kubo formula. While this objection would actually apply to classical systems as well, I will demonstrate that the thermal conductivity is indeed independent of the specific microscopic expression for the energy density and current from which it is derived. This fact results from a kind of gauge invariance stemming from energy conservation and extensivity, which I will illustrate numerically for a classical Lennard-Jones fluid. I will then introduce an expression for the adiabatic energy flux, derived within density-functional theory, that allows simulating atomic heat transport using equilibrium ab initio molecular dynamics. The resulting methodology is demonstrated by comparing results from ab-initio and classical molecular-dynamics simulations of a model liquid-Argon system, for which accurate inter-atomic potentials are derived by the force-matching method, and applied to compute the thermal conductivity of heavy water at ambient conditions. The problem of evaluating transport coefficients along with their accuracy from relatively short trajectories is finally addressed and discussed with a few representative examples. Partially funded by the European Union through the MaX Centre of Excellence (Grant No. 676598).

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.

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

Somnath, Suhas; Collins, Liam; Matheson, Michael A.

We develop and implement a multifrequency spectroscopy and spectroscopic imaging mode, referred to as general dynamic mode (GDM), that captures the complete spatially- and stimulus dependent information on nonlinear cantilever dynamics in scanning probe microscopy (SPM). GDM acquires the cantilever response including harmonics and mode mixing products across the entire broadband cantilever spectrum as a function of excitation frequency. GDM spectra substitute the classical measurements in SPM, e.g. amplitude and phase in lock-in detection. Here, GDM is used to investigate the response of a purely capacitively driven cantilever. We use information theory techniques to mine the data and verify themore » findings with governing equations and classical lock-in based approaches. We explore the dependence of the cantilever dynamics on the tip–sample distance, AC and DC driving bias. This approach can be applied to investigate the dynamic behavior of other systems within and beyond dynamic SPM. In conclusion, GDM is expected to be useful for separating the contribution of different physical phenomena in the cantilever response and understanding the role of cantilever dynamics in dynamic AFM techniques.« less

Extending geometrical optics: A Lagrangian theory for vector waves

NASA Astrophysics Data System (ADS)

Ruiz, D. E.

2016-10-01

Even diffraction aside, the commonly known equations of geometrical optics (GO) are not entirely accurate. GO considers wave rays as classical particles, which are completely described by their coordinates and momenta, but rays have another degree of freedom, namely, polarization. As a result, wave rays can behave as particles with spin. A well-known example of polarization dynamics is wave-mode conversion, which can be interpreted as rotation of the (classical) ``wave spin.'' However, there are other less-known manifestations of the wave spin, such as polarization precession and polarization-driven bending of ray trajectories. This talk presents recent advances in extending and reformulating GO as a first-principle Lagrangian theory, whose effective-gauge Hamiltonian governs both mentioned polarization phenomena simultaneously. Examples and numerical results are presented. When applied to classical waves, the theory correctly predicts the polarization-driven divergence of left- and right- polarized electromagnetic waves in isotropic media, such as dielectrics and nonmagnetized plasmas. In the case of particles with spin, the formalism also yields a point-particle Lagrangian model for the Dirac electron, i.e. the relativistic spin-1/2 electron, which includes both the Stern-Gerlach spin potential and the Bargmann-Michel-Telegdi spin precession. Additionally, the same theory contributes, perhaps unexpectedly, to the understanding of ponderomotive effects in both wave and particle dynamics; e.g., the formalism allows to obtain the ponderomotive Hamiltonian for a Dirac electron interacting with an arbitrarily large electromagnetic laser field with spin effects included. Supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.

Rotation in vibration, optimization, and aeroelastic stability problems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1974-01-01

The effects of rotation in the areas of vibrations, dynamic stability, optimization, and aeroelasticity were studied. The governing equations of motion for the study of vibration and dynamic stability of a rapidly rotating deformable body were developed starting from the nonlinear theory of elasticity. Some common features such as the limitations of the classical theory of elasticity, the choice of axis system, the property of self-adjointness, the phenomenon of frequency splitting, shortcomings of stability methods as applied to gyroscopic systems, and the effect of internal and external damping on stability in gyroscopic systems are identified and discussed, and are then applied to three specific problems.

Toward a new modeling of international economics: An attempt to reformulate an international trade model based on real option theory

NASA Astrophysics Data System (ADS)

Fujita, Yasunori

2007-09-01

Reformulation of economics by physics has been carried out intensively to reveal many features of the asset market, which were missed in the classical economic theories. The present paper attempts to shed new light on this field. That is, this paper aims at reformulating the international trade model by making use of the real option theory. Based on such a stochastic dynamic model, we examine how the fluctuation of the foreign exchange rate makes effect on the welfare of the exporting country.

Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current

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

Glorioso, Paolo; Crossley, Michael; Liu, Hong

2017-09-20

Here in this paper we further develop the fluctuating hydrodynamics proposed in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a Z2 symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMSmore » condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.« less

Transitioning NWChem to the Next Generation of Manycore Machines

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

Bylaska, Eric J.; Apra, E; Kowalski, Karol

The NorthWest chemistry (NWChem) modeling software is a popular molecular chemistry simulation software that was designed from the start to work on massively parallel processing supercomputers [1-3]. It contains an umbrella of modules that today includes self-consistent eld (SCF), second order Møller-Plesset perturbation theory (MP2), coupled cluster (CC), multiconguration self-consistent eld (MCSCF), selected conguration interaction (CI), tensor contraction engine (TCE) many body methods, density functional theory (DFT), time-dependent density functional theory (TDDFT), real-time time-dependent density functional theory, pseudopotential plane-wave density functional theory (PSPW), band structure (BAND), ab initio molecular dynamics (AIMD), Car-Parrinello molecular dynamics (MD), classical MD, hybrid quantum mechanicsmore » molecular mechanics (QM/MM), hybrid ab initio molecular dynamics molecular mechanics (AIMD/MM), gauge independent atomic orbital nuclear magnetic resonance (GIAO NMR), conductor like screening solvation model (COSMO), conductor-like screening solvation model based on density (COSMO-SMD), and reference interaction site model (RISM) solvation models, free energy simulations, reaction path optimization, parallel in time, among other capabilities [4]. Moreover, new capabilities continue to be added with each new release.« less

Piezoelectrically actuated flextensional micromachined ultrasound transducers--I: theory.

PubMed

Perçin, Gökhan; Khuri-Yakub, Butrus T

2002-05-01

This series of two papers considers piezoelectrically actuated flextensional micromachined ultrasound transducers (PAFMUTs) and consists of theory, fabrication, and experimental parts. The theory presented in this paper is developed for an ultrasound transducer application presented in the second part. In the absence of analytical expressions for the equivalent circuit parameters of a flextensional transducer, it is difficult to calculate its optimal parameters and dimensions and difficult to choose suitable materials. The influence of coupling between flexural and extensional deformation and that of coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flextensional transducer are analyzed using two analytical methods: classical thin (Kirchhoff) plate theory and Mindlin plate theory. Classical thin plate theory and Mindlin plate theory are applied to derive two-dimensional plate equations for the transducer and to calculate the coupled electromechanical field variables such as mechanical displacement and electrical input impedance. In these methods, the variations across the thickness direction vanish by using the bending moments per unit length or stress resultants. Thus, two-dimensional plate equations for a step-wise laminated circular plate are obtained as well as two different solutions to the corresponding systems. An equivalent circuit of the transducer is also obtained from these solutions.

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.

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium.

PubMed

Hone, Tyler D; Voth, Gregory A

2004-10-01

Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids. (c) 2004 American Institute of Physics

A Dynamic Stimulus-Driven Model of Signal Detection

ERIC Educational Resources Information Center

Turner, Brandon M.; Van Zandt, Trisha; Brown, Scott

2011-01-01

Signal detection theory forms the core of many current models of cognition, including memory, choice, and categorization. However, the classic signal detection model presumes the a priori existence of fixed stimulus representations--usually Gaussian distributions--even when the observer has no experience with the task. Furthermore, the classic…

On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

PubMed Central

Malhado, João Pedro; Bearpark, Michael J.; Hynes, James T.

2014-01-01

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field. PMID:25485263

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

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

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

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

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

A census of the expected properties of classical Milky Way dwarfs in Milgromian dynamics

NASA Astrophysics Data System (ADS)

Lüghausen, F.; Famaey, B.; Kroupa, P.

2014-07-01

Prompted by the recent successful predictions of the internal dynamics of Andromeda's satellite galaxies, we revisit the classical Milky Way dwarf spheroidal satellites Draco, Sculptor, Sextans, Carina and Fornax in the framework of Milgromian dynamics (MOND). We use for the first time a Poisson solver with adaptive mesh refinement (AMR) in order to account simultaneously for the gravitational influence of the Milky Way and its satellites. This allows us to rigorously model the important external field effect (EFE) of Milgromian dynamics, which can reduce the effective acceleration significantly. We make predictions on the dynamical mass-to-light ratio (Mdyn/L) expected to be measured by an observer who assumes Newtonian dynamics to be valid. We show that Milgromian dynamics predicts typical Mdyn/L ≈ 10-50 M⊙/L⊙. The results for the most luminous ones, Fornax and Sculptor, agree well with available velocity dispersion data. Moreover, the central power-law slopes of the dynamical masses agree exceedingly well with values inferred observationally from velocity dispersion measurements. The results for Sextans, Carina and Draco are low compared to usually quoted observational estimates, as already pointed out by Angus. For Milgromian dynamics to survive further observational tests in these objects, one would thus need that either (a) previous observational findings based on velocity dispersion measurements have overestimated the dynamical mass due to, e.g. binaries and contaminant outliers, (b) the satellites are not in virial equilibrium due to the Milky Way tidal field, or (c) the specific theory used here does not describe the EFE correctly (e.g. the EFE could be practically negligible in some other theories), or a combination of (a)-(c).

Imaging via complete cantilever dynamic detection: General dynamic mode imaging and spectroscopy in scanning probe microscopy

DOE PAGES

Somnath, Suhas; Collins, Liam; Matheson, Michael A.; ...

2016-09-08

We develop and implement a multifrequency spectroscopy and spectroscopic imaging mode, referred to as general dynamic mode (GDM), that captures the complete spatially- and stimulus dependent information on nonlinear cantilever dynamics in scanning probe microscopy (SPM). GDM acquires the cantilever response including harmonics and mode mixing products across the entire broadband cantilever spectrum as a function of excitation frequency. GDM spectra substitute the classical measurements in SPM, e.g. amplitude and phase in lock-in detection. Here, GDM is used to investigate the response of a purely capacitively driven cantilever. We use information theory techniques to mine the data and verify themore » findings with governing equations and classical lock-in based approaches. We explore the dependence of the cantilever dynamics on the tip–sample distance, AC and DC driving bias. This approach can be applied to investigate the dynamic behavior of other systems within and beyond dynamic SPM. In conclusion, GDM is expected to be useful for separating the contribution of different physical phenomena in the cantilever response and understanding the role of cantilever dynamics in dynamic AFM techniques.« less

Phylogenetic escalation and decline of plant defense strategies

PubMed Central

Agrawal, Anurag A.; Fishbein, Mark

2008-01-01

As the basal resource in most food webs, plants have evolved myriad strategies to battle consumption by herbivores. Over the past 50 years, plant defense theories have been formulated to explain the remarkable variation in abundance, distribution, and diversity of secondary chemistry and other defensive traits. For example, classic theories of enemy-driven evolutionary dynamics have hypothesized that defensive traits escalate through the diversification process. Despite the fact that macroevolutionary patterns are an explicit part of defense theories, phylogenetic analyses have not been previously attempted to disentangle specific predictions concerning (i) investment in resistance traits, (ii) recovery after damage, and (iii) plant growth rate. We constructed a molecular phylogeny of 38 species of milkweed and tested four major predictions of defense theory using maximum-likelihood methods. We did not find support for the growth-rate hypothesis. Our key finding was a pattern of phyletic decline in the three most potent resistance traits (cardenolides, latex, and trichomes) and an escalation of regrowth ability. Our neontological approach complements more common paleontological approaches to discover directional trends in the evolution of life and points to the importance of natural enemies in the macroevolution of species. The finding of macroevolutionary escalating regowth ability and declining resistance provides a window into the ongoing coevolutionary dynamics between plants and herbivores and suggests a revision of classic plant defense theory. Where plants are primarily consumed by specialist herbivores, regrowth (or tolerance) may be favored over resistance traits during the diversification process. PMID:18645183

Metastability and nucleation in the 2D-Potts ferromagnet

NASA Astrophysics Data System (ADS)

de Berganza, Miguel Ibáñez

2009-01-01

The nature of the temperature-driven transition of the 2D q>4-Potts model, and the associated metastability, are studied. The problem was firstly investigated by Binder [1,2] in 1981, who discussed the existence of metastable states in a temperature interval below the critical point, which is first-order for q>4. Starting from the droplet expansion theory for the 2D Potts condensation point (Meunier & Morel, 2000 [3]), we compare the metastability derived from the theory with the dynamic metastability found with a local updating rule dynamics. The results are interpreted in terms of the microscopic mechanisms of nucleation, and compared to those described by Classical Nucleation Theory for the Ising model in an external field, which result to be different in several aspects.

Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics

NASA Astrophysics Data System (ADS)

Gryb, Sean

2012-04-01

In this PhD thesis, we develop a new approach to classical gravity starting from Mach's principles and the idea that the local shape of spatial configurations is fundamental. This new theory, "shape dynamics", is equivalent to general relativity but differs in an important respect: shape dynamics is a theory of dynamic conformal 3-geometry, not a theory of spacetime. Equivalence is achieved by trading foliation invariance for local conformal invariance (up to a global scale). After the trading, what is left is a gauge theory invariant under 3d diffeomorphisms and conformal transformations that preserve the volume of space. The local canonical constraints are linear and the constraint algebra closes with structure constants. Shape dynamics, thus, provides a novel new starting point for quantum gravity. The procedure for the trading of symmetries was inspired by a technique called "best matching". We explain best matching and its relation to Mach's principles. The key features of best matching are illustrated through finite dimensional toy models. A general picture is then established where relational theories are treated as gauge theories on configuration space. Shape dynamics is then constructed by applying best matching to conformal geometry. We then study shape dynamics in more detail by computing its Hamiltonian and Hamilton-Jacobi functional perturbatively. This thesis is intended as a pedagogical but complete introduction to shape dynamics and the Machian ideas that led to its discovery. The reader is encouraged to start with the introduction, which gives a conceptual outline and links to the relevant sections in the text for a more rigorous exposition. When full rigor is lacking, references to the literature are given. It is hoped that this thesis may provide a starting point for anyone interested in learning about shape dynamics.

SIAM conference on applications of dynamical systems

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

Not Available

1992-01-01

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

SIAM conference on applications of dynamical systems. Abstracts and author index

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

Not Available

1992-12-31

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

High temperature phonon dispersion in graphene using classical molecular dynamics

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

Anees, P., E-mail: anees@igcar.gov.in; Panigrahi, B. K.; Valsakumar, M. C., E-mail: anees@igcar.gov.in

2014-04-24

Phonon dispersion and phonon density of states of graphene are calculated using classical molecular dynamics simulations. In this method, the dynamical matrix is constructed based on linear response theory by computing the displacement of atoms during the simulations. The computed phonon dispersions show excellent agreement with experiments. The simulations are done in both NVT and NPT ensembles at 300 K and found that the LO/TO modes are getting hardened at the Γ point. The NPT ensemble simulations capture the anharmonicity of the crystal accurately and the hardening of LO/TO modes is more pronounced. We also found that at 300 Kmore » the C-C bond length reduces below the equilibrium value and the ZA bending mode frequency becomes imaginary close to Γ along K-Γ direction, which indicates instability of the flat 2D graphene sheets.« less

DFT-derived reactive potentials for the simulation of activated processes: the case of CdTe and CdTe:S.

PubMed

Hu, Xiao Liang; Ciaglia, Riccardo; Pietrucci, Fabio; Gallet, Grégoire A; Andreoni, Wanda

2014-06-19

We introduce a new ab initio derived reactive potential for the simulation of CdTe within density functional theory (DFT) and apply it to calculate both static and dynamical properties of a number of systems (bulk solid, defective structures, liquid, surfaces) at finite temperature. In particular, we also consider cases with low sulfur concentration (CdTe:S). The analysis of DFT and classical molecular dynamics (MD) simulations performed with the same protocol leads to stringent performance tests and to a detailed comparison of the two schemes. Metadynamics techniques are used to empower both Car-Parrinello and classical molecular dynamics for the simulation of activated processes. For the latter, we consider surface reconstruction and sulfur diffusion in the bulk. The same procedures are applied using previously proposed force fields for CdTe and CdTeS materials, thus allowing for a detailed comparison of the various schemes.

Effective field theory of dissipative fluids

DOE PAGES

Crossley, Michael; Glorioso, Paolo; Liu, Hong

2017-09-20

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMSmore » condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.« less

Effective field theory of dissipative fluids

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

Crossley, Michael; Glorioso, Paolo; Liu, Hong

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMSmore » condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.« less

Ensembles and Experiments in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Neumaier, Arnold

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

Physics of risk and uncertainty in quantum decision making

NASA Astrophysics Data System (ADS)

Yukalov, V. I.; Sornette, D.

2009-10-01

The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion in precise mathematical terms, we distinguish three types of inconsistency: time inconsistency, planning paradox, and inconsistency occurring in some discounting effects. While time inconsistency is well accounted for in classical decision theory, the planning paradox is in contradiction with classical utility theory. It finds a natural explanation in the frame of the Quantum Decision Theory. Different types of discounting effects are analyzed and shown to enjoy a straightforward explanation within the suggested theory. We also introduce a general methodology based on self-similar approximation theory for deriving the evolution equations for the probabilities of future prospects. This provides a novel classification of possible discount factors, which include the previously known cases (exponential or hyperbolic discounting), but also predicts a novel class of discount factors that decay to a strictly positive constant for very large future time horizons. This class may be useful to deal with very long-term discounting situations associated with intergenerational public policy choices, encompassing issues such as global warming and nuclear waste disposal.

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.

What is Quantum Information?

NASA Astrophysics Data System (ADS)

Lombardi, Olimpia; Fortin, Sebastian; Holik, Federico; López, Cristian

2017-04-01

Preface; Introduction; Part I. About the Concept of Information: 1. About the concept of information Sebastian Fortin and Olimpia Lombardi; 2. Representation, information, and theories of information Armond Duwell; 3. Information, communication, and manipulability Olimpia Lombardi and Cristian López; Part II. Information and quantum mechanics: 4. Quantum versus classical information Jeffrey Bub; 5. Quantum information and locality Dennis Dieks; 6. Pragmatic information in quantum mechanics Juan Roederer; 7. Interpretations of quantum theory: a map of madness Adán Cabello; Part III. Probability, Correlations, and Information: 8. On the tension between ontology and epistemology in quantum probabilities Amit Hagar; 9. Inferential versus dynamical conceptions of physics David Wallace; 10. Classical models for quantum information Federico Holik and Gustavo Martin Bosyk; 11. On the relative character of quantum correlations Guido Bellomo and Ángel Ricardo Plastino; Index.

The Examination of Reliability According to Classical Test and Generalizability on a Job Performance Scale

ERIC Educational Resources Information Center

Yelboga, Atilla; Tavsancil, Ezel

2010-01-01

In this research, the classical test theory and generalizability theory analyses were carried out with the data obtained by a job performance scale for the years 2005 and 2006. The reliability coefficients obtained (estimated) from the classical test theory and generalizability theory analyses were compared. In classical test theory, test retest…

Modeling light-induced charge transfer dynamics across a metal-molecule-metal junction: Bridging classical electrodynamics and quantum dynamics

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

Hu, Zixuan; Ratner, Mark A.; Seideman, Tamar, E-mail: t-seideman@northwestern.edu

2014-12-14

We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify ourmore » approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement.« less

Chandrasekhar's dynamical friction and non-extensive statistics

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

Silva, J.M.; Lima, J.A.S.; De Souza, R.E.

2016-05-01

The motion of a point like object of mass M passing through the background potential of massive collisionless particles ( m || M ) suffers a steady deceleration named dynamical friction. In his classical work, Chandrasekhar assumed a Maxwellian velocity distribution in the halo and neglected the self gravity of the wake induced by the gravitational focusing of the mass M . In this paper, by relaxing the validity of the Maxwellian distribution due to the presence of long range forces, we derive an analytical formula for the dynamical friction in the context of the q -nonextensive kinetic theory. Inmore » the extensive limiting case ( q = 1), the classical Gaussian Chandrasekhar result is recovered. As an application, the dynamical friction timescale for Globular Clusters spiraling to the galactic center is explicitly obtained. Our results suggest that the problem concerning the large timescale as derived by numerical N -body simulations or semi-analytical models can be understood as a departure from the standard extensive Maxwellian regime as measured by the Tsallis nonextensive q -parameter.« less

Next Generation Extended Lagrangian Quantum-based Molecular Dynamics

NASA Astrophysics Data System (ADS)

Negre, Christian

2017-06-01

A new framework for extended Lagrangian first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended Lagrangian formulation of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.

Use of Direct Dynamics Simulations to Determine Unimolecular Reaction Paths and Arrhenius Parameters for Large Molecules.

PubMed

Yang, Li; Sun, Rui; Hase, William L

2011-11-08

In a previous study (J. Chem. Phys.2008, 129, 094701) it was shown that for a large molecule, with a total energy much greater than its barrier for decomposition and whose vibrational modes are harmonic oscillators, the expressions for the classical Rice-Ramsperger-Kassel-Marcus (RRKM) (i.e., RRK) and classical transition-state theory (TST) rate constants become equivalent. Using this relationship, a molecule's unimolecular rate constants versus temperature may be determined from chemical dynamics simulations of microcanonical ensembles for the molecule at different total energies. The simulation identifies the molecule's unimolecular pathways and their Arrhenius parameters. In the work presented here, this approach is used to study the thermal decomposition of CH3-NH-CH═CH-CH3, an important constituent in the polymer of cross-linked epoxy resins. Direct dynamics simulations, at the MP2/6-31+G* level of theory, were used to investigate the decomposition of microcanonical ensembles for this molecule. The Arrhenius A and Ea parameters determined from the direct dynamics simulation are in very good agreement with the TST Arrhenius parameters for the MP2/6-31+G* potential energy surface. The simulation method applied here may be particularly useful for large molecules with a multitude of decomposition pathways and whose transition states may be difficult to determine and have structures that are not readily obvious.

U1108 performance model

NASA Technical Reports Server (NTRS)

Trachta, G.

1976-01-01

A model of Univac 1108 work flow has been developed to assist in performance evaluation studies and configuration planning. Workload profiles and system configurations are parameterized for ease of experimental modification. Outputs include capacity estimates and performance evaluation functions. The U1108 system is conceptualized as a service network; classical queueing theory is used to evaluate network dynamics.

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.

On observation of position in quantum theory

NASA Astrophysics Data System (ADS)

Kryukov, A.

2018-05-01

Newtonian and Schrödinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a "concentration" near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of a state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space.

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

PubMed

Gao, J

2016-01-01

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. © 2016 Elsevier Inc. All rights reserved.

Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load

NASA Astrophysics Data System (ADS)

Wang, Yuewu; Wu, Dafang

2016-10-01

Dynamic response of an axially functionally graded (AFG) beam under thermal environment subjected to a moving harmonic load is investigated within the frameworks of classical beam theory (CBT) and Timoshenko beam theory (TBT). The Lagrange method is employed to derive the equations of thermal buckling for AFG beam, and then with the critical buckling temperature as a parameter the Newmark-β method is adopted to evaluate the dynamic response of AFG beam under thermal environments. Admissible functions denoting transverse displacement are expressed in simple algebraic polynomial forms. Temperature-dependency of material constituent is considered. The rule of mixture (Voigt model) and Mori-Tanaka (MT) scheme are used to evaluate the beam's effective material properties. A ceramic-metal AFG beam with immovable boundary condition is considered as numerical illustration to show the thermal effects on the dynamic behaviors of the beam subjected to a moving harmonic load.

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.

Is quantum theory a form of statistical mechanics?

NASA Astrophysics Data System (ADS)

Adler, S. L.

2007-05-01

We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

An Introduction to Turbulent Flow

NASA Astrophysics Data System (ADS)

Mathieu, Jean; Scott, Julian

2000-06-01

In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. Turbulent Flows ably meets this need, developing both physical insight and the mathematical framework needed to express the theory. The authors present basic theory and illustrate it with examples of simple turbulent flows and classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by their treatment of spectral analysis and its applications.

The Theory of Canonical Perturbations Applied to Attitude Dynamics and to the Earth Rotation. Osculating and Nonosculating Andoyer Variables

DTIC Science & Technology

2007-06-21

Hiroshi Kinoshita for his extremely valuable consultations on some subtleties of his theory. ME is also grateful to Pini Gurfil , George Kaplan, Jean...that the Andoyer elements are introduced 20 It can be shown ( Gurfil et al. 2007) that the body-frame-related components gi of the angular momentum are...oblate precessing planet. Astron. J. 70, 5–9 (1965) Goldstein, H.: Classical Mechanics. 2nd ed. Addison-Wesley, Reading MA (1981) Gurfil , P., Elipe

Towards a second law for Lovelock theories

NASA Astrophysics Data System (ADS)

Bhattacharyya, Sayantani; Haehl, Felix M.; Kundu, Nilay; Loganayagam, R.; Rangamani, Mukund

2017-03-01

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

Quantum Theories of Self-Localization

NASA Astrophysics Data System (ADS)

Bernstein, Lisa Joan

In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

The Symmetries of QCD

ScienceCinema

Chivukula, Sekhar

2017-12-22

The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level.  Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter. 

Computational Insights into Materials and Interfaces for Capacitive Energy Storage

PubMed Central

Zhan, Cheng; Lian, Cheng; Zhang, Yu; Thompson, Matthew W.; Xie, Yu; Wu, Jianzhong; Kent, Paul R. C.; Cummings, Peter T.; Wesolowski, David J.

2017-01-01

Supercapacitors such as electric double‐layer capacitors (EDLCs) and pseudocapacitors are becoming increasingly important in the field of electrical energy storage. Theoretical study of energy storage in EDLCs focuses on solving for the electric double‐layer structure in different electrode geometries and electrolyte components, which can be achieved by molecular simulations such as classical molecular dynamics (MD), classical density functional theory (classical DFT), and Monte‐Carlo (MC) methods. In recent years, combining first‐principles and classical simulations to investigate the carbon‐based EDLCs has shed light on the importance of quantum capacitance in graphene‐like 2D systems. More recently, the development of joint density functional theory (JDFT) enables self‐consistent electronic‐structure calculation for an electrode being solvated by an electrolyte. In contrast with the large amount of theoretical and computational effort on EDLCs, theoretical understanding of pseudocapacitance is very limited. In this review, we first introduce popular modeling methods and then focus on several important aspects of EDLCs including nanoconfinement, quantum capacitance, dielectric screening, and novel 2D electrode design; we also briefly touch upon pseudocapactive mechanism in RuO2. We summarize and conclude with an outlook for the future of materials simulation and design for capacitive energy storage. PMID:28725531

Performance of some nucleation theories with a nonsharp droplet-vapor interface.

PubMed

Napari, Ismo; Julin, Jan; Vehkamäki, Hanna

2010-10-21

Nucleation theories involving the concept of nonsharp boundary between the droplet and vapor are compared to recent molecular dynamics (MD) simulation data of Lennard-Jones vapors at temperatures above the triple point. The theories are diffuse interface theory (DIT), extended modified liquid drop-dynamical nucleation theory (EMLD-DNT), square gradient theory (SGT), and density functional theory (DFT). Particular attention is paid to thermodynamic consistency in the comparison: the applied theories either use or, with a proper parameter adjustment, result in the same values of equilibrium vapor pressure, bulk liquid density, and surface tension as the MD simulations. Realistic pressure-density correlations are also used. The best agreement between the simulated nucleation rates and calculations is obtained from DFT, SGT, and EMLD-DNT, all of which, in the studied temperature range, show deviations of less than one order of magnitude in the nucleation rate. DIT underestimates the nucleation rate by up to two orders of magnitude. DFT and SGT give the best estimate of the molecular content of the critical nuclei. Overall, at the vapor conditions of this study, all the investigated theories perform better than classical nucleation theory in predicting nucleation rates.

Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

NASA Astrophysics Data System (ADS)

Pavon, Michele

1996-07-01

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

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.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

PubMed Central

2016-01-01

The nucleation of crystals in liquids is one of nature’s most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments. PMID:27228560

Relational evolution of effectively interacting group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi

2017-03-01

We study the impact of effective interactions onto relationally evolving group field theory (GFT) condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations.

PubMed

Sosso, Gabriele C; Chen, Ji; Cox, Stephen J; Fitzner, Martin; Pedevilla, Philipp; Zen, Andrea; Michaelides, Angelos

2016-06-22

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Selectivity trend of gas separation through nanoporous graphene

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

Liu, Hongjun; Chen, Zhongfang; Dai, Sheng

2015-04-15

By means of molecular dynamics (MD) simulations, we demonstrate that porous graphene can efficiently separate gases according to their molecular sizes. The flux sequence from the classical MD simulation is H{sub 2}>CO{sub 2}≫N{sub 2}>Ar>CH{sub 4}, which generally follows the trend in the kinetic diameters. This trend is also confirmed from the fluxes based on the computed free energy barriers for gas permeation using the umbrella sampling method and kinetic theory of gases. Both brute-force MD simulations and free-energy calcualtions lead to the flux trend consistent with experiments. Case studies of two compositions of CO{sub 2}/N{sub 2} mixtures further demonstrate themore » separation capability of nanoporous graphene. - Graphical abstract: Classical molecular dynamics simulations show the flux trend of H{sub 2}>CO{sub 2}≫N{sub 2}>Ar>CH{sub 4} for their permeation through a porous graphene, in excellent agreement with a recent experiment. - Highlights: • Classical MD simulations show the flux trend of H{sub 2}>CO{sub 2}≫N{sub 2}>Ar>CH{sub 4} for their permeation through a porous graphene. • Free energy calculations yield permeation barriers for those gases. • Selectivities for several gas pairs are estimated from the free-energy barriers and the kinetic theory of gases. • The selectivity trend is in excellent agreement with a recent experiment.« less

Diagrammar in classical scalar field theory

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

Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com; Gozzi, E., E-mail: gozzi@ts.infn.it; INFN, Sezione di Trieste

2011-09-15

In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplifymore » the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.« less

Li + solvation and kinetics of Li +–BF 4 -/PF 6 - ion pairs in ethylene carbonate. A molecular dynamics study with classical rate theories

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

Chang, Tsun-Mei; Dang, Liem X.

Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine in this paper the ethylene carbonate (EC) exchange process between the first and second solvation shells around Li + and the dissociation kinetics of ion pairs Li +–[BF 4] and Li +–[PF 6] in this solvent. We calculate the exchange rates using transition state theory and correct them with transmission coefficients computed by the reactive flux, Impey, Madden, and McDonald approaches, and Grote-Hynes theory. We found that the residence times of EC around Li + ions varied from 60 to 450 ps, depending on themore » correction method used. We found that the relaxation times changed significantly from Li +–[BF 4] to Li +–[PF 6] ion pairs in EC. Finally, our results also show that, in addition to affecting the free energy of dissociation in EC, the anion type also significantly influences the dissociation kinetics of ion pairing.« less

Li + solvation and kinetics of Li +–BF 4 -/PF 6 - ion pairs in ethylene carbonate. A molecular dynamics study with classical rate theories

DOE PAGES

Chang, Tsun-Mei; Dang, Liem X.

2017-07-19

Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine in this paper the ethylene carbonate (EC) exchange process between the first and second solvation shells around Li + and the dissociation kinetics of ion pairs Li +–[BF 4] and Li +–[PF 6] in this solvent. We calculate the exchange rates using transition state theory and correct them with transmission coefficients computed by the reactive flux, Impey, Madden, and McDonald approaches, and Grote-Hynes theory. We found that the residence times of EC around Li + ions varied from 60 to 450 ps, depending on themore » correction method used. We found that the relaxation times changed significantly from Li +–[BF 4] to Li +–[PF 6] ion pairs in EC. Finally, our results also show that, in addition to affecting the free energy of dissociation in EC, the anion type also significantly influences the dissociation kinetics of ion pairing.« less

Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates.

PubMed

Cendagorta, Joseph R; Powers, Anna; Hele, Timothy J H; Marsalek, Ondrej; Bačić, Zlatko; Tuckerman, Mark E

2016-11-30

Clathrate hydrates hold considerable promise as safe and economical materials for hydrogen storage. Here we present a quantum mechanical study of H 2 and D 2 diffusion through a hexagonal face shared by two large cages of clathrate hydrates over a wide range of temperatures. Path integral molecular dynamics simulations are used to compute the free-energy profiles for the diffusion of H 2 and D 2 as a function of temperature. Ring polymer molecular dynamics rate theory, incorporating both exact quantum statistics and approximate quantum dynamical effects, is utilized in the calculations of the H 2 and D 2 diffusion rates in a broad temperature interval. We find that the shape of the quantum free-energy profiles and their height relative to the classical free energy barriers at a given temperature, as well as the rate of diffusion, are strongly affected by competing quantum effects: above 25 K, zero-point energy (ZPE) perpendicular to the reaction path for diffusion between cavities decreases the quantum rate compared to the classical rate, whereas at lower temperatures tunneling outcompetes the ZPE and as a result the quantum rate is greater than the classical rate.

Loop quantum cosmology of Bianchi IX: effective dynamics

NASA Astrophysics Data System (ADS)

Corichi, Alejandro; Montoya, Edison

2017-03-01

We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N  =  V and N  =  1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k  =  0,1 FLRW as well as Bianchi I, II, and VII0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.

Synchronisation of chaos and its applications

NASA Astrophysics Data System (ADS)

Eroglu, Deniz; Lamb, Jeroen S. W.; Pereira, Tiago

2017-07-01

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order. We survey the main theory behind complete, generalised and phase synchronisation phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.

A model with chaotic scattering and reduction of wave packets

NASA Astrophysics Data System (ADS)

Guarneri, Italo

2018-03-01

Some variants of Smilansky’s model of a particle interacting with harmonic oscillators are examined in the framework of scattering theory. A dynamical proof is given of the existence of wave operators. Analysis of a classical version of the model provides a transparent picture for the spectral transition to which the quantum model owes its renown, and for the underlying dynamical behaviour. The model is thereby classified as an extreme case of chaotic scattering, with aspects related to wave packet reduction and irreversibility.

Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

John, Christopher; Spura, Thomas; Habershon, Scott; Kühne, Thomas D.

2016-04-01

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

Universality in quantum chaos and the one-parameter scaling theory.

PubMed

García-García, Antonio M; Wang, Jiao

2008-02-22

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.

Flory-Stockmayer analysis on reprocessable polymer networks

NASA Astrophysics Data System (ADS)

Li, Lingqiao; Chen, Xi; Jin, Kailong; Torkelson, John

Reprocessable polymer networks can undergo structure rearrangement through dynamic chemistries under proper conditions, making them a promising candidate for recyclable crosslinked materials, e.g. tires. This research field has been focusing on various chemistries. However, there has been lacking of an essential physical theory explaining the relationship between abundancy of dynamic linkages and reprocessability. Based on the classical Flory-Stockmayer analysis on network gelation, we developed a similar analysis on reprocessable polymer networks to quantitatively predict the critical condition for reprocessability. Our theory indicates that it is unnecessary for all bonds to be dynamic to make the resulting network reprocessable. As long as there is no percolated permanent network in the system, the material can fully rearrange. To experimentally validate our theory, we used a thiol-epoxy network model system with various dynamic linkage compositions. The stress relaxation behavior of resulting materials supports our theoretical prediction: only 50 % of linkages between crosslinks need to be dynamic for a tri-arm network to be reprocessable. Therefore, this analysis provides the first fundamental theoretical platform for designing and evaluating reprocessable polymer networks. We thank McCormick Research Catalyst Award Fund and ISEN cluster fellowship (L. L.) for funding support.

Gravitational forces and moments on spacecraft

NASA Technical Reports Server (NTRS)

Kane, T. R.; Likins, P. W.

1975-01-01

The solution of problems of attitude dynamics of spacecraft and the influence of gravitational forces and moments is examined. Arguments are presented based on Newton's law of gravitation, and employing the methods of Newtonian (vectorial) mechanics, with minimal recourse to the classical concepts of potential theory. The necessary ideas were developed and relationships were established to permit the representation of gravitational forces and moments exerted on bodies in space by other bodies, both in terms involving the mass distribution properties of the bodies, and in terms of vector operations on those scalar functions classically described as gravitational potential functions.

Why, Mrs. Robinson? The seduction of teenage boys by women in classic films.

PubMed

Colarusso, Calvin A

2014-09-01

Utilizing three classic films, and psychoanalytic developmental theory, this paper explores the conscious and unconscious reasons why older women become sexually involved with teenage boys. After a presentation of aspects of young adult and midlife female development and a psychodynamic explanation for the developmental similarities between adolescence and menopause, each of the three films is summarized. The dynamics behind the women's behavior, as presented in the films, are discussed. The third section of the paper discusses similarities and differences among the three women and the negative effects on the boys' development.

Brønsted acidity of protic ionic liquids: a modern ab initio valence bond theory perspective.

PubMed

Patil, Amol Baliram; Mahadeo Bhanage, Bhalchandra

2016-09-21

Room temperature ionic liquids (ILs), especially protic ionic liquids (PILs), are used in many areas of the chemical sciences. Ionicity, the extent of proton transfer, is a key parameter which determines many physicochemical properties and in turn the suitability of PILs for various applications. The spectrum of computational chemistry techniques applied to investigate ionic liquids includes classical molecular dynamics, Monte Carlo simulations, ab initio molecular dynamics, Density Functional Theory (DFT), CCSD(t) etc. At the other end of the spectrum is another computational approach: modern ab initio Valence Bond Theory (VBT). VBT differs from molecular orbital theory based methods in the expression of the molecular wave function. The molecular wave function in the valence bond ansatz is expressed as a linear combination of valence bond structures. These structures include covalent and ionic structures explicitly. Modern ab initio valence bond theory calculations of representative primary and tertiary ammonium protic ionic liquids indicate that modern ab initio valence bond theory can be employed to assess the acidity and ionicity of protic ionic liquids a priori.

The dance of molecules: new dynamical perspectives on highly excited molecular vibrations.

PubMed

Kellman, Michael E; Tyng, Vivian

2007-04-01

At low energies, molecular vibrational motion is described by the normal modes model. This model breaks down at higher energy, with strong coupling between normal modes and onset of chaotic dynamics. New anharmonic modes are born in bifurcations, or branchings of the normal modes. Knowledge of these new modes is obtained through the window of frequency-domain spectroscopy, using techniques of nonlinear classical dynamics. It may soon be possible to "watch" molecular rearrangement reactions spectroscopically. Connections are being made with reaction rate theories, condensed phase systems, and motions of electrons in quantum dots.

Dynamic facial expressions of emotion transmit an evolving hierarchy of signals over time.

PubMed

Jack, Rachael E; Garrod, Oliver G B; Schyns, Philippe G

2014-01-20

Designed by biological and social evolutionary pressures, facial expressions of emotion comprise specific facial movements to support a near-optimal system of signaling and decoding. Although highly dynamical, little is known about the form and function of facial expression temporal dynamics. Do facial expressions transmit diagnostic signals simultaneously to optimize categorization of the six classic emotions, or sequentially to support a more complex communication system of successive categorizations over time? Our data support the latter. Using a combination of perceptual expectation modeling, information theory, and Bayesian classifiers, we show that dynamic facial expressions of emotion transmit an evolving hierarchy of "biologically basic to socially specific" information over time. Early in the signaling dynamics, facial expressions systematically transmit few, biologically rooted face signals supporting the categorization of fewer elementary categories (e.g., approach/avoidance). Later transmissions comprise more complex signals that support categorization of a larger number of socially specific categories (i.e., the six classic emotions). Here, we show that dynamic facial expressions of emotion provide a sophisticated signaling system, questioning the widely accepted notion that emotion communication is comprised of six basic (i.e., psychologically irreducible) categories, and instead suggesting four. Copyright © 2014 Elsevier Ltd. All rights reserved.

Reaction rate theory: What it was, where is it today, and where is it going?

NASA Astrophysics Data System (ADS)

Pollak, Eli; Talkner, Peter

2005-06-01

A brief history is presented, outlining the development of rate theory during the past century. Starting from Arrhenius [Z. Phys. Chem. 4, 226 (1889)], we follow especially the formulation of transition state theory by Wigner [Z. Phys. Chem. Abt. B 19, 203 (1932)] and Eyring [J. Chem. Phys. 3, 107 (1935)]. Transition state theory (TST) made it possible to obtain quick estimates for reaction rates for a broad variety of processes even during the days when sophisticated computers were not available. Arrhenius' suggestion that a transition state exists which is intermediate between reactants and products was central to the development of rate theory. Although Wigner gave an abstract definition of the transition state as a surface of minimal unidirectional flux, it took almost half of a century until the transition state was precisely defined by Pechukas [Dynamics of Molecular Collisions B, edited by W. H. Miller (Plenum, New York, 1976)], but even this only in the realm of classical mechanics. Eyring, considered by many to be the father of TST, never resolved the question as to the definition of the activation energy for which Arrhenius became famous. In 1978, Chandler [J. Chem. Phys. 68, 2959 (1978)] finally showed that especially when considering condensed phases, the activation energy is a free energy, it is the barrier height in the potential of mean force felt by the reacting system. Parallel to the development of rate theory in the chemistry community, Kramers published in 1940 [Physica (Amsterdam) 7, 284 (1940)] a seminal paper on the relation between Einstein's theory of Brownian motion [Einstein, Ann. Phys. 17, 549 (1905)] and rate theory. Kramers' paper provided a solution for the effect of friction on reaction rates but left us also with some challenges. He could not derive a uniform expression for the rate, valid for all values of the friction coefficient, known as the Kramers turnover problem. He also did not establish the connection between his approach and the TST developed by the chemistry community. For many years, Kramers' theory was considered as providing a dynamic correction to the thermodynamic TST. Both of these questions were resolved in the 1980s when Pollak [J. Chem. Phys. 85, 865 (1986)] showed that Kramers' expression in the moderate to strong friction regime could be derived from TST, provided that the bath, which is the source of the friction, is handled at the same level as the system which is observed. This then led to the Mel'nikov-Pollak-Grabert-Hänggi [Mel'nikov and Meshkov, J. Chem. Phys. 85, 1018 (1986); Pollak, Grabert, and Hänggi, J. Chem. Phys. 91, 4073 (1989)] solution of the turnover problem posed by Kramers. Although classical rate theory reached a high level of maturity, its quantum analog leaves the theorist with serious challenges to this very day. As noted by Wigner [Trans. Faraday Soc. 34, 29 (1938)], TST is an inherently classical theory. A definite quantum TST has not been formulated to date although some very useful approximate quantum rate theories have been invented. The successes and challenges facing quantum rate theory are outlined. An open problem which is being investigated intensively is rate theory away from equilibrium. TST is no longer valid and cannot even serve as a conceptual guide for understanding the critical factors which determine rates away from equilibrium. The nonequilibrium quantum theory is even less well developed than the classical, and suffers from the fact that even today, we do not know how to solve the real time quantum dynamics for systems with "many" degrees of freedom.

On the Relationship Between Classical Test Theory and Item Response Theory: From One to the Other and Back.

PubMed

Raykov, Tenko; Marcoulides, George A

2016-04-01

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete nature of the observed items. Two distinct observational equivalence approaches are outlined that render the item response models from corresponding classical test theory-based models, and can each be used to obtain the former from the latter models. Similarly, classical test theory models can be furnished using the reverse application of either of those approaches from corresponding item response models.

On the transition between two-phase and single-phase interface dynamics in multicomponent fluids at supercritical pressures

NASA Astrophysics Data System (ADS)

Dahms, Rainer N.; Oefelein, Joseph C.

2013-09-01

A theory that explains the operating pressures where liquid injection processes transition from exhibiting classical two-phase spray atomization phenomena to single-phase diffusion-dominated mixing is presented. Imaging from a variety of experiments have long shown that under certain conditions, typically when the pressure of the working fluid exceeds the thermodynamic critical pressure of the liquid phase, the presence of discrete two-phase flow processes become diminished. Instead, the classical gas-liquid interface is replaced by diffusion-dominated mixing. When and how this transition occurs, however, is not well understood. Modern theory still lacks a physically based model to quantify this transition and the precise mechanisms that lead to it. In this paper, we derive a new model that explains how the transition occurs in multicomponent fluids and present a detailed analysis to quantify it. The model applies a detailed property evaluation scheme based on a modified 32-term Benedict-Webb-Rubin equation of state that accounts for the relevant real-fluid thermodynamic and transport properties of the multicomponent system. This framework is combined with Linear Gradient Theory, which describes the detailed molecular structure of the vapor-liquid interface region. Our analysis reveals that the two-phase interface breaks down not necessarily due to vanishing surface tension forces, but due to thickened interfaces at high subcritical temperatures coupled with an inherent reduction of the mean free molecular path. At a certain point, the combination of reduced surface tension, the thicker interface, and reduced mean free molecular path enter the continuum length scale regime. When this occurs, inter-molecular forces approach that of the multicomponent continuum where transport processes dominate across the interfacial region. This leads to a continuous phase transition from compressed liquid to supercritical mixture states. Based on this theory, a regime diagram for liquid injection is developed that quantifies the conditions under which classical sprays transition to dense-fluid jets. It is shown that the chamber pressure required to support diffusion-dominated mixing dynamics depends on the composition and temperature of the injected liquid and ambient gas. To illustrate the method and analysis, we use conditions typical of diesel engine injection. We also present a companion set of high-speed images to provide experimental validation of the presented theory. The basic theory is quite general and applies to a wide range of modern propulsion and power systems such as liquid rockets, gas turbines, and reciprocating engines. Interestingly, the regime diagram associated with diesel engine injection suggests that classical spray phenomena at typical injection conditions do not occur.

Nonlinear Synergistic Emergence and Predictability in Complex Systems: Theory and Hydro-Climatic Applications

NASA Astrophysics Data System (ADS)

Perdigão, Rui A. P.; Hall, Julia; Pires, Carlos A. L.; Blöschl, Günter

2017-04-01

Classical and stochastic dynamical system theories assume structural coherence and dynamic recurrence with invariants of motion that are not necessarily so. These are grounded on the unproven assumption of universality in the dynamic laws derived from statistical kinematic evaluation of non-representative empirical records. As a consequence, the associated formulations revolve around a restrictive set of configurations and intermittencies e.g. in an ergodic setting, beyond which any predictability is essentially elusive. Moreover, dynamical systems are fundamentally framed around dynamic codependence among intervening processes, i.e. entail essentially redundant interactions such as couplings and feedbacks. That precludes synergistic cooperation among processes that, whilst independent from each other, jointly produce emerging dynamic behaviour not present in any of the intervening parties. In order to overcome these fundamental limitations, we introduce a broad class of non-recursive dynamical systems that formulate dynamic emergence of unprecedented states in a fundamental synergistic manner, with fundamental principles in mind. The overall theory enables innovations to be predicted from the internal system dynamics before any a priori information is provided about the associated dynamical properties. The theory is then illustrated to anticipate, from non-emergent records, the spatiotemporal emergence of multiscale hyper chaotic regimes, critical transitions and structural coevolutionary changes in synthetic and real-world complex systems. Example applications are provided within the hydro-climatic context, formulating and dynamically forecasting evolving hydro-climatic distributions, including the emergence of extreme precipitation and flooding in a structurally changing hydro-climate system. Validation is then conducted with a posteriori verification of the simulated dynamics against observational records. Agreement between simulations and observations is confirmed with robust nonlinear information diagnostics.

Quantum gravity in timeless configuration space

NASA Astrophysics Data System (ADS)

Gomes, Henrique

2017-12-01

On the path towards quantum gravity we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims to attenuate that friction, by encoding gravity in the timeless configuration space of spatial fields with dynamics given by a path integral. The framework demands that boundary conditions for this path integral be uniquely given, but unlike other approaches where they are prescribed—such as the no-boundary and the tunneling proposals—here I postulate basic principles to identify boundary conditions in a large class of theories. Uniqueness arises only if a reduced configuration space can be defined and if it has a profoundly asymmetric fundamental structure. These requirements place strong restrictions on the field and symmetry content of theories encompassed here; shape dynamics is one such theory. When these constraints are met, any emerging theory will have a Born rule given merely by a particular volume element built from the path integral in (reduced) configuration space. Also as in other boundary proposals, Time, including space-time, emerges as an effective concept; valid for certain curves in configuration space but not assumed from the start. When some such notion of time becomes available, conservation of (positive) probability currents ensues. I show that, in the appropriate limits, a Schrödinger equation dictates the evolution of weakly coupled source fields on a classical gravitational background. Due to the asymmetry of reduced configuration space, these probabilities and currents avoid a known difficulty of standard WKB approximations for Wheeler DeWitt in minisuperspace: the selection of a unique Hamilton–Jacobi solution to serve as background. I illustrate these constructions with a simple example of a full quantum gravitational theory (i.e. not in minisuperspace) for which the formalism is applicable, and give a formula for calculating gravitational semi-classical relative probabilities in it.

Tree-level correlations in the strong field regime

NASA Astrophysics Data System (ADS)

Gelis, François

2017-09-01

We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.

Role of stacking disorder in ice nucleation

NASA Astrophysics Data System (ADS)

Lupi, Laura; Hudait, Arpa; Peters, Baron; Grünwald, Michael; Gotchy Mullen, Ryan; Nguyen, Andrew H.; Molinero, Valeria

2017-11-01

The freezing of water affects the processes that determine Earth’s climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates. Such rate predictions are based on extrapolations using classical nucleation theory, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling and free energy calculations with the mW water model to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

NASA Astrophysics Data System (ADS)

Gerstmayr, Johannes; Irschik, Hans

2008-12-01

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

Role of stacking disorder in ice nucleation.

PubMed

Lupi, Laura; Hudait, Arpa; Peters, Baron; Grünwald, Michael; Gotchy Mullen, Ryan; Nguyen, Andrew H; Molinero, Valeria

2017-11-08

The freezing of water affects the processes that determine Earth's climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates. Such rate predictions are based on extrapolations using classical nucleation theory, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling and free energy calculations with the mW water model to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

Stochastic evolutionary dynamics in minimum-effort coordination games

NASA Astrophysics Data System (ADS)

Li, Kun; Cong, Rui; Wang, Long

2016-08-01

The minimum-effort coordination game draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the predictions of classical game theory. Here, we combine evolutionary game theory and coalescence theory to investigate this game in finite populations. Both analytic results and individual-based simulations show that effort costs play a key role in the evolution of contribution levels, which is in good agreement with those observed experimentally. Besides well-mixed populations, set structured populations have also been taken into consideration. Therein we find that large number of sets and moderate migration rate greatly promote effort levels, especially for high effort costs.

From the limits of the classical model of sensitometric curves to a realistic model based on the percolation theory for GafChromic EBT films.

PubMed

del Moral, F; Vázquez, J A; Ferrero, J J; Willisch, P; Ramírez, R D; Teijeiro, A; López Medina, A; Andrade, B; Vázquez, J; Salvador, F; Medal, D; Salgado, M; Muñoz, V

2009-09-01

Modern radiotherapy uses complex treatments that necessitate more complex quality assurance procedures. As a continuous medium, GafChromic EBT films offer suitable features for such verification. However, its sensitometric curve is not fully understood in terms of classical theoretical models. In fact, measured optical densities and those predicted by the classical models differ significantly. This difference increases systematically with wider dose ranges. Thus, achieving the accuracy required for intensity-modulated radiotherapy (IMRT) by classical methods is not possible, plecluding their use. As a result, experimental parametrizations, such as polynomial fits, are replacing phenomenological expressions in modern investigations. This article focuses on identifying new theoretical ways to describe sensitometric curves and on evaluating the quality of fit for experimental data based on four proposed models. A whole mathematical formalism starting with a geometrical version of the classical theory is used to develop new expressions for the sensitometric curves. General results from the percolation theory are also used. A flat-bed-scanner-based method was chosen for the film analysis. Different tests were performed, such as consistency of the numeric results for the proposed model and double examination using data from independent researchers. Results show that the percolation-theory-based model provides the best theoretical explanation for the sensitometric behavior of GafChromic films. The different sizes of active centers or monomer crystals of the film are the basis of this model, allowing acquisition of information about the internal structure of the films. Values for the mean size of the active centers were obtained in accordance with technical specifications. In this model, the dynamics of the interaction between the active centers of GafChromic film and radiation is also characterized by means of its interaction cross-section value. The percolation model fulfills the accuracy requirements for quality-control procedures when large ranges of doses are used and offers a physical explanation for the film response.

An Application of Evolutionary Game Theory to Social Dilemmas: The Traveler's Dilemma and the Minimum Effort Coordination Game

PubMed Central

Iyer, Swami; Reyes, Joshua; Killingback, Timothy

2014-01-01

The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games. PMID:24709851

An application of evolutionary game theory to social dilemmas: the traveler's dilemma and the minimum effort coordination game.

PubMed

Iyer, Swami; Reyes, Joshua; Killingback, Timothy

2014-01-01

The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games.

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.

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

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

Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Isakov, Sergei V.; Boixo, Sergio; Mazzola, Guglielmo; Troyer, Matthias; Neven, Hartmut

2017-01-01

We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N .

Thermal conductance at atomically clean and disordered silicon/aluminum interfaces: A molecular dynamics simulation study

NASA Astrophysics Data System (ADS)

Ih Choi, Woon; Kim, Kwiseon; Narumanchi, Sreekant

2012-09-01

Thermal resistance between layers impedes effective heat dissipation in electronics packaging applications. Thermal conductance for clean and disordered interfaces between silicon (Si) and aluminum (Al) was computed using realistic Si/Al interfaces and classical molecular dynamics with the modified embedded atom method potential. These realistic interfaces, which include atomically clean as well as disordered interfaces, were obtained using density functional theory. At 300 K, the magnitude of interfacial conductance due to phonon-phonon scattering obtained from the classical molecular dynamics simulations was approximately five times higher than the conductance obtained using analytical elastic diffuse mismatch models. Interfacial disorder reduced the thermal conductance due to increased phonon scattering with respect to the atomically clean interface. Also, the interfacial conductance, due to electron-phonon scattering at the interface, was greater than the conductance due to phonon-phonon scattering. This indicates that phonon-phonon scattering is the bottleneck for interfacial transport at the semiconductor/metal interfaces. The molecular dynamics modeling predictions for interfacial thermal conductance for a 5-nm disordered interface between Si/Al were in-line with recent experimental data in the literature.

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.

Development of a composite tailoring procedure for airplane wing

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Zhang, Sen

1995-01-01

The development of a composite wing box section using a higher order-theory is proposed for accurate and efficient estimation of both static and dynamic responses. The theory includes the effect of through-the-thickness transverse shear deformations which is important in laminated composites and is ignored in the classical approach. The box beam analysis is integrated with an aeroelastic analysis to investigate the effect of composite tailoring using a formal design optimization technique. A hybrid optimization procedure is proposed for addressing both continuous and discrete design variables.

Fractal universe and quantum gravity.

PubMed

Calcagni, Gianluca

2010-06-25

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

Quantum gravity extension of the inflationary scenario.

PubMed

Agullo, Ivan; Ashtekar, Abhay; Nelson, William

2012-12-21

Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This preinflationary dynamics also opens a small window for novel effects, e.g., a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early Universe.

Scale-independent inflation and hierarchy generation

DOE PAGES

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

2016-10-20

We discuss models involving two scalar fields coupled to classical gravity that satisfy the general criteria: (i) the theory has no mass input parameters, (ii) classical scale symmetry is broken only throughmore » $$-\\frac{1}{12}\\varsigma \\phi^2 R$$ couplings where $$\\varsigma$$ departs from the special conformal value of $1$; (iii) the Planck mass is dynamically generated by the vacuum expectations values (VEVs) of the scalars (iv) there is a stage of viable inflation associated with slow roll in the two--scalar potential; (v) the final vacuum has a small to vanishing cosmological constant and an hierarchically small ratio of the VEVs and the ratio of the scalar masses to the Planck scale. In addition, this assumes the paradigm of classical scale symmetry as a custodial symmetry of large hierarchies.« less

Dynamical Crossovers in Prethermal Critical States.

PubMed

Chiocchetta, Alessio; Gambassi, Andrea; Diehl, Sebastian; Marino, Jamir

2017-03-31

We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions

NASA Astrophysics Data System (ADS)

van der Meer, Berend; Lathouwers, Emma; Smallenburg, Frank; Filion, Laura

2017-12-01

Using computer simulations, we study the dynamics and interactions of interstitial particles in hard-sphere interstitial solid solutions. We calculate the free-energy barriers associated with their diffusion for a range of size ratios and densities. By applying classical transition state theory to these free-energy barriers, we predict the diffusion coefficients, which we find to be in good agreement with diffusion coefficients as measured using event-driven molecular dynamics simulations. These results highlight that transition state theory can capture the interstitial dynamics in the hard-sphere model system. Additionally, we quantify the interactions between the interstitials. We find that, apart from excluded volume interactions, the interstitial-interstitial interactions are almost ideal in our system. Lastly, we show that the interstitial diffusivity can be inferred from the large-particle fluctuations alone, thus providing an empirical relationship between the large-particle fluctuations and the interstitial diffusivity.

Deterministic Chaos: Proposal of an Informal Educational Activity Aimed at High School Students

ERIC Educational Resources Information Center

Greco, Valeria; Spagnolo, Salvatore

2016-01-01

Chaos theory is not present in the Italian school curricula and textbooks in spite of being present in many topics of classical physics and in everyday life. Chaotic dynamics, in fact, are involved in phenomena easily accessible to everyone or in events experienced by most people in their lives (the dripping of a faucet which keeps people awoken…

Skinner-Rusk unified formalism for higher-order systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2012-07-01

The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems.

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

Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

Color instabilities in the quark-gluon plasma

NASA Astrophysics Data System (ADS)

Mrówczyński, Stanisław; Schenke, Björn; Strickland, Michael

2017-04-01

When the quark-gluon plasma (QGP) - a system of deconfined quarks and gluons - is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. We begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh-Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, are analyzed in detail. Particular attention is paid to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches - purely classical or quantum - to simulate the temporal evolution of an unstable quark-gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.

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

Mrówczyński, Stanisław; Schenke, Björn; Strickland, Michael

When the quark–gluon plasma (QGP) – a system of deconfined quarks and gluons – is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. Here, we begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh–Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, aremore » analyzed in detail. We pay particular attention to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches – purely classical or quantum – to simulate the temporal evolution of an unstable quark–gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.« less

Molecular dynamics simulations of disjoining pressure effects in ultra-thin water films on a metal surface

NASA Astrophysics Data System (ADS)

Hu, Han; Sun, Ying

2013-11-01

Disjoining pressure, the excess pressure in an ultra-thin liquid film as a result of van der Waals interactions, is important in lubrication, wetting, flow boiling, and thin film evaporation. The classic theory of disjoining pressure is developed for simple monoatomic liquids. However, real world applications often utilize water, a polar liquid, for which fundamental understanding of disjoining pressure is lacking. In the present study, molecular dynamics (MD) simulations are used to gain insights into the effect of disjoining pressure in a water thin film. Our MD models were firstly validated against Derjaguin's experiments on gold-gold interactions across a water film and then verified against disjoining pressure in an argon thin film using the Lennard-Jones potential. Next, a water thin film adsorbed on a gold surface was simulated to examine the change of vapor pressure with film thickness. The results agree well with the classic theory of disjoining pressure, which implies that the polar nature of water molecules does not play an important role. Finally, the effects of disjoining pressure on thin film evaporation in nanoporous membrane and on bubble nucleation are discussed.

Color instabilities in the quark–gluon plasma

DOE PAGES

Mrówczyński, Stanisław; Schenke, Björn; Strickland, Michael

2017-04-09

When the quark–gluon plasma (QGP) – a system of deconfined quarks and gluons – is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. Here, we begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh–Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, aremore » analyzed in detail. We pay particular attention to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches – purely classical or quantum – to simulate the temporal evolution of an unstable quark–gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.« less

On the Relationship between Classical Test Theory and Item Response Theory: From One to the Other and Back

ERIC Educational Resources Information Center

Raykov, Tenko; Marcoulides, George A.

2016-01-01

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

The contrasting roles of Planck's constant in classical and quantum theories

NASA Astrophysics Data System (ADS)

Boyer, Timothy H.

2018-04-01

We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

Quantum dynamical simulation of the scattering of Ar from a frozen LiF(100) surface based on a first principles interaction potential

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

Azuri, Asaf; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il

2015-07-07

In-plane two and three dimensional diffraction patterns are computed for the vertical scattering of an Ar atom from a frozen LiF(100) surface. Suitable collimation of the incoming wavepacket serves to reveal the quantum mechanical diffraction. The interaction potential is based on a fit to an ab initio potential calculated using density functional theory with dispersion corrections. Due to the potential coupling found between the two horizontal surface directions, there are noticeable differences between the quantum angular distributions computed for two and three dimensional scattering. The quantum results are compared to analogous classical Wigner computations on the same surface and withmore » the same conditions. The classical dynamics largely provides the envelope for the quantum diffractive scattering. The classical results also show that the corrugation along the [110] direction of the surface is smaller than along the [100] direction, in qualitative agreement with experimental observations of unimodal and bimodal scattering for the [110] and [100] directions, respectively.« less

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.

Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow

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

Rana, A.; Ravichandran, R.; Park, J. H.

The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method.more » Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23(1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical and non-classical laws remain similar for shear stress and normal heat flux.« less

Investigating chaotic wake dynamics past a flapping airfoil and the role of vortex interactions behind the chaotic transition

NASA Astrophysics Data System (ADS)

Bose, Chandan; Sarkar, Sunetra

2018-04-01

The present study investigates the complex vortex interactions in two-dimensional flow-field behind a symmetric NACA0012 airfoil undergoing a prescribed periodic pitching-plunging motion in low Reynolds number regime. The flow-field transitions from periodic to chaotic through a quasi-periodic route as the plunge amplitude is gradually increased. This study unravels the role of the complex interactions that take place among the main vortex structures in making the unsteady flow-field transition from periodicity to chaos. The leading-edge separation plays a key role in providing the very first trigger for aperiodicity. Subsequent mechanisms like shredding, merging, splitting, and collision of vortices in the near-field that propagate and sustain the disturbance have also been followed and presented. These fundamental mechanisms are seen to give rise to spontaneous and irregular formation of new vortex couples at arbitrary locations, which are the primary agencies for sustaining chaos in the flow-field. The interactions have been studied for each dynamical state to understand the course of transition in the flow-field. The qualitative changes observed in the flow-field are manifestation of changes in the underlying dynamical system. The overall dynamics are established in the present study by means of robust quantitative measures derived from classical and non-classical tools from the dynamical system theory. As the present analysis involves a high fidelity multi-unknown system, non-classical dynamical tools such as recurrence-based time series methods are seen to be very efficient. Moreover, their application is novel in the context of pitch-plunge flapping flight.

Dynamical gauge effects in an open quantum network

NASA Astrophysics Data System (ADS)

Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan

2016-05-01

We describe new experimental techniques for simulation of high-energy field theories based on an analogy between open thermodynamic systems and effective dynamical gauge-fields following SU(2) × U(1) Yang-Mills models. By coupling near-resonant laser-modes to atoms moving in a disordered optical environment, we create an open system which exhibits a non-equilibrium phase transition between two steady-state behaviors, exhibiting scale-invariant behavior near the transition. By measuring transport of atoms through the disordered network, we observe two distinct scaling behaviors, corresponding to the classical and quantum limits for the dynamical gauge field. This behavior is loosely analogous to dynamical gauge effects in quantum chromodynamics, and can mapped onto generalized open problems in theoretical understanding of quantized non-Abelian gauge theories. Additional, the scaling behavior can be understood from the geometric structure of the gauge potential and linked to the measure of information in the local disordered potential, reflecting an underlying holographic principle. We acknowledge support from NSF Award No.1068570, and the Charles E. Kaufman Foundation.

Dynamics of anisotropies close to a cosmological bounce in quantum gravity

NASA Astrophysics Data System (ADS)

de Cesare, Marco; Oriti, Daniele; Pithis, Andreas G. A.; Sakellariadou, Mairi

2018-01-01

We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of SU(2) , and in the regime of the effective cosmological dynamics corresponding to the bouncing region replacing the classical singularity, well approximated by the free GFT dynamics. In this particular example, we identify a region in the parameter space of the model such that perturbations can be large at the bounce but become negligible away from it, i.e. when the background enters the non-linear regime. We also study the departures from perfect isotropy by introducing specific quantities, such as the surface-area-to-volume ratio and the effective volume per quantum, which make them quantitative.

Steinberg ``AUDIOMAPS" Music Appreciation-Via-Understanding: Special-Relativity + Expectations "Quantum-Theory": a Quantum-ACOUSTO/MUSICO-Dynamics (QA/MD)

NASA Astrophysics Data System (ADS)

Steinberg, R.; Siegel, E.

2010-03-01

``AUDIOMAPS'' music enjoyment/appreciation-via-understanding methodology, versus art, music-dynamics evolves, telling a story in (3+1)-dimensions: trails, frames, timbres, + dynamics amplitude vs. music-score time-series (formal-inverse power- spectrum) surprisingly closely parallels (3+1)-dimensional Einstein(1905) special-relativity ``+'' (with its enjoyment- expectations) a manifestation of quantum-theory expectation- values, together a music quantum-ACOUSTO/MUSICO-dynamics (QA/MD). Analysis via Derrida deconstruction enabled Siegel- Baez ``Category-Semantics'' ``FUZZYICS''=``CATEGORYICS (``SON of 'TRIZ") classic Aristotle ``Square-of-Opposition" (SoO) DEduction-logic, irrespective of Boon-Klimontovich versus Voss- Clark[PRL(77)] music power-spectrum analysis sampling- time/duration controversy: part versus whole, shows that ``AUDIOMAPS" QA/MD reigns supreme as THE music appreciation-via- analysis tool for the listener in musicology!!! Connection to Deutsch-Hartmann-Levitin[This is Your Brain on Music,(2006)] brain/mind-barrier brain/mind-music connection is both subtle and compelling and immediate!!!

Taking-On: A Grounded Theory of Addressing Barriers in Task Completion

ERIC Educational Resources Information Center

Austinson, Julie Ann

2011-01-01

This study of taking-on was conducted using classical grounded theory methodology (Glaser, 1978, 1992, 1998, 2001, 2005; Glaser & Strauss, 1967). Classical grounded theory is inductive, empirical, and naturalistic; it does not utilize manipulation or constrained time frames. Classical grounded theory is a systemic research method used to generate…

Bounds on the power of proofs and advice in general physical theories.

PubMed

Lee, Ciarán M; Hoban, Matty J

2016-06-01

Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that [Formula: see text] is contained in [Formula: see text], which does not make use of any uniquely quantum structure-such as the fact that observables correspond to self-adjoint operators-and thus may be of independent interest.

Classical nucleation theory in the phase-field crystal model

NASA Astrophysics Data System (ADS)

Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas

2018-04-01

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

Classical nucleation theory in the phase-field crystal model.

PubMed

Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas

2018-04-01

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

Fully compressible solutions for early stage Richtmyer–Meshkov instability

DOE PAGES

Margolin, Len G.; Reisner, Jon Michael

2016-10-27

Here, we will consider the effects of compressibility and viscosity on the early dynamics of the Richtmyer–Meshkov instability (RMI). In particular, we will combine theory, scaling, and high resolution simulation of RMI to probe the details of the initial compression and the subsequent viscous damping as a shock interacts with a density discontinuity. We will propose a refinement of the classic 1D model for the linear regime of RMI that, for small initial perturbation wavelengths, more accurately reproduces the 2D dynamics of a fully resolved numerical simulation.

Hamiltonization of Solids of Revolution Through Reduction

NASA Astrophysics Data System (ADS)

Balseiro, Paula

2017-12-01

In this paper, we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of Balseiro (Arch Ration Mech Anal 214:453-501, 2014) and Balseiro and Garcia-Naranjo (Arch Ration Mech Anal 205(1):267-310, 2012). We illustrate the theory with classical examples describing the dynamics of solids of revolution rolling without sliding on a plane. In these cases, using the existence of two conserved quantities we obtain, by means of gauge transformations and symmetry reduction, genuine Poisson brackets describing the reduced dynamics.

Robust Control Analysis of Hydraulic Turbine Speed

NASA Astrophysics Data System (ADS)

Jekan, P.; Subramani, C.

2018-04-01

An effective control strategy for the hydro-turbine governor in time scenario is adjective for this paper. Considering the complex dynamic characteristic and the uncertainty of the hydro-turbine governor model and taking the static and dynamic performance of the governing system as the ultimate goal, the designed logic combined the classical PID control theory with artificial intelligence used to obtain the desired output. The used controller will be a variable control techniques, therefore, its parameters can be adaptively adjusted according to the information about the control error signal.

A reformulation of mechanics and electrodynamics.

PubMed

Pinheiro, Mario J

2017-07-01

Classical mechanics, as commonly taught in engineering and science, are confined to the conventional Newtonian theory. But classical mechanics has not really changed in substance since Newton formulation, describing simultaneous rotation and translation of objects with somewhat complicate drawbacks, risking interpretation of forces in non-inertial frames. In this work we introduce a new variational principle for out-of-equilibrium, rotating systems, obtaining a set of two first order differential equations that introduces a thermodynamic-mechanistic time into Newton's dynamical equation, and revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. The results is a more consistent formulation of dynamics and electrodynamics, explaining natural phenomena as the outcome from a balance between energy and entropy, embedding translational with rotational motion into a single equation, showing centrifugal and Coriolis force as derivatives from the transport of angular momentum, and offering a natural method to handle variational problems, as shown with the brachistochrone problem. In consequence, a new force term appears, the topological torsion current, important for spacecraft dynamics. We describe a set of solved problems showing the potential of a competing technique, with significant interest to electrodynamics as well. We expect this new approach to have impact in a large class of scientific and technological problems.

On the classic and modern theories of matching.

PubMed

McDowell, J J

2005-07-01

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.

Projective limits of state spaces I. Classical formalism

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2017-01-01

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski (1977) and Andrzej Okołów (2009, 2013, 2014), which describes the states of a quantum (field) theory as projective families of density matrices. A short reading guide to the series can be found in [27]. The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds [27, subsection 2.1]. In particular, this allows us to discuss accurately the issues hindering an easy implementation of the dynamics in this context, and to formulate a strategy for overcoming them [27, subsection 4.1].

Classical Coset Hamiltonian for the Electronic Motion and its Application to Anderson Localization and Hammett Equation

NASA Astrophysics Data System (ADS)

Xing, Guan; Wu, Guo-Zhen

2001-02-01

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings of this algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.

General Relativity without paradigm of space-time covariance, and resolution of the problem of time

NASA Astrophysics Data System (ADS)

Soo, Chopin; Yu, Hoi-Lai

2014-01-01

The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full space-time covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. The deep divide between quantum mechanics and conventional canonical formulations of quantum gravity is overcome with a Schrödinger equation for quantum geometrodynamics that describes evolution in intrinsic time. Unitary time development with gauge-invariant temporal ordering is also viable. All Kuchar observables become physical; and classical space-time, with direct correlation between its proper times and intrinsic time intervals, emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein's theory, but also prompts natural extensions and improvements towards a well behaved quantum theory of gravity. It is a consistent canonical scheme to discuss Horava-Lifshitz theories with intrinsic time evolution, and of the many possible alternatives that respect 3-covariance (rather than the more restrictive 4-covariance of Einstein's theory), Horava's "detailed balance" form of the Hamiltonian constraint is essentially pinned down by this framework. Issues in quantum gravity that depend on radiative corrections and the rigorous definition and regularization of the Hamiltonian operator are not addressed in this work.

Theories of Matter, Space and Time; Classical theories

NASA Astrophysics Data System (ADS)

Evans, N.; King, S. F.

2017-12-01

This book and its sequel ('Theories of Matter Space and Time: Quantum Theories') are taken from third and fourth year undergraduate Physics courses at Southampton University, UK. The aim of both books is to move beyond the initial courses in classical mechanics, special relativity, electromagnetism, and quantum theory to more sophisticated views of these subjects and their interdependence. The goal is to guide undergraduates through some of the trickier areas of theoretical physics with concise analysis while revealing the key elegance of each subject. The first chapter introduces the key areas of the principle of least action, an alternative treatment of Newtownian dynamics, that provides new understanding of conservation laws. In particular, it shows how the formalism evolved from Fermat's principle of least time in optics. The second introduces special relativity leading quickly to the need and form of four-vectors. It develops four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment; then returns to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again, it then returns to the action principle to formulate minimal substitution for an electrically charged particle.

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.

Neural dynamic optimization for control systems. I. Background.

PubMed

Seong, C Y; Widrow, B

2001-01-01

The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper mainly describes the background and motivations for the development of NDO, while the two other subsequent papers of this topic present the theory of NDO and demonstrate the method with several applications including control of autonomous vehicles and of a robot arm, respectively.

Neural dynamic optimization for control systems.III. Applications.

PubMed

Seong, C Y; Widrow, B

2001-01-01

For pt.II. see ibid., p. 490-501. The paper presents neural dynamic optimization (NDO) as a method of optimal feedback control for nonlinear multi-input-multi-output (MIMO) systems. The main feature of NDO is that it enables neural networks to approximate the optimal feedback solution whose existence dynamic programming (DP) justifies, thereby reducing the complexities of computation and storage problems of the classical methods such as DP. This paper demonstrates NDO with several applications including control of autonomous vehicles and of a robot-arm, while the two other companion papers of this topic describes the background for the development of NDO and present the theory of the method, respectively.

Classical Field Theory and the Stress-Energy Tensor

NASA Astrophysics Data System (ADS)

Swanson, Mark S.

2015-09-01

This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory. The variational form of classical mechanics and continuum field theory are both developed in the time-honored graduate level text by Goldstein et al (2001). An introduction to classical field theory from a somewhat different perspective is available in Soper (2008). Basic classical field theory is often treated in books on quantum field theory. Two excellent texts where this is done are Greiner and Reinhardt (1996) and Peskin and Schroeder (1995). Green's function techniques are presented in Arfken et al (2013).

The Mochi project: a field theory approach to plasma dynamics and self-organization

NASA Astrophysics Data System (ADS)

You, Setthivoine; von der Linden, Jens; Lavine, Eric Sander; Card, Alexander; Carroll, Evan

2016-10-01

The Mochi project is designed to study the interaction between plasma flows and magnetic fields from the point-of-view of canonical flux tubes. The Mochi Labjet experiment is being commissioned after achieving first plasma. Analytical and numerical tools are being developed to visualize canonical flux tubes. One analytical tool described here is a field theory approach to plasma dynamics and self-organization. A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. This work is supported by by US DOE Grant DE-SC0010340.

A kinetic theory for age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Chou, Tom; Greenman, Chris

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.

Survival and weak chaos.

PubMed

Nee, Sean

2018-05-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Survival and weak chaos

PubMed Central

2018-01-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as ‘infant mortality’. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality—sensu engineering—without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy. PMID:29892407

Adaptive modeling, identification, and control of dynamic structural systems. I. Theory

USGS Publications Warehouse

Safak, Erdal

1989-01-01

A concise review of the theory of adaptive modeling, identification, and control of dynamic structural systems based on discrete-time recordings is presented. Adaptive methods have four major advantages over the classical methods: (1) Removal of the noise from the signal is done over the whole frequency band; (2) time-varying characteristics of systems can be tracked; (3) systems with unknown characteristics can be controlled; and (4) a small segment of the data is needed during the computations. Included in the paper are the discrete-time representation of single-input single-output (SISO) systems, models for SISO systems with noise, the concept of stochastic approximation, recursive prediction error method (RPEM) for system identification, and the adaptive control. Guidelines for model selection and model validation and the computational aspects of the method are also discussed in the paper. The present paper is the first of two companion papers. The theory given in the paper is limited to that which is necessary to follow the examples for applications in structural dynamics presented in the second paper.

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.

Comprehensive study of the dynamics of a classical Kitaev Spin Liquid

NASA Astrophysics Data System (ADS)

Samarakoon, Anjana; Banerjee, Arnab; Batista, Cristian; Kamiya, Yoshitomo; Tennant, Alan; Nagler, Stephen

Quantum spin liquids (QSLs) have achieved great interest in both theoretical and experimental condensed matter physics due to their remarkable topological properties. Among many different candidates, the Kitaev model on the honeycomb lattice is a 2D prototypical QSL which can be experimentally studied in materials based on iridium or ruthenium.Here we study the spin-1/2 Kitaev model using classical Monte-Carlo and semiclassical spin dynamics of classical spins on a honeycomb lattice. Both real and reciprocal space pictures highlighting the differences and similarities of the results to the linear spin wave theory will be discussed in terms dispersion relations of the pure-Kitaev limit and beyond. Interestingly, this technique could capture some of the salient features of the exact quantum solution of the Kitaev model, such as features resembling the Majorana-like mode comparable to the Kitaev energy, which is spectrally narrowed compared to the quantum result, can be explained by magnon excitations on fluctuating onedimensional manifolds (loops). Hence the difference from the classical limit to the quantum limit can be understood by the fractionalization of a magnon to Majorana fermions. The calculations will be directly compared with our neutron scattering data on α-RuCl3 which is a prime candidate for experimental realization of Kitaev physics.

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium.

PubMed

Qian, Hong; Beard, Daniel A

2005-04-22

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.

Efficient Quantum Pseudorandomness.

PubMed

Brandão, Fernando G S L; Harrow, Aram W; Horodecki, Michał

2016-04-29

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in many cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.

Normalization in Lie algebras via mould calculus and applications

NASA Astrophysics Data System (ADS)

Paul, Thierry; Sauzin, David

2017-11-01

We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.

First-principles simulations of heat transport

NASA Astrophysics Data System (ADS)

Puligheddu, Marcello; Gygi, Francois; Galli, Giulia

2017-11-01

Advances in understanding heat transport in solids were recently reported by both experiment and theory. However an efficient and predictive quantum simulation framework to investigate thermal properties of solids, with the same complexity as classical simulations, has not yet been developed. Here we present a method to compute the thermal conductivity of solids by performing ab initio molecular dynamics at close to equilibrium conditions, which only requires calculations of first-principles trajectories and atomic forces, thus avoiding direct computation of heat currents and energy densities. In addition the method requires much shorter sequential simulation times than ordinary molecular dynamics techniques, making it applicable within density functional theory. We discuss results for a representative oxide, MgO, at different temperatures and for ordered and nanostructured morphologies, showing the performance of the method in different conditions.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

NASA Astrophysics Data System (ADS)

Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

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

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling.

PubMed

Bonfanti, Matteo; Jackson, Bret; Hughes, Keith H; Burghardt, Irene; Martinazzo, Rocco

2015-09-28

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics.

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.

Proton relays in anomalous carbocations dictate spectroscopy, stability, and mechanisms: case studies on C2H5+ and C3H3.

PubMed

Sager, LeeAnn M; Iyengar, Srinivasan S

2017-10-18

We present a detailed analysis of the anomalous carbocations: C 2 H 5 + and C 3 H 3 + . This work involves (a) probing electronic structural properties, (b) ab initio dynamics simulations over a range of internal energies, (c) analysis of reduced dimensional potential surfaces directed along selected conformational transition pathways, (d) dynamically averaged vibrational spectra computed from ab initio dynamics trajectories, and (e) two-dimensional time-frequency analysis to probe conformational dynamics. Key findings are as follows: (i) as noted in our previous study on C 2 H 3 + , it appears that these non-classical carbocations are stabilized by delocalized nuclear frameworks and "proton shuttles". We analyze this nuclear delocalization and find critical parallels between conformational changes in C 2 H 3 + , C 2 H 5 + , and C 3 H 3 + . (ii) The vibrational signatures of C 2 H 5 + are dominated by the "bridge-proton" conformation, but also show critical contributions from the "classical" configuration, which is a transition state at almost all levels of theory. This result is further substantiated through two-dimensional time-frequency analysis and is at odds with earlier explanations of the experimental spectra, where frequencies close to the classical region were thought to arise from an impurity. While this is still possible, our results here indicate an additional (perhaps more likely) explanation that involves the "classical" isomer. (iii) Finally, in the case of C 3 H 3 + our explanation of the experimental result includes the presence of multiple, namely, "cyclic", "straight", and propargyl, configurations. Proton shuttles and nuclear delocalization, reminiscent of those seen in the case of C 2 H 3 + , were seen all through and have a critical role in all our observations.

Molecular dynamics approach to dissipative relativistic hydrodynamics: Propagation of fluctuations

NASA Astrophysics Data System (ADS)

Shahsavar, Leila; Ghodrat, Malihe; Montakhab, Afshin

2016-12-01

Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of first-order hydrodynamic theories for nonperfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity, and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected, in the low temperature classical regime all theories give the same results, consistent with the numerics. In the high temperature extremely relativistic regime, not all considered theories are distinguishable from one another. However, in the intermediate regime, a meaningful distinction exists in the predictions of various theories considered here. We find that the predictions of the recent formulation due to Tsumura, Kunihiro, and Ohnishi are more consistent with our numerical results than the traditional theories: the Meixner, modified Eckart, and modified Marle-Stewart theories.

Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Collapse of the soap-film bridge - Quasistatic description

NASA Astrophysics Data System (ADS)

Cryer, Steven A.; Steen, Paul H.

1992-11-01

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.

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.

Perpetual extraction of work from a nonequilibrium dynamical system under Markovian feedback control

NASA Astrophysics Data System (ADS)

Kosugi, Taichi

2013-09-01

By treating both control parameters and dynamical variables as probabilistic variables, we develop a succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a Markovian feedback control. It is demonstrated that a problem for perpetual extraction of work in a nonequilibrium system is reduced to a problem of Markov chain in the higher-dimensional phase space. We derive a version of the detailed fluctuation theorem, which was originally derived for classical nonequilibrium systems by Horowitz and Vaikuntanathan [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.82.061120 82, 061120 (2010)], in a form suitable for the analyses of perpetual extraction of work. Since our theory is formulated for generic dynamics of probability distribution function in phase space, its application to a physical system is straightforward. As simple applications of the theory, two exactly solvable models are analyzed. The one is a nonequilibrium two-state system and the other is a particle confined to a one-dimensional harmonic potential in thermal equilibrium. For the former example, it is demonstrated that the observer on the transitory steps to the stationary state can lose energy and that work larger than that achieved in the stationary state can be extracted. For the latter example, it is demonstrated that the optimal protocol for the extraction of work via repeated measurements can differ from that via a single measurement. The validity of our version of the detailed fluctuation theorem, which determines the upper bound of the expected work in the stationary state, is also confirmed for both examples. These observations provide useful insights into exploration for realistic modeling of a machine that extracts work from its environment.

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

Driven topological systems in the classical limit

NASA Astrophysics Data System (ADS)

Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel

2017-03-01

Periodically driven quantum systems can exhibit topologically nontrivial behavior, even when their quasienergy bands have zero Chern numbers. Much work has been conducted on noninteracting quantum-mechanical models where this kind of behavior is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The noninteracting model, proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013), 10.1103/PhysRevX.3.031005], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time-dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.

Characterization of classical static noise via qubit as probe

NASA Astrophysics Data System (ADS)

Javed, Muhammad; Khan, Salman; Ullah, Sayed Arif

2018-03-01

The dynamics of quantum Fisher information (QFI) of a single qubit coupled to classical static noise is investigated. The analytical relation for QFI fixes the optimal initial state of the qubit that maximizes it. An approximate limit for the time of coupling that leads to physically useful results is identified. Moreover, using the approach of quantum estimation theory and the analytical relation for QFI, the qubit is used as a probe to precisely estimate the disordered parameter of the environment. Relation for optimal interaction time with the environment is obtained, and condition for the optimal measurement of the noise parameter of the environment is given. It is shown that all values, in the mentioned range, of the noise parameter are estimable with equal precision. A comparison of our results with the previous studies in different classical environments is made.

Influence of Material Distribution on Impact Resistance of Hybrid Composites

NASA Technical Reports Server (NTRS)

Abatan, Ayu; Hu, Hurang

1998-01-01

Impact events occur in a wide variety of circumstances. A typical example is a bullet impacting a target made of composite material. These impact events produce time-varying loads on a structure that can result in damage. As a first step to understanding the damage resistance issue in composite laminates, an accurate prediction of the transient response during an impact event is necessary. The analysis of dynamic loadings on laminated composite plates has undergone considerable development recently. Rayleigh-Ritz energy method was used to determine the impact response of laminated plates. The impact response of composite plates using shear deformation plate theory was analyzed. In recent work a closed-form solution was obtained for a rectangular plate with four edges simply supported subjected to a center impact load using classical plate theory. The problem was further investigated and the analysis results compared of both classical plate theory and shear deformation theory, and found that classical plate theory predicts very accurate results for the range of small deformations considered. In this study, the influence of cross sectional material distribution on the comparative impact responses of hybrid metal laminates subjected to low and medium velocity impacts is investigated. A simple linear model to evaluate the magnitude of the impact load is proposed first, and it establishes a relation between the impact velocity and the impact force. Then a closed-form solution for impact problem is presented. The results were compared with the finite element analysis results. For an 11 layer-hybrid laminate, the impact response as a function of material distribution in cross-section is presented. With equal areal weight, the effect of the number of laminate layers on the impact resistance is also investigated. Finally, the significance of the presented results is discussed.

Nonrelativistic para-Lorentzian mechanics

NASA Astrophysics Data System (ADS)

Vargas, J. G.

1981-04-01

After reviewing the foundations of special relativity and the room left for rival theories, a set of nonrelativistic para-Lorentzian transformations is derived uniquely, based on (a) a weaker first principle, (b) the requirement that the transformations sought do not give rise to the clock “paradox” (in a refined version), and (c) the compliance of the transformations with the classical experiments of Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell. The corresponding dynamics is developed. Most of the experimental support of special relativity is reconsidered in the light of the new theory. It is concluded that the relativity of simultaneity has so far not been tested.

Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench.

PubMed

Banerjee, D; Dalmonte, M; Müller, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P

2012-10-26

Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

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)].

Electronic Properties of High-Tc Superconductors. The Normal and the Superconducting State of High-Tc Materials. Proceedings of the International Winter School held in Kirchberg, Tyrol on March 7 - 14, 1992

DTIC Science & Technology

1992-03-14

overdoped Lal. 66 Sr0 34 CuO4 . 1. Introduction Understanding the normal state charge and spin dynamics of cuprates is closely tied to an explanation of high...frequency of the tank circuit of 160 MHz. As predicted by theory [191, the SQUID noise is reduced significantly when using the higher frequency. This...emphasized that the spin excitation gap is not decreasing with temperature as expected in the classical BCS theory . An other astonishing result is

Application of Canonical Effective Methods to Background-Independent Theories

NASA Astrophysics Data System (ADS)

Buyukcam, Umut

Effective formalisms play an important role in analyzing phenomena above some given length scale when complete theories are not accessible. In diverse exotic but physically important cases, the usual path-integral techniques used in a standard Quantum Field Theory approach seldom serve as adequate tools. This thesis exposes a new effective method for quantum systems, called the Canonical Effective Method, which owns particularly wide applicability in backgroundindependent theories as in the case of gravitational phenomena. The central purpose of this work is to employ these techniques to obtain semi-classical dynamics from canonical quantum gravity theories. Application to non-associative quantum mechanics is developed and testable results are obtained. Types of non-associative algebras relevant for magnetic-monopole systems are discussed. Possible modifications of hypersurface deformation algebra and the emergence of effective space-times are presented. iii.

A model of adaptive decision-making from representation of information environment by quantum fields.

PubMed

Bagarello, F; Haven, E; Khrennikov, A

2017-11-13

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

A model of adaptive decision-making from representation of information environment by quantum fields

NASA Astrophysics Data System (ADS)

Bagarello, F.; Haven, E.; Khrennikov, A.

2017-10-01

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Interactions between Obsessional Symptoms and Interpersonal Ambivalences in Psychodynamic Therapy: An Empirical Case Study

PubMed Central

Cornelis, Shana; Desmet, Mattias; Van Nieuwenhove, Kimberly L. H. D.; Meganck, Reitske; Willemsen, Jochem; Inslegers, Ruth; Feyaerts, Jasper

2017-01-01

The classical symptom specificity hypothesis (Blatt, 1974) particularly associates obsessional symptoms to interpersonal behavior directed at autonomy and separation from others. Cross-sectional group research, however, has yielded inconsistent findings on this predicted association, and a previous empirical case study (Cornelis et al., in press; see Chapter 2) documented obsessional pathology to be rooted in profound ambivalences between autonomous and dependent interpersonal dynamics. Therefore, in the present empirical case study, concrete operationalizations of the classical symptom specificity hypothesis are contrasted to alternative hypotheses based on the observed complexities in Chapter 2. Dynamic associations between obsessional symptoms and interpersonal functioning is further explored, aiming at further contribution to theory building (i.e., through suggestions for potential hypothesis-refinement; Stiles, 2009). Similar to the first empirical case study (Chapter 1), Consensual Qualitative Research for Case studies is used to quantitatively and qualitatively describe the longitudinal, clinical interplay between obsessional symptoms and interpersonal dynamics throughout the process of supportive-expressive psychodynamic therapy. In line with findings from Chapter 1, findings reveal close associations between obsessions and interpersonal dynamics, and therapist interventions focusing on interpersonal conflicts are documented as related to interpersonal and symptomatic alterations. Observations predominantly accord to the ambivalence-hypothesis rather than to the classical symptom specificity hypothesis. Yet, meaningful differences are observed in concrete manifestations of interpersonal ambivalences within significant relationships. Findings are again discussed in light of conceptual and methodological considerations; and limitations and future research indications are addressed. PMID:28649214

Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.; Santhanam, M. S.

2017-01-01

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. Measures of quantum correlations do not have a classical analog and yet are influenced by classical dynamics. In this work, by modeling the quantum kicked top as a multiqubit system, the effect of classical bifurcations on measures of quantum correlations such as the quantum discord, geometric discord, and Meyer and Wallach Q measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of trivial fixed points of the kicked top, the scaling function decays as a power law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the Q measure. We also suggest that it can have experimental consequences.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators.

PubMed

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H-S; Ahn, Jaewook

2018-05-04

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators

NASA Astrophysics Data System (ADS)

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H.-S.; Ahn, Jaewook

2018-05-01

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

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).

Generalized classical and quantum signal theories

NASA Astrophysics Data System (ADS)

Rundblad, E.; Labunets, V.; Novak, P.

2005-05-01

In this paper we develop two topics and show their inter- and cross-relation. The first centers on general notions of the generalized classical signal theory on finite Abelian hypergroups. The second concerns the generalized quantum hyperharmonic analysis of quantum signals (Hermitean operators associated with classical signals). We study classical and quantum generalized convolution hypergroup algebras of classical and quantum signals.

Viable inflationary evolution from Einstein frame loop quantum cosmology

NASA Astrophysics Data System (ADS)

de Haro, Jaume; Odintsov, S. D.; Oikonomou, V. K.

2018-04-01

In this work we construct a bottom-up reconstruction technique for loop quantum cosmology scalar-tensor theories, from the observational indices. Particularly, the reconstruction technique is based on fixing the functional form of the scalar-to-tensor ratio as a function of the e -foldings number. The aim of the technique is to realize viable inflationary scenarios, and the only assumption that must hold true in order for the reconstruction technique to work is that the dynamical evolution of the scalar field obeys the slow-roll conditions. We use two functional forms for the scalar-to-tensor ratio, one of which corresponds to a popular inflationary class of models, the α attractors. For the latter, we calculate the leading order behavior of the spectral index and we demonstrate that the resulting inflationary theory is viable and compatible with the latest Planck and BICEP2/Keck-Array data. In addition, we find the classical limit of the theory, and as we demonstrate, the loop quantum cosmology corrected theory and the classical theory are identical at leading order in the perturbative expansion quantified by the parameter ρc, which is the critical density of the quantum theory. Finally, by using the formalism of slow-roll scalar-tensor loop quantum cosmology, we investigate how several inflationary potentials can be realized by the quantum theory, and we calculate directly the slow-roll indices and the corresponding observational indices. In addition, the f (R ) gravity frame picture is presented.

Mixed quantum-classical simulation of the hydride transfer reaction catalyzed by dihydrofolate reductase based on a mapped system-harmonic bath model

NASA Astrophysics Data System (ADS)

Xu, Yang; Song, Kai; Shi, Qiang

2018-03-01

The hydride transfer reaction catalyzed by dihydrofolate reductase is studied using a recently developed mixed quantum-classical method to investigate the nuclear quantum effects on the reaction. Molecular dynamics simulation is first performed based on a two-state empirical valence bond potential to map the atomistic model to an effective double-well potential coupled to a harmonic bath. In the mixed quantum-classical simulation, the hydride degree of freedom is quantized, and the effective harmonic oscillator modes are treated classically. It is shown that the hydride transfer reaction rate using the mapped effective double-well/harmonic-bath model is dominated by the contribution from the ground vibrational state. Further comparison with the adiabatic reaction rate constant based on the Kramers theory confirms that the reaction is primarily vibrationally adiabatic, which agrees well with the high transmission coefficients found in previous theoretical studies. The calculated kinetic isotope effect is also consistent with the experimental and recent theoretical results.

Break-up dynamics of fluctuating liquid threads

PubMed Central

Petit, Julien; Rivière, David; Kellay, Hamid; Delville, Jean-Pierre

2012-01-01

The thinning dynamics of a liquid neck before break-up, as may happen when a drop detaches from a faucet or a capillary, follows different rules and dynamic scaling laws depending on the importance of inertia, viscous stresses, or capillary forces. If now the thinning neck reaches dimensions comparable to the thermally excited interfacial fluctuations, as for nanojet break-up or the fragmentation of thermally annealed nanowires, these fluctuations should play a dominant role according to recent theory and observations. Using near-critical interfaces, we here fully characterize the universal dynamics of this thermal fluctuation-dominated regime and demonstrate that the cross-over from the classical two-fluid pinch-off scenario of a liquid thread to the fluctuation-dominated regime occurs at a well-defined neck radius proportional to the thermal length scale. Investigating satellite drop formation, we also show that at the level of the cross-over between these two regimes it is more probable to produce monodisperse droplets because fluctuation-dominated pinch-off may allow the unique situation where satellite drop formation can be inhibited. Nonetheless, the interplay between the evolution of the neck profiles from the classical to the fluctuation-dominated regime and the satellites’ production remains to be clarified. PMID:23090994

The Butterfly and the Photon:. New Perspectives on Unpredictability, and the Notion of Casual Reality, in Quantum Physics

NASA Astrophysics Data System (ADS)

Palmer, T. N.

2012-12-01

This essay discusses a proposal that draws together the three great revolutionary theories of 20th Century physics: quantum theory, relativity theory and chaos theory. Motivated by the Bohmian notion of implicate order, and what in chaos theory would be described as a strange attractor, the proposal attributes special ontological significance to certain non-computable, dynamically invariant state-space geometries for the universe as a whole. Studying the phenomenon of quantum interference, it is proposed to understand quantum wave-particle duality, and indeed classical electromagnetism, in terms of particles in space time and waves on this state space geometry. Studying the EPR experiment, the acausal constraints that this invariant geometry provides on spatially distant degrees of freedom, provides a way for the underlying dynamics to be consistent with the Bell theorem, yet be relativistically covariant ("nonlocality without nonlocality"). It is suggested that the physical basis for such non-computable geometries lies in properties of gravity with the information irreversibility implied by black hole no-hair theorems being crucial. In conclusion it is proposed that quantum theory may be emergent from an extended theory of gravity which is geometric not only in space time, but also in state space. Such a notion would undermine most current attempts to "quantise gravity".

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

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.

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

Dang, Liem X.; Vo, Quynh N.; Nilsson, Mikael

We report one of the first simulations using a classical rate theory approach to predict the mechanism of the exchange process between water and aqueous uranyl ions. Using our water and ion-water polarizable force fields and molecular dynamics techniques, we computed the potentials of mean force for the uranyl ion-water pair as the function of pressures at ambient temperature. Subsequently, these simulated potentials of mean force were used to calculate rate constants using the transition rate theory; the time dependent transmission coefficients were also examined using the reactive flux method and Grote-Hynes treatments of the dynamic response of the solvent.more » The computed activation volumes using transition rate theory and the corrected rate constants are positive, thus the mechanism of this particular water-exchange is a dissociative process. We discuss our rate theory results and compare them with previously studies in which non-polarizable force fields were used. This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. The calculations were carried out using computer resources provided by the Office of Basic Energy Sciences.« less

Holography as a highly efficient renormalization group flow. I. Rephrasing gravity

NASA Astrophysics Data System (ADS)

Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan

2016-07-01

We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.

Adsorption of Aqueous Crude Oil Components on the Basal Surfaces of Clay Minerals: Molecular Simulations Including Salinity and Temperature Effects

DOE PAGES

Greathouse, J. A.; Cygan, R. T.; Fredrich, J. T.; ...

2017-09-28

Molecular simulations of the adsorption of representative organic molecules onto the basal surfaces of various clay minerals were used to assess the mechanisms of enhanced oil recovery associated with salinity changes and water flooding. Simulations at the density functional theory (DFT) and classical levels provide insights into the molecular structure, binding energy, and interfacial behavior of saturate, aromatic, and resin molecules near clay mineral surfaces. Periodic DFT calculations reveal binding geometries and ion pairing mechanisms at mineral surfaces while also providing a basis for validating the classical force field approach. Through classical molecular dynamics simulations, the influence of aqueous cationsmore » at the interface and the role of water solvation are examined to better evaluate the dynamical nature of cation-organic complexes and their co-adsorption onto the clay surfaces. The extent of adsorption is controlled by the hydrophilic nature and layer charge of the clay mineral. All organic species studied showed preferential adsorption on hydrophobic mineral surfaces. However, the anionic form of the resin (decahydro-2-naphthoic acid)—expected to be prevalent at near-neutral pH conditions in petroleum reservoirs—readily adsorbs to the hydrophilic kaolinite surface through a combination of cation pairing and hydrogen bonding with surface hydroxyl groups. Analysis of cation-organic pairing in both the adsorbed and desorbed states reveals a strong preference for organic anions to coordinate with divalent calcium ions rather than monovalent sodium ions, lending support to current theories regarding low-salinity water flooding.« less

Adsorption of Aqueous Crude Oil Components on the Basal Surfaces of Clay Minerals: Molecular Simulations Including Salinity and Temperature Effects

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

Greathouse, J. A.; Cygan, R. T.; Fredrich, J. T.

Molecular simulations of the adsorption of representative organic molecules onto the basal surfaces of various clay minerals were used to assess the mechanisms of enhanced oil recovery associated with salinity changes and water flooding. Simulations at the density functional theory (DFT) and classical levels provide insights into the molecular structure, binding energy, and interfacial behavior of saturate, aromatic, and resin molecules near clay mineral surfaces. Periodic DFT calculations reveal binding geometries and ion pairing mechanisms at mineral surfaces while also providing a basis for validating the classical force field approach. Through classical molecular dynamics simulations, the influence of aqueous cationsmore » at the interface and the role of water solvation are examined to better evaluate the dynamical nature of cation-organic complexes and their co-adsorption onto the clay surfaces. The extent of adsorption is controlled by the hydrophilic nature and layer charge of the clay mineral. All organic species studied showed preferential adsorption on hydrophobic mineral surfaces. However, the anionic form of the resin (decahydro-2-naphthoic acid)—expected to be prevalent at near-neutral pH conditions in petroleum reservoirs—readily adsorbs to the hydrophilic kaolinite surface through a combination of cation pairing and hydrogen bonding with surface hydroxyl groups. Analysis of cation-organic pairing in both the adsorbed and desorbed states reveals a strong preference for organic anions to coordinate with divalent calcium ions rather than monovalent sodium ions, lending support to current theories regarding low-salinity water flooding.« less

Cosmic superstrings: Observable remnants of brane inflation

NASA Astrophysics Data System (ADS)

Wyman, Mark Charles

Brane inflation provides a natural dynamical model for the physics which underlie the inflationary paradigm. Besides their inflationary predictions, brane models imply another observable consequence: cosmic strings. In this dissertation I outline the background of how cosmic strings arise in brane inflationary models and how the properties of the strings and the models are mutually tied (Chapter 2). I then use cosmological observations to put limits on the properties of any actually-existing cosmic string network (Chapter 3). Next, I study the question of how cosmic superstrings, as the cosmic strings arising from string theory are known, could be distinct from classical gauge- theory cosmic strings. In particular, I propose an analytical model for the cosmological evolution of a network of binding cosmic strings (Chapter 4); I also describe the distinctive gravitational lensing phenomena that are caused by binding strings (Chapter 5). Finally, I lay out the background for the numerical study of a gauge theory model for the dynamics of cosmic superstring binding (Chapter 6).

Nonmonotonic Classical Magnetoconductivity of a Two-Dimensional Electron Gas in a Disordered Array of Obstacles

NASA Astrophysics Data System (ADS)

Siboni, N. H.; Schluck, J.; Pierz, K.; Schumacher, H. W.; Kazazis, D.; Horbach, J.; Heinzel, T.

2018-02-01

Magnetotransport measurements in combination with molecular dynamics simulations on two-dimensional disordered Lorentz gases in the classical regime are reported. In quantitative agreement between experiment and simulation, the magnetoconductivity displays a pronounced peak as a function of the perpendicular magnetic field B which cannot be explained by existing kinetic theories. This peak is linked to the onset of a directed motion of the electrons along the contour of the disordered obstacle matrix when the cyclotron radius becomes smaller than the size of the obstacles. This directed motion leads to transient superdiffusive motion and strong scaling corrections in the vicinity of the insulator-to-conductor transitions of the Lorentz gas.

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation and a challenge for kinetic theory

DOE PAGES

Berges, J.; Schlichting, S.; Boguslavski, K.; ...

2015-11-05

In [Phys. Rev. Lett. 114, 061601 (2015)], we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and N-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of amore » Bose-Einstein condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-N expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. In this study, we argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.« less

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation and a challenge for kinetic theory

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

Berges, J.; Schlichting, S.; Boguslavski, K.

In [Phys. Rev. Lett. 114, 061601 (2015)], we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and N-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of amore » Bose-Einstein condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-N expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. In this study, we argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.« less

On information, negentropy and H-theorem

NASA Astrophysics Data System (ADS)

Chakrabarti, C. G.; Sarker, N. G.

1983-09-01

The paper deals with the imprtance of the Kullback descrimination information in the statistical characterization of negentropy of non-equilibrium state and the irreversibility of a classical dynamical system. The theory based on the Kullback discrimination information as the H-function gives new insight into the interrelation between the concepts of coarse-graining and the principle of sufficiency leading to important statistical characterization of thermal equilibrium of a closed system.

Density-Gradient Theory: A Macroscopic Approach to Quantum Confinement and Tunneling in Semiconductor Devices

DTIC Science & Technology

2011-01-01

that are attractive as luminescent biolabels, and possibly also for optoelectronic devices and solar cells . The equilibrium nature of such situations...The boundary layers as- sociated with the diffusion and Debye lengths are familiar, while that of LQ defines the layer in which the quantum in...circuits, transmission lines Diffusion -drift, density-gradient Semi-classical electron dynamics, Boltzmann transport Schrödinger, density- matrix, Wigner

Torsional vibrations of shafts of mechanical systems

NASA Astrophysics Data System (ADS)

Gulevsky, V. A.; Belyaev, A. N.; Trishina, T. V.

2018-03-01

The aim of the research is to compare the calculated dependencies for determining the equivalent rigidity of a mechanical system and to come to an agreement on the methods of compiling dynamic models for systems with elastic reducer couplings in applied and classical oscillation theories. As a result of the analysis, it was revealed that most of the damage in the mechanisms and their details is due to the appearance of oscillations due to the dynamic impact of various factors: shock and alternating loads, unbalanced parts of machines, etc. Therefore, the designer at the design stage, and the engineer in the process of operation should provide the possibility of regulating the oscillatory processes both in details and machines by means of creating rational designs, as well as the use of special devices such as vibration dampers, various vibrators with optimal characteristics. A method is proposed for deriving a formula for determining the equivalent stiffness of a double-mass oscillating system of a multistage reducer with elastic reducer links without taking into account the internal losses and inertia of its elements, which gives a result completely coinciding with the result obtained by the classical theory of small mechanical oscillations and allows eliminating formulas for reducing the moments of inertia of the flywheel masses and the stiffness of the shafts.

Stability enhancement of high Prandtl number chaotic convection in an anisotropic porous layer with feedback control

NASA Astrophysics Data System (ADS)

Mahmud, M. N.

2018-04-01

The chaotic dynamical behaviour of thermal convection in an anisotropic porous layer subject to gravity, heated from below and cooled from above, is studied based on theory of dynamical system in the presence of feedback control. The extended Darcy model, which includes the time derivative has been employed in the momentum equation to derive a low dimensional Lorenz-like equation by using Galerkin-truncated approximation. The classical fourth-order Runge-Kutta method is used to obtain the numerical solution in order to exemplify the dynamics of the nonlinear autonomous system. The results show that stability enhancement of chaotic convection is feasible via feedback control.

Appearance of metastable B2 phase during solidification of Ni 50 Zr 50 alloy: electrostatic levitation and molecular dynamics simulation studies

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

Quirinale, D. G.; Rustan, G. E.; Wilson, S. R.

2015-02-04

High-energy x-ray diffraction measurements of undercooled, electrostatically levitated Ni 50Zr 50 liquid droplets were performed. The observed solidification pathway proceeded through the nucleation and growth of the metastable B2 phase, which persisted for several seconds before the rapid appearance of the stable B33 phase. This sequence is shown to be consistent with predictions from classical nucleation theory using data obtained from molecular dynamics (MD) simulations. A plausible mechanism for the B2–B33 transformation is proposed and investigated through further MD simulations.

Role of Orbital Dynamics in Spin Relaxation and Weak Antilocalization in Quantum Dots

NASA Astrophysics Data System (ADS)

Zaitsev, Oleg; Frustaglia, Diego; Richter, Klaus

2005-01-01

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.

Characterization of the dynamic behaviour of flax fibre reinforced composites using vibration measurements

NASA Astrophysics Data System (ADS)

El-Hafidi, Ali; Birame Gning, Papa; Piezel, Benoit; Fontaine, Stéphane

2017-10-01

Experimental and numerical methods to identify the linear viscoelastic properties of flax fibre reinforced epoxy (FFRE) composite are presented in this study. The method relies on the evolution of storage modulus and loss factor as observed through the frequency response. Free-free symmetrically guided beams were excited on the dynamic range of 10 Hz to 4 kHz with a swept sine excitation focused around their first modes. A fractional derivative Zener model has been identified to predict the complex moduli. A modified ply constitutive law has been then implemented in a classical laminates theory calculation (CLT) routine.

Cooking strongly coupled plasmas

NASA Astrophysics Data System (ADS)

Clérouin, Jean

2015-09-01

We present the orbital-free method for dense plasmas which allows for efficient variable ionisation molecular dynamics. This approach is a literal application of density functional theory where the use of orbitals is bypassed by a semi-classical estimation of the electron kinetic energy through the Thomas-Fermi theory. Thanks to a coherent definition of ionisation, we evidence a particular regime in which the static structure no longer depends on the temperature: the Γ-plateau. With the help of the well-known Thomas-Fermi scaling laws, we derive the conditions required to obtain a plasma at a given value of the coupling parameter and deduce useful fits. Static and dynamical properties are predicted as well as a a simple equation of state valid on the Γ-plateau. We show that the one component plasma model can be helpful to describe the correlations in real systems.

Two Virasoro symmetries in stringy warped AdS 3

DOE PAGES

Compere, Geoffrey; Guica, Monica; Rodriguez, Maria J.

2014-12-02

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS 3 solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS 3. Consequently, for each consistent choice of boundary conditions in AdS 3, we can define a consistent phase space in warped AdS 3 with identical conserved charges. This way, we easily obtain a Virasoro × Virasoro asymptotic symmetry algebra in warped AdS 3; two different types of Virasoro × Kač-Moody symmetriesmore » are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro × Virasoro asymptotic symmetries can be extended to the entire (linearised) phase space. In conclusion, this implies that, at least at semi-classical level, consistent theories of gravity in warped AdS 3 are described by a two-dimensional conformal field theory, as long as stability is not an issue.« less

Two Virasoro symmetries in stringy warped AdS 3

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

Compere, Geoffrey; Guica, Monica; Rodriguez, Maria J.

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS 3 solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS 3. Consequently, for each consistent choice of boundary conditions in AdS 3, we can define a consistent phase space in warped AdS 3 with identical conserved charges. This way, we easily obtain a Virasoro × Virasoro asymptotic symmetry algebra in warped AdS 3; two different types of Virasoro × Kač-Moody symmetriesmore » are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro × Virasoro asymptotic symmetries can be extended to the entire (linearised) phase space. In conclusion, this implies that, at least at semi-classical level, consistent theories of gravity in warped AdS 3 are described by a two-dimensional conformal field theory, as long as stability is not an issue.« less

An appraisal of the classic forest succession paradigm with the shade tolerance index.

PubMed

Lienard, Jean; Florescu, Ionut; Strigul, Nikolay

2015-01-01

In this paper we revisit the classic theory of forest succession that relates shade tolerance and species replacement and assess its validity to understand patch-mosaic patterns of forested ecosystems of the USA. We introduce a macroscopic parameter called the "shade tolerance index" and compare it to the classic continuum index in southern Wisconsin forests. We exemplify shade tolerance driven succession in White Pine-Eastern Hemlock forests using computer simulations and analyzing approximated chronosequence data from the USDA FIA forest inventory. We describe this parameter across the last 50 years in the ecoregions of mainland USA, and demonstrate that it does not correlate with the usual macroscopic characteristics of stand age, biomass, basal area, and biodiversity measures. We characterize the dynamics of shade tolerance index using transition matrices and delimit geographical areas based on the relevance of shade tolerance to explain forest succession. We conclude that shade tolerance driven succession is linked to climatic variables and can be considered as a primary driving factor of forest dynamics mostly in central-north and northeastern areas in the USA. Overall, the shade tolerance index constitutes a new quantitative approach that can be used to understand and predict succession of forested ecosystems and biogeographic patterns.

Rapid learning dynamics in individual honeybees during classical conditioning.

PubMed

Pamir, Evren; Szyszka, Paul; Scheiner, Ricarda; Nawrot, Martin P

2014-01-01

Associative learning in insects has been studied extensively by a multitude of classical conditioning protocols. However, so far little emphasis has been put on the dynamics of learning in individuals. The honeybee is a well-established animal model for learning and memory. We here studied associative learning as expressed in individual behavior based on a large collection of data on olfactory classical conditioning (25 datasets, 3298 animals). We show that the group-averaged learning curve and memory retention score confound three attributes of individual learning: the ability or inability to learn a given task, the generally fast acquisition of a conditioned response (CR) in learners, and the high stability of the CR during consecutive training and memory retention trials. We reassessed the prevailing view that more training results in better memory performance and found that 24 h memory retention can be indistinguishable after single-trial and multiple-trial conditioning in individuals. We explain how inter-individual differences in learning can be accommodated within the Rescorla-Wagner theory of associative learning. In both data-analysis and modeling we demonstrate how the conflict between population-level and single-animal perspectives on learning and memory can be disentangled.

Rapid learning dynamics in individual honeybees during classical conditioning

PubMed Central

Pamir, Evren; Szyszka, Paul; Scheiner, Ricarda; Nawrot, Martin P.

2014-01-01

Associative learning in insects has been studied extensively by a multitude of classical conditioning protocols. However, so far little emphasis has been put on the dynamics of learning in individuals. The honeybee is a well-established animal model for learning and memory. We here studied associative learning as expressed in individual behavior based on a large collection of data on olfactory classical conditioning (25 datasets, 3298 animals). We show that the group-averaged learning curve and memory retention score confound three attributes of individual learning: the ability or inability to learn a given task, the generally fast acquisition of a conditioned response (CR) in learners, and the high stability of the CR during consecutive training and memory retention trials. We reassessed the prevailing view that more training results in better memory performance and found that 24 h memory retention can be indistinguishable after single-trial and multiple-trial conditioning in individuals. We explain how inter-individual differences in learning can be accommodated within the Rescorla–Wagner theory of associative learning. In both data-analysis and modeling we demonstrate how the conflict between population-level and single-animal perspectives on learning and memory can be disentangled. PMID:25309366

Towards the quantization of Eddington-inspired-Born-Infeld theory

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

Bouhmadi-López, Mariam; Chen, Che-Yu, E-mail: mbl@ubi.pt, E-mail: b97202056@gmail.com

2016-11-01

The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantommore » perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity is expected to be avoided through the quantum approach within the EiBI theory.« less

Li + solvation and kinetics of Li +–BF 4 -/PF 6 - ion pairs in ethylene carbonate. A molecular dynamics study with classical rate theories

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

Chang, Tsun-Mei; Dang, Liem X.

Using our polarizable force-field models and employing classical rate theories of chemical reactions, we examine the ethylene carbonate (EC) exchange process between the first and second solvation shells around Li+ and the dissociation kinetics of ion pairs Li+-[BF4] and Li+-[PF6] in this solvent. We calculate the exchange rates using transition state theory and correct them with transmission coefficients computed by the reactive flux; Impey, Madden, and McDonald approaches; and Grote-Hynes theory. We found the residence times of EC around Li+ ions varied from 70 to 450 ps, depending on the correction method used. We found the relaxation times changed significantlymore » from Li+-[BF4] to Li+-[PF6] ion pairs in EC. Our results also show that, in addition to affecting the free energy of dissociation in EC, the anion type also significantly influence the dissociation kinetics of ion pairing. This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. The calculations were carried out using computer resources provided by the Office of Basic Energy Sciences.« less

Green-Naghdi dynamics of surface wind waves in finite depth

NASA Astrophysics Data System (ADS)

Manna, M. A.; Latifi, A.; Kraenkel, R. A.

2018-04-01

The Miles’ quasi laminar theory of waves generation by wind in finite depth h is presented. In this context, the fully nonlinear Green-Naghdi model equation is derived for the first time. This model equation is obtained by the non perturbative Green-Naghdi approach, coupling a nonlinear evolution of water waves with the atmospheric dynamics which works as in the classic Miles’ theory. A depth-dependent and wind-dependent wave growth γ is drawn from the dispersion relation of the coupled Green-Naghdi model with the atmospheric dynamics. Different values of the dimensionless water depth parameter δ = gh/U 1, with g the gravity and U 1 a characteristic wind velocity, produce two families of growth rate γ in function of the dimensionless theoretical wave-age c 0: a family of γ with h constant and U 1 variable and another family of γ with U 1 constant and h variable. The allowed minimum and maximum values of γ in this model are exhibited.

First-principles variational formulation of polarization effects in geometrical optics

DOE PAGES

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

2015-10-02

The propagation of electromagnetic waves in isotropic dielectric media with local dispersion is studied under the assumption of small but nonvanishing λ/l, where λ is the wavelength and l is the characteristic inhomogeneity scale. It is commonly known that, due to nonzero λ/l, such waves can experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the wave "spin". The present work reports how Lagrangians describing these effects can be deduced, rather than guessed, within a strictly classical theory. In addition to the commonly known ray Lagrangian that features the Berry connection, amore » simple alternative Lagrangian is proposed that naturally has a canonical form. The presented theory captures not only the eigenray dynamics but also the dynamics of continuous-wave fields and rays with mixed polarization, or "entangled" waves. In conclusion, the calculation assumes stationary lossless media with isotropic local dispersion, but generalizations to other media are straightforward.« less

A fuzzy-theory-based behavioral model for studying pedestrian evacuation from a single-exit room

NASA Astrophysics Data System (ADS)

Fu, Libi; Song, Weiguo; Lo, Siuming

2016-08-01

Many mass events in recent years have highlighted the importance of research on pedestrian evacuation dynamics. A number of models have been developed to analyze crowd behavior under evacuation situations. However, few focus on pedestrians' decision-making with respect to uncertainty, vagueness and imprecision. In this paper, a discrete evacuation model defined on the cellular space is proposed according to the fuzzy theory which is able to describe imprecise and subjective information. Pedestrians' percept information and various characteristics are regarded as fuzzy input. Then fuzzy inference systems with rule bases, which resemble human reasoning, are established to obtain fuzzy output that decides pedestrians' movement direction. This model is tested in two scenarios, namely in a single-exit room with and without obstacles. Simulation results reproduce some classic dynamics phenomena discovered in real building evacuation situations, and are consistent with those in other models and experiments. It is hoped that this study will enrich movement rules and approaches in traditional cellular automaton models for evacuation dynamics.

Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

NASA Astrophysics Data System (ADS)

Dahms, Rainer N.

2016-04-01

A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing generally occurs before the liquid length is reached. The significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.

Introduction to Classical Density Functional Theory by a Computational Experiment

ERIC Educational Resources Information Center

Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel

2014-01-01

We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…

Design Equations and Criteria of Orthotropic Composite Panels

DTIC Science & Technology

2013-05-01

33  Appendix A Classical Laminate Theory ( CLT ): ....................................................................... A–1  Appendix...Science London , 1990. NSWCCD-65-TR–2004/16A A–1 Appendix A Classical Laminate Theory ( CLT ): In Section 6 of this report, preliminary design...determined using:  Classical Laminate Theory, CLT , to Predict Equivalent Stiffness Characteristics, First- Ply Strength Note: CLT is valid for

Principles of Discrete Time Mechanics

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2014-04-01

1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.

Insufficiency of the Young’s modulus for illustrating the mechanical behavior of GaN nanowires

NASA Astrophysics Data System (ADS)

Zamani Kouhpanji, Mohammad Reza; Behzadirad, Mahmoud; Feezell, Daniel; Busani, Tito

2018-05-01

We use a non-classical modified couple stress theory including the acceleration gradients (MCST-AG), to precisely demonstrate the size dependency of the mechanical properties of gallium nitride (GaN) nanowires (NWs). The fundamental elastic constants, Young’s modulus and length scales of the GaN NWs were estimated both experimentally, using a novel experimental technique applied to atomic force microscopy, and theoretically, using atomic simulations. The Young’s modulus, static and the dynamic length scales, calculated with the MCST-AG, were found to be 323 GPa, 13 and 14.5 nm, respectively, for GaN NWs from a few nanometers radii to bulk radii. Analyzing the experimental data using the classical continuum theory shows an improvement in the experimental results by introducing smaller error. Using the length scales determined in MCST-AG, we explain the inconsistency of the Young’s moduli reported in recent literature, and we prove the insufficiency of the Young’s modulus for predicting the mechanical behavior of GaN NWs.

Projective limits of state spaces III. Toy-models

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2018-01-01

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013) [1,2], which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). A strategy to implement the dynamics in this formalism was presented in our first paper Lanéry and Thiemann (2017) (see also Lanéry, 2016, section 4), which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrödinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Insufficiency of the Young's modulus for illustrating the mechanical behavior of GaN nanowires.

PubMed

Kouhpanji, Mohammad Reza Zamani; Behzadirad, Mahmoud; Feezell, Daniel; Busani, Tito

2018-05-18

We use a non-classical modified couple stress theory including the acceleration gradients (MCST-AG), to precisely demonstrate the size dependency of the mechanical properties of gallium nitride (GaN) nanowires (NWs). The fundamental elastic constants, Young's modulus and length scales of the GaN NWs were estimated both experimentally, using a novel experimental technique applied to atomic force microscopy, and theoretically, using atomic simulations. The Young's modulus, static and the dynamic length scales, calculated with the MCST-AG, were found to be 323 GPa, 13 and 14.5 nm, respectively, for GaN NWs from a few nanometers radii to bulk radii. Analyzing the experimental data using the classical continuum theory shows an improvement in the experimental results by introducing smaller error. Using the length scales determined in MCST-AG, we explain the inconsistency of the Young's moduli reported in recent literature, and we prove the insufficiency of the Young's modulus for predicting the mechanical behavior of GaN NWs.

Contact Angle and Adhesion Dynamics and Hysteresis on Molecularly Smooth Chemically Homogeneous Surfaces.

PubMed

Chen, Szu-Ying; Kaufman, Yair; Schrader, Alex M; Seo, Dongjin; Lee, Dong Woog; Page, Steven H; Koenig, Peter H; Isaacs, Sandra; Gizaw, Yonas; Israelachvili, Jacob N

2017-09-26

Measuring truly equilibrium adhesion energies or contact angles to obtain the thermodynamic values is experimentally difficult because it requires loading/unloading or advancing/receding boundaries to be measured at rates that can be slower than 1 nm/s. We have measured advancing-receding contact angles and loading-unloading adhesion energies for various systems and geometries involving molecularly smooth and chemically homogeneous surfaces moving at different but steady velocities in both directions, ±V, focusing on the thermodynamic limit of ±V → 0. We have used the Bell Theory (1978) to derive expressions for the dynamic (velocity-dependent) adhesion energies and contact angles suitable for both (i) dynamic adhesion measurements using the classic Johnson-Kendall-Roberts (JKR, 1971) theory of "contact mechanics" and (ii) dynamic contact angle hysteresis measurements of both rolling droplets and syringe-controlled (sessile) droplets on various surfaces. We present our results for systems that exhibited both steady and varying velocities from V ≈ 10 mm/s to 1 nm/s, where in all cases but one, the advancing (V > 0) and receding (V < 0) adhesion energies and/or contact angles converged toward the same theoretical (thermodynamic) values as V → 0. Our equations for the dynamic contact angles are similar to the classic equations of Blake & Haynes (1969) and fitted the experimental adhesion data equally well over the range of velocities studied, although with somewhat different fitting parameters for the characteristic molecular length/dimension or area and characteristic bond formation/rupture lifetime or velocity. Our theoretical and experimental methods and results unify previous kinetic theories of adhesion and contact angle hysteresis and offer new experimental methods for testing kinetic models in the thermodynamic, quasi-static, limit. Our analyses are limited to kinetic effects only, and we conclude that hydrodynamic, i.e., viscous, and inertial effects do not play a role at the interfacial velocities of our experiments, i.e., V < (1-10) mm/s (for water and hexadecane, but for viscous polymers it may be different), consistent with previously reported studies.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

NASA Astrophysics Data System (ADS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

High-Pressure Transport Properties Of Fluids: Theory And Data From Levitated Drops At Combustion-Relevant Temperatures

NASA Technical Reports Server (NTRS)

Bellan, Josette; Harstad, Kenneth; Ohsaka, Kenichi

2003-01-01

Although the high pressure multicomponent fluid conservation equations have already been derived and approximately validated for binary mixtures by this PI, the validation of the multicomponent theory is hampered by the lack of existing mixing rules for property calculations. Classical gas dynamics theory can provide property mixing-rules at low pressures exclusively. While thermal conductivity and viscosity high-pressure mixing rules have been documented in the literature, there is no such equivalent for the diffusion coefficients and the thermal diffusion factors. The primary goal of this investigation is to extend the low pressure mixing rule theory to high pressures and validate the new theory with experimental data from levitated single drops. The two properties that will be addressed are the diffusion coefficients and the thermal diffusion factors. To validate/determine the property calculations, ground-based experiments from levitated drops are being conducted.

The force distribution probability function for simple fluids by density functional theory.

PubMed

Rickayzen, G; Heyes, D M

2013-02-28

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

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.

Renormalization group theory for percolation in time-varying networks.

PubMed

Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

2018-05-22

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

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.

Framework based on communicability and flow to analyze complex network dynamics

NASA Astrophysics Data System (ADS)

Gilson, M.; Kouvaris, N. E.; Deco, G.; Zamora-López, G.

2018-05-01

Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagationlike processes such as random walks. However, networks are often inferred from real-data-forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the flow that describes the interplay between the network connectivity and external inputs. This multivariate measure relates to the concepts of graph communicability and the map equation. We illustrate our theory using the multivariate Ornstein-Uhlenbeck process, which describes stable and non-conservative dynamics, but the formalism can be adapted to other local dynamics for which the Green function is known. We provide applications to classical network examples, such as small-world ring and hierarchical networks. Our theory defines a comprehensive framework that is canonically related to directed and weighted networks, thus paving a way to revise the standards for network analysis, from the pairwise interactions between nodes to the global properties of networks including community detection.

Evolutionary dynamics of the traveler's dilemma and minimum-effort coordination games on complex networks.

PubMed

Iyer, Swami; Killingback, Timothy

2014-10-01

The traveler's dilemma game and the minimum-effort coordination game are social dilemmas that have received significant attention resulting from the fact that the predictions of classical game theory are inconsistent with the results found when the games are studied experimentally. Moreover, both the traveler's dilemma and the minimum-effort coordination games have potentially important applications in evolutionary biology. Interestingly, standard deterministic evolutionary game theory, as represented by the replicator dynamics in a well-mixed population, is also inadequate to account for the behavior observed in these games. Here we study the evolutionary dynamics of both these games in populations with interaction patterns described by a variety of complex network topologies. We investigate the evolutionary dynamics of these games through agent-based simulations on both model and empirical networks. In particular, we study the effects of network clustering and assortativity on the evolutionary dynamics of both games. In general, we show that the evolutionary behavior of the traveler's dilemma and minimum-effort coordination games on complex networks is in good agreement with that observed experimentally. Thus, formulating the traveler's dilemma and the minimum-effort coordination games on complex networks neatly resolves the paradoxical aspects of these games.

Evolutionary dynamics of the traveler's dilemma and minimum-effort coordination games on complex networks

NASA Astrophysics Data System (ADS)

Iyer, Swami; Killingback, Timothy

2014-10-01

The traveler's dilemma game and the minimum-effort coordination game are social dilemmas that have received significant attention resulting from the fact that the predictions of classical game theory are inconsistent with the results found when the games are studied experimentally. Moreover, both the traveler's dilemma and the minimum-effort coordination games have potentially important applications in evolutionary biology. Interestingly, standard deterministic evolutionary game theory, as represented by the replicator dynamics in a well-mixed population, is also inadequate to account for the behavior observed in these games. Here we study the evolutionary dynamics of both these games in populations with interaction patterns described by a variety of complex network topologies. We investigate the evolutionary dynamics of these games through agent-based simulations on both model and empirical networks. In particular, we study the effects of network clustering and assortativity on the evolutionary dynamics of both games. In general, we show that the evolutionary behavior of the traveler's dilemma and minimum-effort coordination games on complex networks is in good agreement with that observed experimentally. Thus, formulating the traveler's dilemma and the minimum-effort coordination games on complex networks neatly resolves the paradoxical aspects of these games.

Qubit dephasing due to low-frequency noise.

NASA Astrophysics Data System (ADS)

Sverdlov, Victor; Rabenstein, Kristian; Averin, Dmitri

2004-03-01

We have numerically investigated the effects of the classical low-frequency noise on the qubit dynamics beyond the standard lowest-order perturbation theory in coupling. Noise is generated as a random process with a correlation function characterized by two parameters, the amplitude v0 and the cut-off frequency 2π/τ. Time evolution of the density matrix was averaged over up to 10^7 noise realizations. Contrary to the relaxation time T_1, which for v_0<ω, where ω is the qubit oscillation frequency, is always given correctly by the ``golden-rule'' expression, the dephasing time deviates from the perturbation-theory result, when (v_0/ω)^2(ωτ) ≥1. In this regime, even for unbiased qubit for which the pure dephasing vanishes in perturbation theory, the dephasing is much larger than it's perturbation-theory value 1/(2 T_1).

Regulative feedback in pattern formation: towards a general relativistic theory of positional information.

PubMed

Jaeger, Johannes; Irons, David; Monk, Nick

2008-10-01

Positional specification by morphogen gradients is traditionally viewed as a two-step process. A gradient is formed and then interpreted, providing a spatial metric independent of the target tissue, similar to the concept of space in classical mechanics. However, the formation and interpretation of gradients are coupled, dynamic processes. We introduce a conceptual framework for positional specification in which cellular activity feeds back on positional information encoded by gradients, analogous to the feedback between mass-energy distribution and the geometry of space-time in Einstein's general theory of relativity. We discuss how such general relativistic positional information (GRPI) can guide systems-level approaches to pattern formation.

Scale-free phenomenon in industries in China

NASA Astrophysics Data System (ADS)

Tang, Da-Hai; Chen, Bo-Kui; Gao, Ya-Chun; Wang, Bing-Hong

2013-12-01

In this paper, we investigate the data of industries in China and find that the frequency distributions of fixed assets and fixed-assets’ investment of industries obey power laws. We show that these power-law modes can be explained by the rules of the Simon Model, rather than the existing investment theories such as the classical investment theory or acceleration principle. Moreover, the mechanism of the investment distribution may be similar to the forest-fire model of self-organizing criticality. By introducing the complex system methods, this research changes the traditional opinion of the investment and gains some meaningful understanding in the dynamics of industries and the economic cycle.

Decoherence and thermalization of a pure quantum state in quantum field theory.

PubMed

Giraud, Alexandre; Serreau, Julien

2010-06-11

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.

Ion-ion dynamic structure factor of warm dense mixtures

DOE PAGES

Gill, N. M.; Heinonen, R. A.; Starrett, C. E.; ...

2015-06-25

In this study, the ion-ion dynamic structure factor of warm dense matter is determined using the recently developed pseudoatom molecular dynamics method [Starrett et al., Phys. Rev. E 91, 013104 (2015)]. The method uses density functional theory to determine ion-ion pair interaction potentials that have no free parameters. These potentials are used in classical molecular dynamics simulations. This constitutes a computationally efficient and realistic model of dense plasmas. Comparison with recently published simulations of the ion-ion dynamic structure factor and sound speed of warm dense aluminum finds good to reasonable agreement. Using this method, we make predictions of the ion-ionmore » dynamical structure factor and sound speed of a warm dense mixture—equimolar carbon-hydrogen. This material is commonly used as an ablator in inertial confinement fusion capsules, and our results are amenable to direct experimental measurement.« less

Generalized probability theories: what determines the structure of quantum theory?

NASA Astrophysics Data System (ADS)

Janotta, Peter; Hinrichsen, Haye

2014-08-01

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from a few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out that non-classical features of single systems can equivalently result from higher-dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features.

Anomalous Chained Turbulence in Actively Driven Flows on Spheres

NASA Astrophysics Data System (ADS)

Mickelin, Oscar; Słomka, Jonasz; Burns, Keaton J.; Lecoanet, Daniel; Vasil, Geoffrey M.; Faria, Luiz M.; Dunkel, Jörn

2018-04-01

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in nonplanar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of antiferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.

Hyperbolic polaritons in nanoparticles

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Rubio, Angel; Guinea, Francisco; Basov, Dimitri; Fogler, Michael

2015-03-01

Hyperbolic optical materials (HM) are characterized by permittivity tensor that has both positive and negative principal values. Collective electromagnetic modes (polaritons) of HM have novel properties promising for various applications including subdiffractional imaging and on-chip optical communication. Hyperbolic response is actively investigated in the context of metamaterials, anisotropic polar insulators, and layered superconductors. We study polaritons in spheroidal HM nanoparticles using Hamiltonian optics. The field equations are mapped to classical dynamics of fictitious particles (wave packets) of an indefinite Hamiltonian. This dynamics is quantized using the Einstein-Brillouin-Keller quantization rule. The eigenmodes are classified as either bulk or surface according to whether their transverse momenta are real or imaginary. To model how such hyperbolic polaritons can be probed by near-field experiments, we compute the field distribution induced inside and outside the spheroid by an external point dipole. At certain magic frequencies the field shows striking geometric patterns whose origin is traced to the classical periodic orbits. The theory is applied to natural hyperbolic materials hexagonal boron nitride and superconducting LaSrCuO.

The trace anomaly and dynamical vacuum energy in cosmology

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

Mottola, Emil

2010-04-30

The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscopic quantum effects. The additional scalar degrees of freedom contained in this effectivemore » action may be understood as responsible for both the Casimir effect in flat spacetime and large quantum backreaction effects at the horizon scale of cosmological spacetimes. These effects of the trace anomaly imply that the cosmological vacuum energy is dynamical, and its value depends on macroscopic boundary conditions at the cosmological horizon scale, rather than sensitivity to the extreme ultraviolet Planck scale.« 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.

Quantum physics in neuroscience and psychology: A neurophysicalmodel of the mind/brain interaction

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

Schwartz, Jeffrey M.; Stapp, Henry P.; Beauregard, Mario

Neuropsychological research on the neural basis of behavior generally posits that brain mechanisms will ultimately suffice to explain all psychologically described phenomena. This assumption stems from the idea that the brain is made up entirely of material particles and fields, and that all causal mechanisms relevant to neuroscience can therefore be formulated solely in terms of properties of these elements. Thus terms having intrinsic mentalistic and/or experiential content (e.g., ''feeling,'' ''knowing,'' and ''effort'') are not included as primary causal factors. This theoretical restriction is motivated primarily by ideas about the natural world that have been known to be fundamentally incorrectmore » for more than three quarters of a century. Contemporary basic physical theory differs profoundly from classical physics on the important matter of how the consciousness of human agents enters into the structure of empirical phenomena. The new principles contradict the older idea that local mechanical processes alone can account for the structure of all observed empirical data. Contemporary physical theory brings directly and irreducibly into the overall causal structure certain psychologically described choices made by human agents about how they will act. This key development in basic physical theory is applicable to neuroscience, and it provides neuroscientists and psychologists with an alternative conceptual framework for describing neural processes. Indeed, due to certain structural features of ion channels critical to synaptic function, contemporary physical theory must in principle be used when analyzing human brain dynamics. The new framework, unlike its classical-physics-based predecessor is erected directly upon, and is compatible with, the prevailing principles of physics, and is able to represent more adequately than classical concepts the neuroplastic mechanisms relevant to the growing number of empirical studies of the capacity of directed attention and mental effort to systematically alter brain function.« less

Quantum physics in neuroscience and psychology: a neurophysical model of mind–brain interaction

PubMed Central

Schwartz, Jeffrey M; Stapp, Henry P; Beauregard, Mario

2005-01-01

Neuropsychological research on the neural basis of behaviour generally posits that brain mechanisms will ultimately suffice to explain all psychologically described phenomena. This assumption stems from the idea that the brain is made up entirely of material particles and fields, and that all causal mechanisms relevant to neuroscience can therefore be formulated solely in terms of properties of these elements. Thus, terms having intrinsic mentalistic and/or experiential content (e.g. ‘feeling’, ‘knowing’ and ‘effort’) are not included as primary causal factors. This theoretical restriction is motivated primarily by ideas about the natural world that have been known to be fundamentally incorrect for more than three-quarters of a century. Contemporary basic physical theory differs profoundly from classic physics on the important matter of how the consciousness of human agents enters into the structure of empirical phenomena. The new principles contradict the older idea that local mechanical processes alone can account for the structure of all observed empirical data. Contemporary physical theory brings directly and irreducibly into the overall causal structure certain psychologically described choices made by human agents about how they will act. This key development in basic physical theory is applicable to neuroscience, and it provides neuroscientists and psychologists with an alternative conceptual framework for describing neural processes. Indeed, owing to certain structural features of ion channels critical to synaptic function, contemporary physical theory must in principle be used when analysing human brain dynamics. The new framework, unlike its classic-physics-based predecessor, is erected directly upon, and is compatible with, the prevailing principles of physics. It is able to represent more adequately than classic concepts the neuroplastic mechanisms relevant to the growing number of empirical studies of the capacity of directed attention and mental effort to systematically alter brain function. PMID:16147524

Possible mechanism for the onset of step-bunching instabilities during the epitaxy of single-species crystalline films

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

Cermelli, Paolo; Jabbour, Michel E.; Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

A thermodynamically consistent continuum theory for single-species, step-flow epitaxy that extends the classical Burton-Cabrera-Frank (BCF) framework is derived from basic considerations. In particular, an expression for the step chemical potential is obtained that contains two energetic contributions--one from the adjacent terraces in the form of the jump in the adatom grand canonical potential and the other from the monolayer of crystallized adatoms that underlies the upper terrace in the form of the nominal bulk chemical potential--thus generalizing the classical Gibbs-Thomson relation to the dynamic, dissipative setting of step-flow growth. The linear stability analysis of the resulting quasistatic free-boundary problem formore » an infinite train of equidistant rectilinear steps yields explicit--i.e., analytical--criteria for the onset of step bunching in terms of the basic physical and geometric parameters of the theory. It is found that, in contrast with the predictions of the classical BCF model, both in the absence as well as in the presence of desorption, a growth regime exists for which step bunching occurs, except possibly in the dilute limit where the train is always stable to step bunching. In the present framework, the onset of one-dimensional instabilities is directly attributed to the energetic influence on the migrating steps of the adjacent terraces. Hence the theory provides a ''minimalist'' alternative to existing theories of step bunching and should be relevant to, e.g., molecular beam epitaxy of GaAs where the equilibrium adatom density is shown by Tersoff, Johnson, and Orr [Phys. Rev. B 78, 282 (1997)] to be extremely high.« less

Realization of non-holonomic constraints and singular perturbation theory for plane dumbbells

NASA Astrophysics Data System (ADS)

Koshkin, Sergiy; Jovanovic, Vojin

2017-10-01

We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method of matching asymptotics of singular perturbation theory when the mass to friction ratio is taken as the small parameter. It turns out that long term behaviors of the frictional and constrained systems may differ dramatically no matter how small the perturbation is, and when this happens is not determined by any transparent feature of the equations of motion. The choice of effective time scales for matching asymptotics is also subtle and non-obvious, and secular terms appearing in them can not be dealt with by the classical methods. Our analysis is based on comparison to analytic solutions, and we present a reduction procedure for plane dumbbells that leads to them in some cases.

Correlation dimension and phase space contraction via extreme value theory

NASA Astrophysics Data System (ADS)

Faranda, Davide; Vaienti, Sandro

2018-04-01

We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: (i) the inverse of the scale parameter gives the correlation dimension and (ii) the extremal index is associated with the rate of phase space contraction for backward iteration, which in dimension 1 and 2, is closely related to the positive Lyapunov exponent and in higher dimensions is related to the metric entropy. We call it the Dynamical Extremal Index. Numerical estimates are straightforward to obtain as they imply just a simple fit to a univariate distribution. Numerical tests range from low dimensional maps, to generalized Henon maps and climate data. The estimates of the indicators are particularly robust even with relatively short time series.

Dynamical tachyons on fuzzy spheres

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

Berenstein, David; Institute for Advanced Study, School of Natural Science, Princeton, New Jersey 08540; Trancanelli, Diego

2011-05-15

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the Berenstein-Maldacena-Nastase plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles, classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills theory on a sphere, of which this system is a truncation. We also set upmore » a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.« less

The atomic scale structure of CXV carbon: wide-angle x-ray scattering and modeling studies.

PubMed

Hawelek, L; Brodka, A; Dore, J C; Honkimaki, V; Burian, A

2013-11-13

The disordered structure of commercially available CXV activated carbon produced from finely powdered wood-based carbon has been studied using the wide-angle x-ray scattering technique, molecular dynamics and density functional theory simulations. The x-ray scattering data has been converted to the real space representation in the form of the pair correlation function via the Fourier transform. Geometry optimizations using classical molecular dynamics based on the reactive empirical bond order potential and density functional theory at the B3LYP/6-31g* level have been performed to generate nanoscale models of CXV carbon consistent with the experimental data. The final model of the structure comprises four chain-like and buckled graphitic layers containing a small percentage of four-fold coordinated atoms (sp(3) defects) in each layer. The presence of non-hexagonal rings in the atomic arrangement has been also considered.

Linking environmental variability to population and community dynamics: Chapter 7

USGS Publications Warehouse

Pantel, Jelena H.; Pendleton, Daniel E.; Walters, Annika W.; Rogers, Lauren A.

2014-01-01

Linking population and community responses to environmental variability lies at the heart of ecology, yet methodological approaches vary and existence of broad patterns spanning taxonomic groups remains unclear. We review the characteristics of environmental and biological variability. Classic approaches to link environmental variability to population and community variability are discussed as are the importance of biotic factors such as life history and community interactions. In addition to classic approaches, newer techniques such as information theory and artificial neural networks are reviewed. The establishment and expansion of observing networks will provide new long-term ecological time-series data, and with it, opportunities to incorporate environmental variability into research. This review can help guide future research in the field of ecological and environmental variability.

Collapse of surface nanobubbles.

PubMed

Chan, Chon U; Chen, Longquan; Arora, Manish; Ohl, Claus-Dieter

2015-03-20

Surface attached nanobubbles populate surfaces submerged in water. These nanobubbles have a much larger contact angle and longer lifetime than predicted by classical theory. Moreover, it is difficult to distinguish them from hydrophobic droplets, e.g., polymeric contamination, using standard atomic force microscopy. Here, we report fast dynamics of a three phase contact line moving over surface nanobubbles, polymeric droplets, and hydrophobic particles. The dynamics is distinct: across polymeric droplets the contact line quickly jumps and hydrophobic particles pin the contact line, while surface nanobubbles rapidly shrink once merging with the contact line, suggesting a method to differentiate nanoscopic gaseous, liquid, and solid structures. Although the collapse process of surface nanobubbles occurs within a few milliseconds, we show that it is dominated by microscopic dynamics rather than bulk hydrodynamics.

The Dynamic Response and Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) Truncated Conical Shells Resting on Elastic Foundations

PubMed Central

Nguyen Dinh, Duc; Nguyen, Pham Dinh

2017-01-01

Based on the classical shell theory, the linear dynamic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundations subjected to dynamic loads is presented. The truncated conical shells are reinforced by single-walled carbon nanotubes (SWCNTs) that vary according to the linear functions of the shell thickness. The motion equations are solved by the Galerkin method and the fourth-order Runge–Kutta method. In numerical results, the influences of geometrical parameters, elastic foundations, natural frequency parameters, and nanotube volume fraction of FG-CNTRC truncated conical shells are investigated. The proposed results are validated by comparing them with those of other authors. PMID:29057821

Rasch-family models are more valuable than score-based approaches for analysing longitudinal patient-reported outcomes with missing data.

PubMed

de Bock, Élodie; Hardouin, Jean-Benoit; Blanchin, Myriam; Le Neel, Tanguy; Kubis, Gildas; Bonnaud-Antignac, Angélique; Dantan, Étienne; Sébille, Véronique

2016-10-01

The objective was to compare classical test theory and Rasch-family models derived from item response theory for the analysis of longitudinal patient-reported outcomes data with possibly informative intermittent missing items. A simulation study was performed in order to assess and compare the performance of classical test theory and Rasch model in terms of bias, control of the type I error and power of the test of time effect. The type I error was controlled for classical test theory and Rasch model whether data were complete or some items were missing. Both methods were unbiased and displayed similar power with complete data. When items were missing, Rasch model remained unbiased and displayed higher power than classical test theory. Rasch model performed better than the classical test theory approach regarding the analysis of longitudinal patient-reported outcomes with possibly informative intermittent missing items mainly for power. This study highlights the interest of Rasch-based models in clinical research and epidemiology for the analysis of incomplete patient-reported outcomes data. © The Author(s) 2013.

Multiscale Experimental and Theoretical Investigations of Spin Crossover FeII Complexes: Examples of [Fe(phen)2(NCS)2] and [Fe(PM-BiA)2(NCS)2

PubMed Central

Matar, Samir F.; Guionneau, Philippe; Chastanet, Guillaume

2015-01-01

For spin crossover (SCO) complexes, computation results are reported and confirmed with experiments at multiscale levels of the isolated molecule and extended solid on the one hand and theory on the other hand. The SCO phenomenon which characterizes organometallics based on divalent iron in an octahedral FeN6-like environment with high spin (HS) and low spin (LS) states involves the LS/HS switching at the cost of small energies provided by temperature, pressure or light, the latter connected with Light-Induced Excited Spin-State Trapping (LIESST) process. Characteristic infra red (IR) and Raman vibration frequencies are computed within density functional theory (DFT) framework. In [Fe(phen)2(NCS)2] a connection of selected frequencies is established with an ultra-fast light-induced LS → HS photoswitching mechanism. In the extended solid, density of state DOS and electron localization function (ELF) are established for both LS and HS forms, leading to characterizion of the compound as an insulator in both spin states with larger gaps for LS configuration, while keeping molecular features in the solid. In [Fe(PM-BiA)2(NCS)2], by combining DFT and classical molecular dynamics, the properties and the domains of existence of the different phases are obtained by expressing the potential energy surfaces in a short range potential for Fe–N interactions. Applying such Fe–N potentials inserted in a classical force field and carrying out molecular dynamics (MD) in so-called “semi-classical MD” calculations, lead to the relative energies of HS/LS configurations of the crystal and to the assessment of the experimental (P, T) phase diagram. PMID:25686037

Classical and quantum cosmology of minimal massive bigravity

NASA Astrophysics Data System (ADS)

Darabi, F.; Mousavi, M.

2016-10-01

In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.

A network dynamics approach to chemical reaction networks

NASA Astrophysics Data System (ADS)

van der Schaft, A. J.; Rao, S.; Jayawardhana, B.

2016-04-01

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.

Dynamically biased statistical model for the ortho/para conversion in the H2 + H3+ → H3+ + H2 reaction.

PubMed

Gómez-Carrasco, Susana; González-Sánchez, Lola; Aguado, Alfredo; Sanz-Sanz, Cristina; Zanchet, Alexandre; Roncero, Octavio

2012-09-07

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007)]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H(5)(+) complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H(5)(+) complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011)] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

Dynamically biased statistical model for the ortho/para conversion in the H2+H3+ --> H3++ H2 reaction

NASA Astrophysics Data System (ADS)

Gómez-Carrasco, Susana; González-Sánchez, Lola; Aguado, Alfredo; Sanz-Sanz, Cristina; Zanchet, Alexandre; Roncero, Octavio

2012-09-01

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007), 10.1063/1.2430711]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H_5^+ complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H_5^+ complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011), 10.1063/1.3587246] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

Telling and Not-Telling: A Classic Grounded Theory of Sharing Life-Stories

ERIC Educational Resources Information Center

Powers, Trudy Lee

2013-01-01

This study of "Telling and Not-Telling" was conducted using the classic grounded theory methodology (Glaser 1978, 1992, 1998; Glaser & Strauss, 1967). This unique methodology systematically and inductively generates conceptual theories from data. The goal is to discover theory that explains, predicts, and provides practical…

A molecular dynamics and ab initio analysis of the electronic structure of single-walled carbon nanotubes adhered to a substrate

NASA Astrophysics Data System (ADS)

Van Der Geest, A. G.; Lu, Z.; Lusk, M. T.; Dunn, M. L.

2011-04-01

Single-wall nanotubes can adhere to planar surfaces via van der Waals forces, and this causes the tubes to deform. We use classical molecular dynamics to estimate this deformation and density functional theory to quantify its impact on electronic band structure. For (n,0) tubes, adhesion causes the maximum bandgap to rise more rapidly with diameter, but the value of the maximum is not affected. The influence of adhesion forces on bandgap was found to correlate with that associated with lateral, uniaxial compression for moderate values of adhesion energy and compressive distortion.

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2011-09-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

Masking effects of speech and music: does the masker's hierarchical structure matter?

PubMed

Shi, Lu-Feng; Law, Yvonne

2010-04-01

Speech and music are time-varying signals organized by parallel hierarchical rules. Through a series of four experiments, this study compared the masking effects of single-talker speech and instrumental music on speech perception while manipulating the complexity of hierarchical and temporal structures of the maskers. Listeners' word recognition was found to be similar between hierarchically intact and disrupted speech or classical music maskers (Experiment 1). When sentences served as the signal, significantly greater masking effects were observed with disrupted than intact speech or classical music maskers (Experiment 2), although not with jazz or serial music maskers, which differed from the classical music masker in their hierarchical structures (Experiment 3). Removing the classical music masker's temporal dynamics or partially restoring it affected listeners' sentence recognition; yet, differences in performance between intact and disrupted maskers remained robust (Experiment 4). Hence, the effect of structural expectancy was largely present across maskers when comparing them before and after their hierarchical structure was purposefully disrupted. This effect seemed to lend support to the auditory stream segregation theory.

Response of a semiconducting infinite medium under two temperature theory with photothermal excitation due to laser pulses

NASA Astrophysics Data System (ADS)

Lotfy, Kh.; Gabr, M. E.

2017-12-01

A novel model of two-dimensional deformations for two-temperature theory at the free surface under the excitation of thermoelastic wave by pulsed laser for a semi-infinite semiconducting medium is studied. The effect of mechanical force during a photothermal process is investigated. The mathematical methods of the Lord-Shulman (LS includes one relaxation time) and Green-Lindsay (GL with two relaxation times) theories as well as the classical dynamical coupled theory (CD) are used. An exact expression for displacement components, force stresses, carrier density and distribution of temperature are obtained using the harmonic wave analysis. Combinations of two-temperature and photothermal theories are obtained analytically. Comparisons of the results are made between the three theories also. The effects of thermoelectric coupling parameter, two-temperature parameter on the displacement component, force stress, carrier density, and distribution of temperature for silicon (Si) medium have been illustrated graphically. The variations of the considered variables with the horizontal distance have been discussed.

Bypassing the malfunction junction in warm dense matter simulations

NASA Astrophysics Data System (ADS)

Cangi, Attila; Pribram-Jones, Aurora

2015-03-01

Simulation of warm dense matter requires computational methods that capture both quantum and classical behavior efficiently under high-temperature and high-density conditions. The state-of-the-art approach to model electrons and ions under those conditions is density functional theory molecular dynamics, but this method's computational cost skyrockets as temperatures and densities increase. We propose finite-temperature potential functional theory as an in-principle-exact alternative that suffers no such drawback. In analogy to the zero-temperature theory developed previously, we derive an orbital-free free energy approximation through a coupling-constant formalism. Our density approximation and its associated free energy approximation demonstrate the method's accuracy and efficiency. A.C. has been partially supported by NSF Grant CHE-1112442. A.P.J. is supported by DOE Grant DE-FG02-97ER25308.

Games of life and death: antibiotic resistance and production through the lens of evolutionary game theory.

PubMed

Conlin, Peter L; Chandler, Josephine R; Kerr, Benjamin

2014-10-01

In this review, we demonstrate how game theory can be a useful first step in modeling and understanding interactions among bacteria that produce and resist antibiotics. We introduce the basic features of evolutionary game theory and explore model microbial systems that correspond to some classical games. Each game discussed defines a different category of social interaction with different resulting population dynamics (exclusion, coexistence, bistability, cycling). We then explore how the framework can be extended to incorporate some of the complexity of natural microbial communities. Overall, the game theoretical perspective helps to guide our expectations about the evolution of some forms of antibiotic resistance and production because it makes clear the precise nature of social interaction in this context. Copyright © 2014 Elsevier Ltd. All rights reserved.

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

DOE PAGES

Argyres, Philip C.; Uensal, Mithat

2012-08-10

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a massmore » gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.« less

Atomic Scale Imaging of Nucleation and Growth Trajectories of an Interfacial Bismuth Nanodroplet.

PubMed

Li, Yingxuan; Bunes, Benjamin R; Zang, Ling; Zhao, Jie; Li, Yan; Zhu, Yunqing; Wang, Chuanyi

2016-02-23

Because of the lack of experimental evidence, much confusion still exists on the nucleation and growth dynamics of a nanostructure, particularly of metal. The situation is even worse for nanodroplets because it is more difficult to induce the formation of a nanodroplet while imaging the dynamic process with atomic resolution. Here, taking advantage of an electron beam to induce the growth of Bi nanodroplets on a SrBi2Ta2O9 platelet under a high resolution transmission electron microscope (HRTEM), we directly observed the detailed growth pathways of Bi nanodroplets from the earliest stage of nucleation that were previously inaccessible. Atomic scale imaging reveals that the dynamics of nucleation involves a much more complex trajectory than previously predicted based on classical nucleation theory (CNT). The monatomic Bi layer was first formed in the nucleation process, which induced the formation of the prenucleated clusters. Following that, critical nuclei for the nanodroplets formed both directly from the addition of atoms to the prenucleated clusters by the classical growth process and indirectly through transformation of an intermediate liquid film based on the Stranski-Krastanov growth mode, in which the liquid film was induced by the self-assembly of the prenucleated clusters. Finally, the growth of the Bi nanodroplets advanced through the classical pathway and sudden droplet coalescence. This study allows us to visualize the critical steps in the nucleation process of an interfacial nanodroplet, which suggests a revision of the perspective of CNT.

Poincaré resonances and the limits of trajectory dynamics.

PubMed Central

Petrosky, T; Prigogine, I

1993-01-01

In previous papers we have shown that the elimination of the resonance divergences in large Poincare systems leads to complex irreducible spectral representations for the Liouville-von Neumann operator. Complex means that time symmetry is broken and irreducibility means that this representation is implementable only by statistical ensembles and not by trajectories. We consider in this paper classical potential scattering. Our theory applies to persistent scattering. Numerical simulations show quantitative agreement with our predictions. PMID:11607428

On the theory of singular optimal controls in dynamic systems with control delay

NASA Astrophysics Data System (ADS)

Mardanov, M. J.; Melikov, T. K.

2017-05-01

An optimal control problem with a control delay is considered, and a more broad class of singular (in classical sense) controls is investigated. Various sequences of necessary conditions for the optimality of singular controls in recurrent form are obtained. These optimality conditions include analogues of the Kelley, Kopp-Moyer, R. Gabasov, and equality-type conditions. In the proof of the main results, the variation of the control is defined using Legendre polynomials.

Consistent Discretization and Canonical, Classical and Quantum Regge Calculus

NASA Astrophysics Data System (ADS)

Gambini, Rodolfo; Pullin, Jorge

We apply the "consistent discretization" technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well-defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. In the Lorentzian case, the framework appears to be naturally free of the "spikes" that plague traditional formulations. It also provides a well-defined recipe for determining the integration measure for quantum Regge calculus.

Finite-block-length analysis in classical and quantum information theory.

PubMed

Hayashi, Masahito

2017-01-01

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.

Finite-block-length analysis in classical and quantum information theory

PubMed Central

HAYASHI, Masahito

2017-01-01

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects. PMID:28302962

Dynamic Simulation of Human Gait Model With Predictive Capability.

PubMed

Sun, Jinming; Wu, Shaoli; Voglewede, Philip A

2018-03-01

In this paper, it is proposed that the central nervous system (CNS) controls human gait using a predictive control approach in conjunction with classical feedback control instead of exclusive classical feedback control theory that controls based on past error. To validate this proposition, a dynamic model of human gait is developed using a novel predictive approach to investigate the principles of the CNS. The model developed includes two parts: a plant model that represents the dynamics of human gait and a controller that represents the CNS. The plant model is a seven-segment, six-joint model that has nine degrees-of-freedom (DOF). The plant model is validated using data collected from able-bodied human subjects. The proposed controller utilizes model predictive control (MPC). MPC uses an internal model to predict the output in advance, compare the predicted output to the reference, and optimize the control input so that the predicted error is minimal. To decrease the complexity of the model, two joints are controlled using a proportional-derivative (PD) controller. The developed predictive human gait model is validated by simulating able-bodied human gait. The simulation results show that the developed model is able to simulate the kinematic output close to experimental data.

Effects of Froude number and geometry on water entry of a 2-D ellipse

NASA Astrophysics Data System (ADS)

Zhang, Xu; Liu, Pei-qing; Qu, Qiu-lin; Wang, Rui; Agarwal, Ramesh K.

2018-05-01

By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics (CFD) results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4πa/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.

Charged nanoparticle attraction in multivalent salt solution: A classical-fluids density functional theory and molecular dynamics study

DOE PAGES

Salerno, K. Michael; Frischknecht, Amalie L.; Stevens, Mark J.

2016-04-08

Here, negatively charged nanoparticles (NPs) in 1:1, 1:2, and 1:3 electrolyte solutions are studied in a primitive ion model using molecular dynamics (MD) simulations and classical density functional theory (DFT). We determine the conditions for attractive interactions between the like-charged NPs. Ion density profiles and NP–NP interaction free energies are compared between the two methods and are found to be in qualitative agreement. The NP interaction free energy is purely repulsive for monovalent counterions, but can be attractive for divalent and trivalent counterions. Using DFT, the NP interaction free energy for different NP diameters and charges is calculated. The depthmore » and location of the minimum in the interaction depend strongly on the NPs’ charge. For certain parameters, the depth of the attractive well can reach 8–10 k BT, indicating that kinetic arrest and aggregation of the NPs due to electrostatic interactions is possible. Rich behavior arises from the geometric constraints of counterion packing at the NP surface. Layering of counterions around the NPs is observed and, as secondary counterion layers form the minimum of the NP–NP interaction free energy shifts to larger separation, and the depth of the free energy minimum varies dramatically. We find that attractive interactions occur with and without NP overcharging.« less

Stix Award: The ponderomotive effect beyond the ponderomotive force

NASA Astrophysics Data System (ADS)

Dodin, I. Y.

2014-10-01

The classical ponderomotive effect (PE) is typically understood as the nonlinear time-average force produced by a rapidly oscillating electromagnetic field on a nonresonant particle. It is instructive to contrast this understanding with the common quantum interpretation of the PE as the ac Stark shift, i.e., phase modulation, or a Kerr effect experienced by the wave function. Then the PE is naturally extended from particles to waves and can be calculated efficiently in general settings, including for strongly nonlinear interactions and resonant dynamics. In particular, photons (plasmons, etc.) are hence seen to have polarizability and contribute to the linear dielectric tensor exactly like ``true'' particles such as electrons and ions. The talk will briefly review the underlying variational theory and some nonintuitive PE-based techniques of wave and particle manipulation that the theory predicts. It will also be shown that the PE can be understood as the cause for the basic properties of both linear and nonlinear waves in plasma, including their dispersion, energy-momentum transport, and various modulational instabilities. Linear collisionless dissipation (both on particles and classical waves, treated on the same footing) also appears merely as a special case of the modulational dynamics. The work was supported by NNSA grant DE274-FG52-08NA28553, DOE contract DE-AC02-09CH11466, and DTRA grant HDTRA1-11-1-0037.

A theory of quantum dynamics of a nanomagnet under excitation

NASA Astrophysics Data System (ADS)

Sham, L. J.

2013-09-01

A quantum treatment of magnetization dynamics of a nanomagnet between a thousand and a million spins may be needed as the magnet interacts with quantum control. The advantage of the all-quantum approach over the classical treatment of magnetization is the accounting for the correlation between the magnet and the control agent and the first-principles source of noise. This supplement to the conference talk will concentrate on an overview of the theory with a presentation of the basic ideas which could have wide applications and illustrations with some results. Details of applications to specific models are or will be published elsewhere. A clear concept of the structure of the ground and excited macrospin states as magnetization rotation states and magnons in the Bloch/Dyson sense gives rise to a consistent theory of the magnetization dynamics of a ferromagnet modeled by the Heisenberg Hamiltonian. An example of quantum control is the spin torque transfer, treated here as a sequence of scatterings of each current electron with the localized electrons of the ferromagnet, yields in each encounter a probability distribution of the magnetization recoil state correlated with each outgoing state of the electron. This picture provides a natural Monte Carlo process for simulation of the dynamics in which the probability is determined by quantum mechanics. The computed results of mean motion, noise and damping of the magnetization will be discussed.

Dynamics of Inhomogeneous Shell Systems Under Non-Stationary Loading (Survey)

NASA Astrophysics Data System (ADS)

Lugovoi, P. Z.; Meish, V. F.

2017-09-01

Experimental works on the determination of dynamics of smooth and stiffened cylindrical shells contacting with a soil medium under various non-stationary loading are reviewed. The results of studying three-layer shells of revolution whose motion equations are obtained within the framework of the hypotheses of the Timoshenko geometrically nonlinear theory are stated. The numerical results for shells with a piecewise or discrete filler enable the analysis of estimation of the influence of geometrical and physical-mechanical parameters of structures on their dynamics and reveal new mechanical effects. Basing on the classical theory of shells and rods, the effect of the discrete arrangement of ribs and coefficients of the Winkler or Pasternak elastic foundation on the normal frequencies and modes of rectangular planar cylindrical and spherical shells is studied. The number and shape of dispersion curves for longitudinal harmonic waves in a stiffened cylindrical shell are determined. The equations of vibrations of ribbed shells of revolution on Winkler or Pasternak elastic foundation are obtained using the geometrically nonlinear theory and the Timoshenko hypotheses. On applying the integral-interpolational method, numerical algorithms are developed and the corresponding non-stationary problems are solved. The special attention is paid to the statement and solution of coupled problems on the dynamical interaction of cylindrical or spherical shells with the soil water-saturated medium of different structure.

Novel view on the mechanism of water-assisted proton transfer in the DNA bases: bulk water hydration.

PubMed

Furmanchuk, Al'ona; Isayev, Olexandr; Gorb, Leonid; Shishkin, Oleg V; Hovorun, Dmytro M; Leszczynski, Jerzy

2011-03-14

In the present work, the conventional static ab initio picture of a water-assisted mechanism of the tautomerization of Nucleic Acid Bases (NABs) in an aqueous environment is enhanced by the classical and Car-Parrinello molecular dynamics simulations. The inclusion of the dynamical contribution is vital because the formation and longevity of the NAB-water bridge complexes represent decisive factors for further tautomerization. The results of both molecular dynamic techniques indicate that the longest time when such complexes exist is significantly shorter than the time required for proton transfer suggested by the static ab initio level of theory. New rate constants of tautomerization corrected for the dynamic effect of environment are proposed based on the first principles molecular dynamics data. Those values are used for the evaluation of a water-assisted mechanism that is feasible in such biological systems as E. coli cell.

Quantum decision-maker theory and simulation

NASA Astrophysics Data System (ADS)

Zak, Michail; Meyers, Ronald E.; Deacon, Keith S.

2000-07-01

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics. The autonomy of the decision making process is achieved by a feedback from the mental to motor dynamics which changes the stochastic matrix based upon the probability distribution. This feedback replaces unavailable external information by an internal knowledge- base stored in the mental model in the form of probability distributions. As a result, the coupled motor-mental dynamics is described by a nonlinear version of Markov chains which can decrease entropy without an external source of information. Applications to common sense based decisions as well as to evolutionary games are discussed. An example exhibiting self-organization is computed using quantum computer simulation. Force on force and mutual aircraft engagements using the quantum decision maker dynamics are considered.

Universality classes of fluctuation dynamics in hierarchical complex systems

NASA Astrophysics Data System (ADS)

Macêdo, A. M. S.; González, Iván R. Roa; Salazar, D. S. P.; Vasconcelos, G. L.

2017-03-01

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

Koopman-von Neumann formulation of classical Yang-Mills theories: I

NASA Astrophysics Data System (ADS)

Carta, P.; Gozzi, E.; Mauro, D.

2006-03-01

In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.

a Classical Isodual Theory of Antimatter and its Prediction of Antigravity

NASA Astrophysics Data System (ADS)

Santilli, Ruggero Maria

An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatment of matter and antimatter in due time, and as the classical foundations of an axiomatically consistent inclusion of gravitation in unified gauge theories recently appeared elsewhere, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with corresponding formulations at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is antiautomorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also antiautomorphic (and more generally, antiisomorphic), yet it is applicable beginning at the classical level and then persists at the quantum level where it becomes equivalent to charge conjugation. We therefore present, apparently for the first time, the classical isodual theory of antimatter, we identify the physical foundations of the theory as being the novel isodual Galilean, special and general relativities, and we show the compatibility of the theory with all available classical experimental data on antimatter. We identify the classical foundations of the prediction of antigravity for antimatter in the field of matter (or vice-versa) without any claim on its validity, and defer its resolution to specifically identified experiments. We identify the novel, classical, isodual electromagnetic waves which are predicted to be emitted by antimatter, the so-called space-time machine based on a novel non-Newtonian geometric propulsion, and other implications of the theory. We also introduce, apparently for the first time, the isodual space and time inversions and show that they are nontrivially different than the conventional ones, thus offering a possibility for the future resolution whether far away galaxies and quasars are made up of matter or of antimatter. The paper ends with the indication that the studies are at their first infancy, and indicates some of the open problems. To avoid a prohibitive length, the paper is restricted to the classical treatment, while studies on operator profiles are treated elsewhere.

Dopamine and Caffeine Encapsulation within Boron Nitride (14,0) Nanotubes: Classical Molecular Dynamics and First Principles Calculations.

PubMed

García-Toral, Dolores; González-Melchor, Minerva; Rivas-Silva, Juan F; Meneses-Juárez, Efraín; Cano-Ordaz, José; H Cocoletzi, Gregorio

2018-06-07

Classical molecular dynamics (MD) and density functional theory (DFT) calculations are developed to investigate the dopamine and caffeine encapsulation within boron nitride (BN) nanotubes (NT) with (14,0) chirality. Classical MD studies are done at canonical and isobaric-isothermal conditions at 298 K and 1 bar in explicit water. Results reveal that both molecules are attracted by the nanotube; however, only dopamine is able to enter the nanotube, whereas caffeine moves in its vicinity, suggesting that both species can be transported: the first by encapsulation and the second by drag. Findings are analyzed using the dielectric behavior, pair correlation functions, diffusion of the species, and energy contributions. The DFT calculations are performed according to the BLYP approach and applying the atomic base of the divided valence 6-31g(d) orbitals. The geometry optimization uses the minimum-energy criterion, accounting for the total charge neutrality and multiplicity of 1. Adsorption energies in the dopamine encapsulation indicate physisorption, which induces the highly occupied molecular orbital-lower unoccupied molecular orbital gap reduction yielding a semiconductor behavior. The charge redistribution polarizes the BNNT/dopamine and BNNT/caffeine structures. The work function decrease and the chemical potential values suggest the proper transport properties in these systems, which may allow their use in nanobiomedicine.

An Appraisal of the Classic Forest Succession Paradigm with the Shade Tolerance Index

PubMed Central

Lienard, Jean; Florescu, Ionut; Strigul, Nikolay

2015-01-01

In this paper we revisit the classic theory of forest succession that relates shade tolerance and species replacement and assess its validity to understand patch-mosaic patterns of forested ecosystems of the USA. We introduce a macroscopic parameter called the “shade tolerance index” and compare it to the classic continuum index in southern Wisconsin forests. We exemplify shade tolerance driven succession in White Pine-Eastern Hemlock forests using computer simulations and analyzing approximated chronosequence data from the USDA FIA forest inventory. We describe this parameter across the last 50 years in the ecoregions of mainland USA, and demonstrate that it does not correlate with the usual macroscopic characteristics of stand age, biomass, basal area, and biodiversity measures. We characterize the dynamics of shade tolerance index using transition matrices and delimit geographical areas based on the relevance of shade tolerance to explain forest succession. We conclude that shade tolerance driven succession is linked to climatic variables and can be considered as a primary driving factor of forest dynamics mostly in central-north and northeastern areas in the USA. Overall, the shade tolerance index constitutes a new quantitative approach that can be used to understand and predict succession of forested ecosystems and biogeographic patterns. PMID:25658092

Consumer effects on the vital rates of their resource can determine the outcome of competition between consumers.

PubMed

Lee, Charlotte T; Miller, Tom E X; Inouye, Brian D

2011-10-01

Current competition theory does not adequately address the fact that competitors may affect the survival, growth, and reproductive rates of their resources. Ecologically important interactions in which consumers affect resource vital rates range from parasitism and herbivory to mutualism. We present a general model of competition that explicitly includes consumer-dependent resource vital rates. We build on the classic MacArthur model of competition for multiple resources, allowing direct comparison with expectations from established concepts of resource-use overlap. Consumers share a stage-structured resource population but may use the different stages to different extents, as they do the different independent resources in the classic model. Here, however, the stages are dynamically linked via consumer-dependent vital rates. We show that consumers' effects on resource vital rates result in two important departures from classic results. First, consumers can coexist despite identical use of resource stages, provided each competitor shifts the resource stage distribution toward stages that benefit other species. Second, consumers specializing on different resource stages can compete strongly, possibly resulting in competitive exclusion despite a lack of resource stage-use overlap. Our model framework demonstrates the critical role that consumer-dependent resource vital rates can play in competitive dynamics in a wide range of biological systems.

Simple improvements to classical bubble nucleation models.

PubMed

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

2015-08-01

We revisit classical nucleation theory (CNT) for the homogeneous bubble nucleation rate and improve the classical formula using a correct prefactor in the nucleation rate. Most of the previous theoretical studies have used the constant prefactor determined by the bubble growth due to the evaporation process from the bubble surface. However, the growth of bubbles is also regulated by the thermal conduction, the viscosity, and the inertia of liquid motion. These effects can decrease the prefactor significantly, especially when the liquid pressure is much smaller than the equilibrium one. The deviation in the nucleation rate between the improved formula and the CNT can be as large as several orders of magnitude. Our improved, accurate prefactor and recent advances in molecular dynamics simulations and laboratory experiments for argon bubble nucleation enable us to precisely constrain the free energy barrier for bubble nucleation. Assuming the correction to the CNT free energy is of the functional form suggested by Tolman, the precise evaluations of the free energy barriers suggest the Tolman length is ≃0.3σ independently of the temperature for argon bubble nucleation, where σ is the unit length of the Lennard-Jones potential. With this Tolman correction and our prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.

Effects of lateral diffusion on morphology and dynamics of a microscopic lattice-gas model of pulsed electrodeposition.

PubMed

Frank, Stefan; Roberts, Daniel E; Rikvold, Per Arne

2005-02-08

The influence of nearest-neighbor diffusion on the decay of a metastable low-coverage phase (monolayer adsorption) in a square lattice-gas model of electrochemical metal deposition is investigated by kinetic Monte Carlo simulations. The phase-transformation dynamics are compared to the well-established Kolmogorov-Johnson-Mehl-Avrami theory. The phase transformation is accelerated by diffusion, but remains in accord with the theory for continuous nucleation up to moderate diffusion rates. At very high diffusion rates the phase-transformation kinetic shows a crossover to instantaneous nucleation. Then, the probability of medium-sized clusters is reduced in favor of large clusters. Upon reversal of the supersaturation, the adsorbate desorbs, but large clusters still tend to grow during the initial stages of desorption. Calculation of the free energy of subcritical clusters by enumeration of lattice animals yields a quasiequilibrium distribution which is in reasonable agreement with the simulation results. This is an improvement relative to classical droplet theory, which fails to describe the distributions, since the macroscopic surface tension is a bad approximation for small clusters.

A computational fluid dynamics approach to nucleation in the water-sulfuric acid system.

PubMed

Herrmann, E; Brus, D; Hyvärinen, A-P; Stratmann, F; Wilck, M; Lihavainen, H; Kulmala, M

2010-08-12

This study presents a computational fluid dynamics modeling approach to investigate the nucleation in the water-sulfuric acid system in a flow tube. On the basis of an existing experimental setup (Brus, D.; Hyvärinen, A.-P.; Viisanen, Y.; Kulmala, M.; Lihavainen, H. Atmos. Chem. Phys. 2010, 10, 2631-2641), we first establish the effect of convection on the flow profile. We then proceed to simulate nucleation for relative humidities of 10, 30, and 50% and for sulfuric acid concentration between 10(9) to 3 x 10(10) cm(-3). We describe the nucleation zone in detail and determine how flow rate and relative humidity affect its characteristics. Experimental nucleation rates are compared to rates gained from classical binary and kinetic nucleation theory as well as cluster activation theory. For low RH values, kinetic theory yields the best agreement with experimental results while binary nucleation best reproduces the experimental nucleation behavior at 50% relative humidity. Particle growth is modeled for an example case at 50% relative humidity. The final simulated diameter is very close to the experimental result.

Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

Quantum Chaos

NASA Astrophysics Data System (ADS)

Casati, Giulio; Chirikov, Boris

2006-11-01

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

Quantum Chaos

NASA Astrophysics Data System (ADS)

Casati, Giulio; Chirikov, Boris

1995-04-01

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

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…

Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

NASA Astrophysics Data System (ADS)

Dahmen, David; Bos, Hannah; Helias, Moritz

2016-07-01

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections. The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random, and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate nonlinear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units. The linearized theory yields an expansion of the correlation and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.

Communication: Two-step explosion processes of highly charged fullerene cations C{sub 60}{sup q+} (q = 20–60)

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

Yamazaki, Kaoru; Nakamura, Takashi; Kanno, Manabu

2014-09-28

To establish the fundamental understanding of the fragmentation dynamics of highly positive charged nano- and bio-materials, we carried out on-the-fly classical trajectory calculations on the fragmentation dynamics of C{sub 60}{sup q+} (q = 20–60). We used the UB3LYP/3-21G level of density functional theory and the self-consistent charge density-functional based tight-binding theory. For q ≥ 20, we found that a two-step explosion mechanism governs the fragmentation dynamics: C{sub 60}{sup q+} first ejects singly and multiply charged fast atomic cations C{sup z+} (z ≥ 1) via Coulomb explosions on a timescale of 10 fs to stabilize the remaining core cluster. Thermal evaporationsmore » of slow atomic and molecular fragments from the core cluster subsequently occur on a timescale of 100 fs to 1 ps. Increasing the charge q makes the fragments smaller. This two-step mechanism governs the fragmentation dynamics in the most likely case that the initial kinetic energy accumulated upon ionization to C{sub 60}{sup q+} by ion impact or X-ray free electron laser is larger than 100 eV.« less

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

NASA Astrophysics Data System (ADS)

Jang, Seogjoo; Voth, Gregory A.

2016-02-01

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

Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electron transfer

NASA Astrophysics Data System (ADS)

Cotton, Stephen J.; Igumenshchev, Kirill; Miller, William H.

2014-08-01

It has recently been shown [S. J. Cotton and W. H. Miller, J. Chem. Phys. 139, 234112 (2013)] that a symmetrical windowing quasi-classical (SQC) approach [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] applied to the Meyer-Miller model [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] for the electronic degrees of freedom in electronically non-adiabatic dynamics is capable of quantitatively reproducing quantum mechanical results for a variety of test applications, including cases where "quantum" coherence effects are significant. Here we apply this same SQC methodology, within a flux-side correlation function framework, to calculate thermal rate constants corresponding to several proposed models of electron transfer processes [P. Huo, T. F. Miller III, and D. F. Coker, J. Chem. Phys. 139, 151103 (2013); A. R. Menzeleev, N. Ananth, and T. F. Miller III, J. Chem. Phys. 135, 074106 (2011)]. Good quantitative agreement with Marcus Theory is obtained over several orders of magnitude variation in non-adiabatic coupling. Moreover, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory is also reproduced with good accuracy by this very simple classical approach. The SQC treatment is also applied to a recent model of photoinduced proton coupled electron transfer [C. Venkataraman, A. V. Soudackov, and S. Hammes-Schiffer, J. Chem. Phys. 131, 154502 (2009)] and population decay of the photoexcited donor state is found to be in reasonable agreement with results calculated via reduced density matrix theory.

Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electron transfer

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

Cotton, Stephen J.; Igumenshchev, Kirill; Miller, William H., E-mail: millerwh@berkeley.edu

It has recently been shown [S. J. Cotton and W. H. Miller, J. Chem. Phys. 139, 234112 (2013)] that a symmetrical windowing quasi-classical (SQC) approach [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] applied to the Meyer-Miller model [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] for the electronic degrees of freedom in electronically non-adiabatic dynamics is capable of quantitatively reproducing quantum mechanical results for a variety of test applications, including cases where “quantum” coherence effects are significant. Here we apply this same SQC methodology, within a flux-side correlation functionmore » framework, to calculate thermal rate constants corresponding to several proposed models of electron transfer processes [P. Huo, T. F. Miller III, and D. F. Coker, J. Chem. Phys. 139, 151103 (2013); A. R. Menzeleev, N. Ananth, and T. F. Miller III, J. Chem. Phys. 135, 074106 (2011)]. Good quantitative agreement with Marcus Theory is obtained over several orders of magnitude variation in non-adiabatic coupling. Moreover, the “inverted regime” in thermal rate constants (with increasing bias) known from Marcus Theory is also reproduced with good accuracy by this very simple classical approach. The SQC treatment is also applied to a recent model of photoinduced proton coupled electron transfer [C. Venkataraman, A. V. Soudackov, and S. Hammes-Schiffer, J. Chem. Phys. 131, 154502 (2009)] and population decay of the photoexcited donor state is found to be in reasonable agreement with results calculated via reduced density matrix theory.« less

A New Approach on the Long Term Dynamics of NEO's Under Yarkovsky Effect.

NASA Astrophysics Data System (ADS)

Peláez, Jesús; Urrutxua, Hodei; Bombardelli, Claudio; Perez-Grande, Isabel

2011-12-01

A classical approach to the many-body problem is that of using special perturbation methods. Nowadays and due to the availability of high-speed computers is an essential tool in Space Dynamics which exhibits a great advantage: it is applicable to any orbit involving any number of bodies and all sorts of astrodynamical problems, especially when these problems fall into regions in which general perturbation theories are absent. One such case is, for example, that Near Earth Objects (NEO's) dynamics. In this field, the Group of Tether Dynamics of UPM (GDT) has developed a new regularisation scheme - called DROMO - which is characterised by only 8 ODE. This new regularisation scheme allows a new approach to the dynamics of NEO's in the long term, specially appropriated to consider the influence of the anisotropic thermal emission (Yarkovsky and YORP effects) on the dynamics. A new project, called NEODROMO, has been started in GDT that aims to provide a reliable tool for the long term dynamics of NEO's.

A note on local BRST cohomology of Yang-Mills type theories with free Abelian factors

NASA Astrophysics Data System (ADS)

Barnich, Glenn; Boulanger, Nicolas

2018-05-01

We extend previous work on antifield dependent local Becchi-Rouet-Stora-Tyutin (BRST) cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free Abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.

Sampling Molecular Conformers in Solution with Quantum Mechanical Accuracy at a Nearly Molecular-Mechanics Cost.

PubMed

Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano

2016-09-13

We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.

Density functional theory based molecular dynamics study of hydration and electronic properties of aqueous La(3+).

PubMed

Terrier, Cyril; Vitorge, Pierre; Gaigeot, Marie-Pierre; Spezia, Riccardo; Vuilleumier, Rodolphe

2010-07-28

Structural and electronic properties of La(3+) immersed in bulk water have been assessed by means of density functional theory (DFT)-based Car-Parrinello molecular dynamics (CPMD) simulations. Correct structural properties, i.e., La(III)-water distances and La(III) coordination number, can be obtained within the framework of Car-Parrinello simulations providing that both the La pseudopotential and conditions of the dynamics (fictitious mass and time step) are carefully set up. DFT-MD explicitly treats electronic densities and is shown here to provide a theoretical justification to the necessity of including polarization when studying highly charged cations such as lanthanoids(III) with classical MD. La(3+) was found to strongly polarize the water molecules located in the first shell, giving rise to dipole moments about 0.5 D larger than those of bulk water molecules. Finally, analyzing Kohn-Sham orbitals, we found La(3+) empty 4f orbitals extremely compact and to a great extent uncoupled from the water conduction band, while the 5d empty orbitals exhibit mixing with unoccupied states of water.

Study of basic physical processes in liquid rocket engines

NASA Technical Reports Server (NTRS)

Wu, S. T.; Chen, C. P.

1992-01-01

Inconsistencies between analytical results and measurements for liquid rocket thrust chamber performance, which escape suitable explanations, have motivated the examination of the basic phys ical modeling formulations as to their unlimited application. The publication of Prof. D. Straub's book, 'Thermofluid-dynamics of Optimized Rocket Propulsions,' further stimulated the interest of understanding the gas dynamic relationships in chemically reacting mixtures. A review of other concepts proposed by Falk-Ruppel (Gibbsian Thermodynamics), Straub (Alternative Theory, AT), Prigogine (Non-Equilibrium Thermodynamics), Boltzmann (Kinetic Theory), and Truesdell (Rational Mechanism) has been made to obtain a better understanding of the Navier-Stokes equation, which is now used extensively for chemically reacting flow treatment in combustion chambers. In addition to the study of the different concepts, two workshops were conducted to clarify some of the issues. The first workshop centered on Falk-Ruppel's new 'dynamics' concept, while the second one concentrated on Straub's AT. In this report brief summaries of the reviewed philosophies are presented and compared with the classical Navier-Stokes formulation in a tabular arrangement. Also the highlights of both workshops are addressed.

Quantum-like dynamics of decision-making

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu

2012-03-01

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the “rational strategy” provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect (“irrationality” of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011) [55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker.

Evaluating gambles using dynamics

NASA Astrophysics Data System (ADS)

Peters, O.; Gell-Mann, M.

2016-02-01

Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.

Applying the Explicit Time Central Difference Method for Numerical Simulation of the Dynamic Behavior of Elastoplastic Flexible Reinforced Plates

NASA Astrophysics Data System (ADS)

Yankovskii, A. P.

2017-12-01

Based on a stepwise algorithm involving central finite differences for the approximation in time, a mathematical model is developed for elastoplastic deformation of cross-reinforced plates with isotropically hardening materials of components of the composition. The model allows obtaining the solution of elastoplastic problems at discrete points in time by an explicit scheme. The initial boundary value problem of the dynamic behavior of flexible plates reinforced in their own plane is formulated in the von Kármán approximation with allowance for their weakened resistance to the transverse shear. With a common approach, the resolving equations corresponding to two variants of the Timoshenko theory are obtained. An explicit "cross" scheme for numerical integration of the posed initial boundary value problem has been constructed. The scheme is consistent with the incremental algorithm used for simulating the elastoplastic behavior of a reinforced medium. Calculations of the dynamic behavior have been performed for elastoplastic cylindrical bending of differently reinforced fiberglass rectangular elongated plates. It is shown that the reinforcement structure significantly affects their elastoplastic dynamic behavior. It has been found that the classical theory of plates is as a rule unacceptable for carrying out the required calculations (except for very thin plates), and the first version of the Timoshenko theory yields reasonable results only in cases of relatively thin constructions reinforced by lowmodulus fibers. Proceeding from the results of the work, it is recommended to use the second variant of the Timoshenko theory (as a more accurate one) for calculations of the elastoplastic behavior of reinforced plates.

The Prediction of Item Parameters Based on Classical Test Theory and Latent Trait Theory

ERIC Educational Resources Information Center

Anil, Duygu

2008-01-01

In this study, the prediction power of the item characteristics based on the experts' predictions on conditions try-out practices cannot be applied was examined for item characteristics computed depending on classical test theory and two-parameters logistic model of latent trait theory. The study was carried out on 9914 randomly selected students…

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.

Any Ontological Model of the Single Qubit Stabilizer Formalism must be Contextual

NASA Astrophysics Data System (ADS)

Lillystone, Piers; Wallman, Joel J.

Quantum computers allow us to easily solve some problems classical computers find hard. Non-classical improvements in computational power should be due to some non-classical property of quantum theory. Contextuality, a more general notion of non-locality, is a necessary, but not sufficient, resource for quantum speed-up. Proofs of contextuality can be constructed for the classically simulable stabilizer formalism. Previous proofs of stabilizer contextuality are known for 2 or more qubits, for example the Mermin-Peres magic square. In the work presented we extend these results and prove that any ontological model of the single qubit stabilizer theory must be contextual, as defined by R. Spekkens, and give a relation between our result and the Mermin-Peres square. By demonstrating that contextuality is present in the qubit stabilizer formalism we provide further insight into the contextuality present in quantum theory. Understanding the contextuality of classical sub-theories will allow us to better identify the physical properties of quantum theory required for computational speed up. This research was supported by CIFAR, the Government of Ontario, and the Government of Canada through NSERC and Industry Canada.

Evaluation of the mathematical and economic basis for conversion processes in the LEAP energy-economy model

NASA Astrophysics Data System (ADS)

Oblow, E. M.

1982-10-01

An evaluation was made of the mathematical and economic basis for conversion processes in the Long-term Energy Analysis Program (LEAP) energy economy model. Conversion processes are the main modeling subunit in LEAP used to represent energy conversion industries and are supposedly based on the classical economic theory of the firm. Questions about uniqueness and existence of LEAP solutions and their relation to classical equilibrium economic theory prompted the study. An analysis of classical theory and LEAP model equations was made to determine their exact relationship. The conclusions drawn from this analysis were that LEAP theory is not consistent with the classical theory of the firm. Specifically, the capacity factor formalism used by LEAP does not support a classical interpretation in terms of a technological production function for energy conversion processes. The economic implications of this inconsistency are suboptimal process operation and short term negative profits in years where plant operation should be terminated. A new capacity factor formalism, which retains the behavioral features of the original model, is proposed to resolve these discrepancies.

(Re)igniting a Sociological Imagination in Adult Education: The Continuing Relevance of Classical Theory

ERIC Educational Resources Information Center

Lange, Elizabeth

2015-01-01

This article argues that sociology has been a foundational discipline for the field of adult education, but it has been largely implicit, until recently. This article contextualizes classical theories of sociology within contemporary critiques, reviews the historical roots of sociology and then briefly introduces the classical theories…

Dynamics of Photoexcited State of Semiconductor Quantum Dots

NASA Astrophysics Data System (ADS)

Trivedi, Dhara J.

In this thesis, non-adiabatic molecular dynamics (NAMD) of excited states in semiconductor quantum dots are investigated. Nanoscale systems provide important opportunities for theory and computation for research because the experimental tools often provide an incomplete picture of the structure and/or function of nanomaterials, and theory can often fill in missing features crucial in understanding what is being measured. The simulation of NAMD is an indispensable tool for understanding complex ultrafast photoinduced processes such as charge and energy transfer, thermal relaxation, and charge recombination. Based on the state-of-the-art ab initio approaches in both the energy and time domains, the thesis presents a comprehensive discussion of the dynamical processes in quantum dots, ranging from the initial photon absorption to the final emission. We investigate the energy relaxation and transfer rates in pure and surface passivated quantum dots of different sizes. The study establishes the fundamental mechanisms of the electron and hole relaxation processes with and without hole traps. We develop and implement more accurate and efficient methods for NAMD. These methods are advantageous over the traditional ones when one encounters classically forbidden transitions. We also explore the effect of decoherence and non-adiabatic couplings on the dynamics. The results indicate significant influence on the accuracy and related computational cost of the simulated dynamics.

Comprehensive nonlocal analysis of piezoelectric nanobeams with surface effects in bending, buckling and vibrations under magneto-electro-thermo-mechanical loading

NASA Astrophysics Data System (ADS)

Ebrahimi-Nejad, Salman; Boreiry, Mahya

2018-03-01

The bending, buckling and vibrational behavior of size-dependent piezoelectric nanobeams under thermo-magneto-mechano-electrical environment are investigated by performing a parametric study, in the presence of surface effects. The Gurtin-Murdoch surface elasticity and Eringen’s nonlocal elasticity theories are applied in the framework of Euler–Bernoulli beam theory to obtain a new non-classical size-dependent beam model for dynamic and static analyses of piezoelectric nanobeams. In order to satisfy the surface equilibrium equations, cubic variation of stress with beam thickness is assumed for the bulk stress component which is neglected in classical beam models. Results are obtained for clamped - simply-supported (C-S) and simply-supported - simply-supported (S-S) boundary conditions using a proposed analytical solution method. Numerical examples are presented to demonstrate the effects of length, surface effects, nonlocal parameter and environmental changes (temperature, magnetic field and external voltage) on deflection, critical buckling load and natural frequency for each boundary condition. Results of this study can serve as benchmarks for the design and analysis of nanostructures of magneto-electro-thermo-elastic materials.

Classical and quantum stability in putative landscapes

DOE PAGES

Dine, Michael

2017-01-18

Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity.more » We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.« less

Complex Economies Have a Lateral Escape from the Poverty Trap

PubMed Central

Pugliese, Emanuele; Chiarotti, Guido L.; Zaccaria, Andrea; Pietronero, Luciano

2017-01-01

We analyze the decisive role played by the complexity of economic systems at the onset of the industrialization process of countries over the past 50 years. Our analysis of the input growth dynamics, considering a further dimension through a recently introduced measure of economic complexity, reveals that more differentiated and more complex economies face a lower barrier (in terms of GDP per capita) when starting the transition towards industrialization. As a consequence, we can extend the classical concept of a one-dimensional poverty trap, by introducing a two-dimensional poverty trap: a country will start the industrialization process if it is rich enough (as in neo-classical economic theories), complex enough (using this new dimension and laterally escaping from the poverty trap), or a linear combination of the two. This naturally leads to the proposal of a Complex Index of Relative Development (CIRD) which shows, when analyzed as a function of the growth due to input, a shape of an upside down parabola similar to that expected from the standard economic theories when considering only the GDP per capita dimension. PMID:28072867

Complex Economies Have a Lateral Escape from the Poverty Trap.

PubMed

Pugliese, Emanuele; Chiarotti, Guido L; Zaccaria, Andrea; Pietronero, Luciano

2017-01-01

We analyze the decisive role played by the complexity of economic systems at the onset of the industrialization process of countries over the past 50 years. Our analysis of the input growth dynamics, considering a further dimension through a recently introduced measure of economic complexity, reveals that more differentiated and more complex economies face a lower barrier (in terms of GDP per capita) when starting the transition towards industrialization. As a consequence, we can extend the classical concept of a one-dimensional poverty trap, by introducing a two-dimensional poverty trap: a country will start the industrialization process if it is rich enough (as in neo-classical economic theories), complex enough (using this new dimension and laterally escaping from the poverty trap), or a linear combination of the two. This naturally leads to the proposal of a Complex Index of Relative Development (CIRD) which shows, when analyzed as a function of the growth due to input, a shape of an upside down parabola similar to that expected from the standard economic theories when considering only the GDP per capita dimension.

Classical and quantum stability in putative landscapes

NASA Astrophysics Data System (ADS)

Dine, Michael

2017-01-01

Landscape analyses often assume the existence of large numbers of fields, N , with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N , eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N ; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. We consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.

Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions.

PubMed

Jiang, Hao; Haji-Akbari, Amir; Debenedetti, Pablo G; Panagiotopoulos, Athanassios Z

2018-01-28

We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the Extended Simple Point Charge (SPC/E) water model. The calculated nucleation rates are significantly lower than the available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.

Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions

NASA Astrophysics Data System (ADS)

Jiang, Hao; Haji-Akbari, Amir; Debenedetti, Pablo G.; Panagiotopoulos, Athanassios Z.

2018-01-01

We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the Extended Simple Point Charge (SPC/E) water model. The calculated nucleation rates are significantly lower than the available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.

Closed string tachyon driving f(R) cosmology

NASA Astrophysics Data System (ADS)

Wang, Peng; Wu, Houwen; Yang, Haitang

2018-05-01

To study quantum effects on the bulk tachyon dynamics, we replace R with f(R) in the low-energy effective action that couples gravity, the dilaton, and the bulk closed string tachyon of bosonic closed string theory and study properties of their classical solutions. The α' corrections of the graviton-dilaton-tachyon system are implemented in the f(R). We obtain the tachyon-induced rolling solutions and show that the string metric does not need to remain fixed in some cases. In the case with H( t=‑∞ ) = , only the R and R2 terms in f(R) play a role in obtaining the rolling solutions with nontrivial metric. The singular behavior of more classical solutions are investigated and found to be modified by quantum effects. In particular, there could exist some classical solutions, in which the tachyon field rolls down from a maximum of the tachyon potential while the dilaton expectation value is always bounded from above during the rolling process.

Parametric resonance in tunable superconducting cavities

NASA Astrophysics Data System (ADS)

Wustmann, Waltraut; Shumeiko, Vitaly

2013-05-01

We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the superconducting quantum interference device (SQUID) attached to the cavity and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum-statistical properties of the noise are addressed such as squeezing spectra, second-order coherence, and two-mode entanglement.

EPRL/FK asymptotics and the flatness problem

NASA Astrophysics Data System (ADS)

Oliveira, José Ricardo

2018-05-01

Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since these models’ relation to classical Einstein gravity is not explicit, an important test of their viabilitiy is the study of asymptotics—the classical theory should be obtained in a limit where quantum effects are negligible, taken to be the limit of large triangle areas in a triangulated manifold with boundary. In this paper we will briefly introduce the EPRL/FK spin foam model and known results about its asymptotics, proceeding then to describe a practical computation of spin foam and semiclassical geometric data for a simple triangulation with only one interior triangle. The results are used to comment on the ‘flatness problem’—a hypothesis raised by Bonzom (2009 Phys. Rev. D 80 064028) suggesting that EPRL/FK’s classical limit only describes flat geometries in vacuum.

General Entanglement Scaling Laws from Time Evolution

NASA Astrophysics Data System (ADS)

Eisert, Jens; Osborne, Tobias J.

2006-10-01

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.

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

Contemporary understanding of riots: Classical crowd psychology, ideology and the social identity approach.

PubMed

Stott, Clifford; Drury, John

2016-04-01

This article explores the origins and ideology of classical crowd psychology, a body of theory reflected in contemporary popularised understandings such as of the 2011 English 'riots'. This article argues that during the nineteenth century, the crowd came to symbolise a fear of 'mass society' and that 'classical' crowd psychology was a product of these fears. Classical crowd psychology pathologised, reified and decontextualised the crowd, offering the ruling elites a perceived opportunity to control it. We contend that classical theory misrepresents crowd psychology and survives in contemporary understanding because it is ideological. We conclude by discussing how classical theory has been supplanted in academic contexts by an identity-based crowd psychology that restores the meaning to crowd action, replaces it in its social context and in so doing transforms theoretical understanding of 'riots' and the nature of the self. © The Author(s) 2016.

Compatible quantum theory

NASA Astrophysics Data System (ADS)

Friedberg, R.; Hohenberg, P. C.

2014-09-01

Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call ‘compatible quantum theory (CQT)’, consists of a ‘microscopic’ part (MIQM), which applies to a closed quantum system of any size, and a ‘macroscopic’ part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths (‘c-truths’), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory requires a macroscopic mechanism for selecting a physical framework, which is part of the macroscopic theory (MAQM). The selection of a physical framework involves the breaking of the microscopic ‘framework symmetry’, which can proceed either phenomenologically as in the standard quantum measurement theory, or more fundamentally by considering the quantum system under study to be a subsystem of a macroscopic quantum system. The decoherent histories formulation of Gell-Mann and Hartle, as well as that of Omnès, are theories of this fundamental type, where the physical framework is selected by a coarse-graining procedure in which the physical phenomenon of decoherence plays an essential role. Various well-known interpretations of QM are described from the perspective of CQT. Detailed definitions and proofs are presented in the appendices.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

JDFTx: Software for joint density-functional theory

DOE PAGES

Sundararaman, Ravishankar; Letchworth-Weaver, Kendra; Schwarz, Kathleen A.; ...

2017-11-14

Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units). This code hosts the development of joint density-functional theory (JDFT) thatmore » combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.« less

JDFTx: Software for joint density-functional theory

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

Sundararaman, Ravishankar; Letchworth-Weaver, Kendra; Schwarz, Kathleen A.

Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units). This code hosts the development of joint density-functional theory (JDFT) thatmore » combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.« less

Influence of an asymmetric ring on the modeling of an orthogonally stiffened cylindrical shell

NASA Technical Reports Server (NTRS)

Rastogi, Naveen; Johnson, Eric R.

1994-01-01

Structural models are examined for the influence of a ring with an asymmetrical cross section on the linear elastic response of an orthogonally stiffened cylindrical shell subjected to internal pressure. The first structural model employs classical theory for the shell and stiffeners. The second model employs transverse shear deformation theories for the shell and stringer and classical theory for the ring. Closed-end pressure vessel effects are included. Interacting line load intensities are computed in the stiffener-to-skin joints for an example problem having the dimensions of the fuselage of a large transport aircraft. Classical structural theory is found to exaggerate the asymmetric response compared to the transverse shear deformation theory.

Two AFC Loops For Low CNR And High Dynamics

NASA Technical Reports Server (NTRS)

Hinedi, Sami M.; Aguirre, Sergio

1992-01-01

Two alternative digital automatic-frequency-control (AFC) loops proposed to acquire (or reacquire) and track frequency of received carrier radio signal. Intended for use where carrier-to-noise ratios (CNR's) low and carrier frequency characterized by high Doppler shift and Doppler rate because of high relative speed and acceleration, respectively, between transmitter and receiver. Either AFC loops used in place of phase-locked loop. New loop concepts integrate ideas from classical spectrum-estimation, digital-phase-locked-loop, and Kalman-Filter theories.

Complex Systems

PubMed Central

Goldberger, Ary L.

2006-01-01

Physiologic systems in health and disease display an extraordinary range of temporal behaviors and structural patterns that defy understanding based on linear constructs, reductionist strategies, and classical homeostasis. Application of concepts and computational tools derived from the contemporary study of complex systems, including nonlinear dynamics, fractals and “chaos theory,” is having an increasing impact on biology and medicine. This presentation provides a brief overview of an emerging area of biomedical research, including recent applications to cardiopulmonary medicine and chronic obstructive lung disease. PMID:16921107

Quantum-like dynamics of decision-making in prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu

2012-03-01

In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.

Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation

NASA Astrophysics Data System (ADS)

Frønsdal, Christian

Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.

Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

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

Dahms, Rainer N.

A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized whichmore » determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing generally occurs before the liquid length is reached. As a result, the significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.« less

Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

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

Dahms, Rainer N., E-mail: Rndahms@sandia.gov

A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized whichmore » determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing generally occurs before the liquid length is reached. The significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.« less

Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

DOE PAGES

Dahms, Rainer N.

2016-04-26

A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized whichmore » determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing generally occurs before the liquid length is reached. As a result, the significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.« less

Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

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

Chen, Tsung-Wei; Chiou, Dah-Wei; Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 106, Taiwan

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the seventh order in 1/E{sub g} (E{sub g}=2mc{sup 2} and m is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of themore » Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the seventh-order again, to be in accord with the classical Hamiltonian as well.« less

Demonstrating the Difference between Classical Test Theory and Item Response Theory Using Derived Test Data

ERIC Educational Resources Information Center

Magno, Carlo

2009-01-01

The present report demonstrates the difference between classical test theory (CTT) and item response theory (IRT) approach using an actual test data for chemistry junior high school students. The CTT and IRT were compared across two samples and two forms of test on their item difficulty, internal consistency, and measurement errors. The specific…

Studying Reliability of Open Ended Mathematics Items According to the Classical Test Theory and Generalizability Theory

ERIC Educational Resources Information Center

Guler, Nese; Gelbal, Selahattin

2010-01-01

In this study, the Classical test theory and generalizability theory were used for determination to reliability of scores obtained from measurement tool of mathematics success. 24 open-ended mathematics question of the TIMSS-1999 was applied to 203 students in 2007-spring semester. Internal consistency of scores was found as 0.92. For…

Relationships among Classical Test Theory and Item Response Theory Frameworks via Factor Analytic Models

ERIC Educational Resources Information Center

Kohli, Nidhi; Koran, Jennifer; Henn, Lisa

2015-01-01

There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior…

Theory and applications survey of decentralized control methods

NASA Technical Reports Server (NTRS)

Athans, M.

1975-01-01

A nonmathematical overview is presented of trends in the general area of decentralized control strategies which are suitable for hierarchical systems. Advances in decentralized system theory are closely related to advances in the so-called stochastic control problem with nonclassical information pattern. The basic assumptions and mathematical tools pertaining to the classical stochastic control problem are outlined. Particular attention is devoted to pitfalls in the mathematical problem formulation for decentralized control. Major conclusions are that any purely deterministic approach to multilevel hierarchical dynamic systems is unlikely to lead to realistic theories or designs, that the flow of measurements and decisions in a decentralized system should not be instantaneous and error-free, and that delays in information exchange in a decentralized system lead to reasonable approaches to decentralized control. A mathematically precise notion of aggregating information is not yet available.

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

Polymer quantization of the Einstein-Rosen wormhole throat

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

Kunstatter, Gabor; Peltola, Ari; Louko, Jorma

2010-01-15

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numericalmore » accuracy, the area spectrum obtained from a Schroedinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.« less

Overview of classical test theory and item response theory for the quantitative assessment of items in developing patient-reported outcomes measures.

PubMed

Cappelleri, Joseph C; Jason Lundy, J; Hays, Ron D

2014-05-01

The US Food and Drug Administration's guidance for industry document on patient-reported outcomes (PRO) defines content validity as "the extent to which the instrument measures the concept of interest" (FDA, 2009, p. 12). According to Strauss and Smith (2009), construct validity "is now generally viewed as a unifying form of validity for psychological measurements, subsuming both content and criterion validity" (p. 7). Hence, both qualitative and quantitative information are essential in evaluating the validity of measures. We review classical test theory and item response theory (IRT) approaches to evaluating PRO measures, including frequency of responses to each category of the items in a multi-item scale, the distribution of scale scores, floor and ceiling effects, the relationship between item response options and the total score, and the extent to which hypothesized "difficulty" (severity) order of items is represented by observed responses. If a researcher has few qualitative data and wants to get preliminary information about the content validity of the instrument, then descriptive assessments using classical test theory should be the first step. As the sample size grows during subsequent stages of instrument development, confidence in the numerical estimates from Rasch and other IRT models (as well as those of classical test theory) would also grow. Classical test theory and IRT can be useful in providing a quantitative assessment of items and scales during the content-validity phase of PRO-measure development. Depending on the particular type of measure and the specific circumstances, the classical test theory and/or the IRT should be considered to help maximize the content validity of PRO measures. Copyright © 2014 Elsevier HS Journals, Inc. All rights reserved.

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.

Chance, determinism and the classical theory of probability.

PubMed

Vasudevan, Anubav

2018-02-01

This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning. Copyright © 2017 Elsevier Ltd. All rights reserved.

Schrödinger Evolution of Self-Gravitating Disks

NASA Astrophysics Data System (ADS)

Batygin, Konstantin

2018-04-01

An understanding of the long-term evolution of self-gravitating disks ranks among the classic problems of dynamical astronomy. In this talk, I will describe an intriguing connection between the secular inclination dynamics of a Lagrange-Laplace disk and the time-dependent Schrödinger equation. Within the context of this formalism, nodal bending waves correspond to the eigen-modes of a quasiparticle’s wavefunction, confined in an infinite square well with boundaries given by the radial extent of the disk. I will further show that external secular perturbations upon self-gravitating disks exhibit a mathematical similarity to quantum scattering theory, yielding an analytic criterion for the gravitational rigidity of a nearly-Keplerian disk under external perturbations.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

NASA Astrophysics Data System (ADS)

Szańkowski, P.; Ramon, G.; Krzywda, J.; Kwiatkowski, D.; Cywiński, Ł.

2017-08-01

A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

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.

Classical plasma dynamics of Mie-oscillations in atomic clusters

NASA Astrophysics Data System (ADS)

Kull, H.-J.; El-Khawaldeh, A.

2018-04-01

Mie plasmons are of basic importance for the absorption of laser light by atomic clusters. In this work we first review the classical Rayleigh-theory of a dielectric sphere in an external electric field and Thomson’s plum-pudding model applied to atomic clusters. Both approaches allow for elementary discussions of Mie oscillations, however, they also indicate deficiencies in describing the damping mechanisms by electrons crossing the cluster surface. Nonlinear oscillator models have been widely studied to gain an understanding of damping and absorption by outer ionization of the cluster. In the present work, we attempt to address the issue of plasmon relaxation in atomic clusters in more detail based on classical particle simulations. In particular, we wish to study the role of thermal motion on plasmon relaxation, thereby extending nonlinear models of collective single-electron motion. Our simulations are particularly adopted to the regime of classical kinetics in weakly coupled plasmas and to cluster sizes extending the Debye-screening length. It will be illustrated how surface scattering leads to the relaxation of Mie oscillations in the presence of thermal motion and of electron spill-out at the cluster surface. This work is intended to give, from a classical perspective, further insight into recent work on plasmon relaxation in quantum plasmas [1].

Singularity-free dislocation dynamics with strain gradient elasticity

NASA Astrophysics Data System (ADS)

Po, Giacomo; Lazar, Markus; Seif, Dariush; Ghoniem, Nasr

2014-08-01

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and non-singular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the non-singular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop self-energy non-divergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of Lome-Cottrell junctions in Al show that the strength of the junction and its configuration are easily obtained, without ad-hoc regularization of the singular fields. Numerical convergence studies related to the implementation of the non-singular theory in DD are presented.

Discriminating micropathogen lineages and their reticulate evolution through graph theory-based network analysis: the case of Trypanosoma cruzi, the agent of Chagas disease.

PubMed

Arnaud-Haond, Sophie; Moalic, Yann; Barnabé, Christian; Ayala, Francisco José; Tibayrenc, Michel

2014-01-01

Micropathogens (viruses, bacteria, fungi, parasitic protozoa) share a common trait, which is partial clonality, with wide variance in the respective influence of clonality and sexual recombination on the dynamics and evolution of taxa. The discrimination of distinct lineages and the reconstruction of their phylogenetic history are key information to infer their biomedical properties. However, the phylogenetic picture is often clouded by occasional events of recombination across divergent lineages, limiting the relevance of classical phylogenetic analysis and dichotomic trees. We have applied a network analysis based on graph theory to illustrate the relationships among genotypes of Trypanosoma cruzi, the parasitic protozoan responsible for Chagas disease, to identify major lineages and to unravel their past history of divergence and possible recombination events. At the scale of T. cruzi subspecific diversity, graph theory-based networks applied to 22 isoenzyme loci (262 distinct Multi-Locus-Enzyme-Electrophoresis -MLEE) and 19 microsatellite loci (66 Multi-Locus-Genotypes -MLG) fully confirms the high clustering of genotypes into major lineages or "near-clades". The release of the dichotomic constraint associated with phylogenetic reconstruction usually applied to Multilocus data allows identifying putative hybrids and their parental lineages. Reticulate topology suggests a slightly different history for some of the main "near-clades", and a possibly more complex origin for the putative hybrids than hitherto proposed. Finally the sub-network of the near-clade T. cruzi I (28 MLG) shows a clustering subdivision into three differentiated lesser near-clades ("Russian doll pattern"), which confirms the hypothesis recently proposed by other investigators. The present study broadens and clarifies the hypotheses previously obtained from classical markers on the same sets of data, which demonstrates the added value of this approach. This underlines the potential of graph theory-based network analysis for describing the nature and relationships of major pathogens, thereby opening stimulating prospects to unravel the organization, dynamics and history of major micropathogen lineages.

Structure-based control of complex networks with nonlinear dynamics

NASA Astrophysics Data System (ADS)

Zanudo, Jorge G. T.; Yang, Gang; Albert, Reka

What can we learn about controlling a system solely from its underlying network structure? Here we use a framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors, regardless of the dynamic details and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of classical structural control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case, but not in specific model instances. This work was supported by NSF Grants PHY 1205840 and IIS 1160995. JGTZ is a recipient of a Stand Up To Cancer - The V Foundation Convergence Scholar Award.

Pair production in classical Stueckelberg-Horwitz-Piron electrodynamics

NASA Astrophysics Data System (ADS)

Land, Martin

2015-05-01

We calculate pair production from bremsstrahlung as a classical effect in Stueckelberg-Horwitz electrodynamics. In this framework, worldlines are traced out dynamically through the evolution of events xμ(τ) parameterized by a chronological time τ that is independent of the spacetime coordinates. These events, defined in an unconstrained 8D phase space, interact through five τ-dependent gauge fields induced by the event evolution. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit. In particular, the total mass-energy-momentum of particles and fields is conserved, but the mass-shell constraint is lifted from individual interacting events, so that the Feynman-Stueckelberg interpretation of pair creation/annihilation is implemented in classical mechanics. We consider a three-stage interaction which when parameterized by the laboratory clock x0 appears as (1) particle-1 scatters on a heavy nucleus to produce bremsstrahlung, (2) the radiation field produces a particle/antiparticle pair, (3) the antiparticle is annihilated with particle-2 in the presence of a second heavy nucleus. When parameterized in chronological time τ, the underlying process develops as (1) particle-2 scatters on the second nucleus and begins evolving backward in time with negative energy, (2) particle-1 scatters on the first nucleus and releases bremsstrahlung, (3) particle-2 absorbs radiation which returns it to forward time evolution with positive energy.

Quantum-mechanical analysis of low-gain free-electron laser oscillators

NASA Astrophysics Data System (ADS)

Fares, H.; Yamada, M.; Chiadroni, E.; Ferrario, M.

2018-05-01

In the previous classical theory of the low-gain free-electron laser (FEL) oscillators, the electron is described as a point-like particle, a delta function in the spatial space. On the other hand, in the previous quantum treatments, the electron is described as a plane wave with a single momentum state, a delta function in the momentum space. In reality, an electron must have statistical uncertainties in the position and momentum domains. Then, the electron is neither a point-like charge nor a plane wave of a single momentum. In this paper, we rephrase the theory of the low-gain FEL where the interacting electron is represented quantum mechanically by a plane wave with a finite spreading length (i.e., a wave packet). Using the concepts of the transformation of reference frames and the statistical quantum mechanics, an expression for the single-pass radiation gain is derived. The spectral broadening of the radiation is expressed in terms of the spreading length of an electron, the relaxation time characterizing the energy spread of electrons, and the interaction time. We introduce a comparison between our results and those obtained in the already known classical analyses where a good agreement between both results is shown. While the correspondence between our results and the classical results are shown, novel insights into the electron dynamics and the interaction mechanism are presented.

Dressing the post-Newtonian two-body problem and classical effective field theory

NASA Astrophysics Data System (ADS)

Kol, Barak; Smolkin, Michael

2009-12-01

We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling post-Newtonian (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain nonlinear worldline vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a nonrelativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.

Structural, dynamic and photophysical properties of a fluorescent dye incorporated in an amorphous hydrophobic polymer bundle.

PubMed

De Mitri, N; Prampolini, G; Monti, S; Barone, V

2014-08-21

The properties of a low molecular weight organic dye, namely 4-naphthyloxy-1-methoxy-2,2,6,6-tetramethylpiperidine, covalently bound to an apolar polyolefin were investigated by means of a multi-level approach, combining classical molecular dynamics simulations, based on purposely parameterized force fields, and quantum mechanical calculations based on density functional theory (DFT) and its time-dependent extension (TD-DFT). The structure and dynamics of the dye in its embedding medium were analyzed and discussed taking the entangling effect of the surrounding polymer into account, and also by comparing the results to those obtained for a different environment, i.e. toluene solution. Finally, the influence was investigated of long lived cages found in the polymeric embedding on photophysical properties, in terms of the slow and fast dye's internal dynamics, by comparing computed IR and UV spectra with their experimental counterparts.

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.

The Six Fundamental Characteristics of Chaos and Their Clinical Relevance to Psychiatry: a New Hypothesis for the Origin of Psychosis

NASA Astrophysics Data System (ADS)

Schmid, Gary Bruno

Underlying idea: A new hypothesis about how the mental state of psychosis may arise in the brain as a "linear" information processing pathology is briefly introduced. This hypothesis is proposed in the context of a complementary approach to psychiatry founded in the logical paradigm of chaos theory. To best understand the relation between chaos theory and psychiatry, the semantic structure of chaos theory is analyzed with the help of six general, and six specific, fundamental characteristics which can be directly inferred from empirical observations on chaotic systems. This enables a mathematically and physically stringent perspective on psychological phenomena which until now could only be grasped intuitively: Chaotic systems are in a general sense dynamic, intrinsically coherent, deterministic, recursive, reactive and structured: in a specific sense, self-organizing, unpredictable, nonreproducible, triadic, unstable and self-similar. To a great extent, certain concepts of chaos theory can be associated with corresponding concepts in psychiatry, psychology and psychotherapy, thus enabling an understanding of the human psyche in general as a (fractal) chaotic system and an explanation of certain mental developments, such as the course of schizophrenia, the course of psychosis and psychotherapy as chaotic processes. General overview: A short comparison and contrast of classical and chaotic physical theory leads to four postulates and one hypothesis motivating a new, dynamic, nonlinear approach to classical, causal psychiatry: Process-Oriented PSYchiatry or "POPSY", for short. Four aspects of the relationship between chaos theory and POPSY are discussed: (1) The first of these, namely, Identification of Chaos / Picture of Illness involves a definition of Chaos / Psychosis and a discussion of the 6 logical characteristics of each. This leads to the concept of dynamical disease (definition, characteristics and examples) and to the idea of "psychological disturbance as dynamical illness". On the one hand, it is argued that the developmental course of psychosis is chaotic. On the other hand, we propose the hypothesis that the mental state of psychosis may be a linear information processing pathology. (2) The second aspect under discussion is the Assessment of Chaos / Diagnosis of Illness. In order to better understand how POPSY research treats this aspect, we take a look at the 3 different classes of (non-quantum) motion as models of 3 different possible courses of illness and outline present-day methods available for the quantitative assessment of chaotic (fractal) motion. (3) The third aspect, namely. Prediction of Chaos / Prognosis of Illness considers how each of these 3 classes of motion implies a different way of looking into the future: linear-causal, statistical and nonlinear-fractal, respectively (4) The fourth aspect of the relationship between chaos theory and POPSY, Control of Chaos / Treatment of Illness, is shown to have certain implications to complementary medicine. This paper completes with a short summary, conclusion and a closing remark.

Cosmological singularities and bounce in Cartan-Einstein theory

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

Lucat, Stefano; Prokopec, Tomislav, E-mail: s.lucat@students.uu.nl, E-mail: t.prokopec@uu.nl

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh ( in-in ) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins inmore » a thermal state and find that—instead of a big crunch singularity—the Universe with torsion undergoes a bounce . We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative, presumably because fermion production contributes negatively to the energy-momentum tensor. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations) and quantum (in the sense that we include fermionic loop contributions).« less

Cosmological singularities and bounce in Cartan-Einstein theory

NASA Astrophysics Data System (ADS)

Lucat, Stefano; Prokopec, Tomislav

2017-10-01

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh (in-in) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins in a thermal state and find that—instead of a big crunch singularity—the Universe with torsion undergoes a bounce. We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative, presumably because fermion production contributes negatively to the energy-momentum tensor. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations) and quantum (in the sense that we include fermionic loop contributions).

Kinetic theory of age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.